Question:
Simplify this expression: (45 - 27*y**3)*(-83*y - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2241*y**4 + 594*y**3 - 3735*y - 990

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45 - 27*y**3)*(-83*y - 22)
Expanding the part (-83*y - 22) using the distributive property, and we got: (-83*y)*(45 - 27*y**3) - 22*(45 - 27*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-83*y)*(45 - 27*y**3) - 22*(45 - 27*y**3)</replace>
Simplifying the partial expression: -22*(45 - 27*y**3)
Expanding the part (45 - 27*y**3) using the distributive property, and we got: -27*y**3*(-22) + 45*(-22)
Replacing -22*(45 - 27*y**3) with -27*y**3*(-22) + 45*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-83*y)*(45 - 27*y**3) - 27*y**3*(-22) - 990</replace>
Simplifying the partial expression: (-83*y)*(45 - 27*y**3)
Expanding the part (45 - 27*y**3) using the distributive property, and we got: (-83*y)*(-27*y**3) + 45*(-83*y)
Replacing (-83*y)*(45 - 27*y**3) with (-83*y)*(-27*y**3) + 45*(-83*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-83*y)*(-27*y**3) + 45*(-83)*y - 27*y**3*(-22) - 990</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**3)*-22 = 594*y**3
  (-27*y**3)*(-83*y) = 2241*y**4
  45*-83*y = -3735*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2241*y**4 + 594*y**3 - 3735*y - 990</replace>
No more calculations needed.
<answer>2241*y**4 + 594*y**3 - 3735*y - 990</answer>


Question:
Calculate the following: (-3*z**3 - 11*z**2)*(-18*z**3 + 26*z**2 + 33*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 54*z**6 + 120*z**5 - 385*z**4 - 363*z**3


Question:
Calculate the following: (49*y**2 + 9)*(-28*y**3 - 17*y**2 - 16*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49*y**2 + 9)*(-28*y**3 - 17*y**2 - 16*y)
Expanding the part (49*y**2 + 9) using the distributive property, and we got: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) + 9*(-28*y**3 - 17*y**2 - 16*y)
<replace-#Step 1>#Step 2:
Current expression: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) + 9*(-28*y**3 - 17*y**2 - 16*y)</replace>
Simplifying the partial expression: 9*(-28*y**3 - 17*y**2 - 16*y)
Expanding the part (-28*y**3 - 17*y**2 - 16*y) using the distributive property, and we got: -16*y*9 - 17*y**2*9 - 28*y**3*9
Replacing 9*(-28*y**3 - 17*y**2 - 16*y) with -16*y*9 - 17*y**2*9 - 28*y**3*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -16*y*9 - 17*y**2*9 + (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) - 28*y**3*9</replace>
Simplifying the partial expression: (49*y**2)*(-28*y**3 - 17*y**2 - 16*y)
Expanding the part (-28*y**3 - 17*y**2 - 16*y) using the distributive property, and we got: (-16*y)*(49*y**2) + (-17*y**2)*(49*y**2) + (49*y**2)*(-28*y**3)
Replacing (49*y**2)*(-28*y**3 - 17*y**2 - 16*y) with (-16*y)*(49*y**2) + (-17*y**2)*(49*y**2) + (49*y**2)*(-28*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*y)*(49*y**2) - 16*y*9 + (-17*y**2)*(49*y**2) - 17*y**2*9 + (49*y**2)*(-28*y**3) - 28*y**3*9</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*y**3)*9 = -252*y**3
  (-28*y**3)*(49*y**2) = -1372*y**5
  (-17*y**2)*9 = -153*y**2
  (-17*y**2)*(49*y**2) = -833*y**4
  (-16*y)*9 = -144*y
  (-16*y)*(49*y**2) = -784*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1372*y**5 - 833*y**4 - 784*y**3 - 252*y**3 - 153*y**2 - 144*y</replace>
Combining like terms, got -1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y
<replace-#Step 5>#Step 6:
Current expression: -1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y</replace>
No more calculations needed.
<answer>-1372*y**5 - 833*y**4 - 1036*y**3 - 153*y**2 - 144*y</answer>


Question:
Calculate the following: (16*y**2 + 6)*(-23*y**3 + 29*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -368*y**5 + 326*y**3 + 174*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*y**2 + 6)*(-23*y**3 + 29*y)
Expanding the part (16*y**2 + 6) using the distributive property, and we got: (16*y**2)*(-23*y**3 + 29*y) + 6*(-23*y**3 + 29*y)
<replace-#Step 1>#Step 2:
Current expression: (16*y**2)*(-23*y**3 + 29*y) + 6*(-23*y**3 + 29*y)</replace>
Simplifying the partial expression: 6*(-23*y**3 + 29*y)
Expanding the part (-23*y**3 + 29*y) using the distributive property, and we got: (29*y)*6 - 23*y**3*6
Replacing 6*(-23*y**3 + 29*y) with (29*y)*6 - 23*y**3*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*y)*6 + (16*y**2)*(-23*y**3 + 29*y) - 23*y**3*6</replace>
Simplifying the partial expression: (16*y**2)*(-23*y**3 + 29*y)
Expanding the part (-23*y**3 + 29*y) using the distributive property, and we got: (29*y)*(16*y**2) + (16*y**2)*(-23*y**3)
Replacing (16*y**2)*(-23*y**3 + 29*y) with (29*y)*(16*y**2) + (16*y**2)*(-23*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (29*y)*(16*y**2) + (29*y)*6 + (16*y**2)*(-23*y**3) - 23*y**3*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*y**3)*6 = -138*y**3
  (-23*y**3)*(16*y**2) = -368*y**5
  (29*y)*6 = 174*y
  (29*y)*(16*y**2) = 464*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -368*y**5 - 138*y**3 + 464*y**3 + 174*y</replace>
Combining like terms, got -368*y**5 + 326*y**3 + 174*y
<replace-#Step 5>#Step 6:
Current expression: -368*y**5 + 326*y**3 + 174*y</replace>
No more calculations needed.
<answer>-368*y**5 + 326*y**3 + 174*y</answer>


Question:
Simplify this expression: (-33*y - 48)*(-34*y**3 + 48*y**2 - 40*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1122*y**4 + 48*y**3 - 984*y**2 + 1920*y


Question:
Calculate the following: (43*y - 15)*(25*y**3 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1075*y**4 - 375*y**3 - 2107*y + 735

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*y - 15)*(25*y**3 - 49)
Expanding the part (25*y**3 - 49) using the distributive property, and we got: (25*y**3)*(43*y - 15) - 49*(43*y - 15)
<replace-#Step 1>#Step 2:
Current expression: (25*y**3)*(43*y - 15) - 49*(43*y - 15)</replace>
Simplifying the partial expression: -49*(43*y - 15)
Expanding the part (43*y - 15) using the distributive property, and we got: (43*y)*(-49) - 15*(-49)
Replacing -49*(43*y - 15) with (43*y)*(-49) - 15*(-49) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*y)*(-49) + (25*y**3)*(43*y - 15) + 735</replace>
Simplifying the partial expression: (25*y**3)*(43*y - 15)
Expanding the part (43*y - 15) using the distributive property, and we got: -375*y**3 + (43*y)*(25*y**3)
Replacing (25*y**3)*(43*y - 15) with -375*y**3 + (43*y)*(25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -15*25*y**3 + (43*y)*(25*y**3) + (43*y)*(-49) + 735</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*y)*-49 = -2107*y
  (43*y)*(25*y**3) = 1075*y**4
  -15*25*y**3 = -375*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1075*y**4 - 375*y**3 - 2107*y + 735</replace>
No more calculations needed.
<answer>1075*y**4 - 375*y**3 - 2107*y + 735</answer>


Question:
Calculate the following: -1650*z
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1650*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -1650*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -1650*z</replace>
No more calculations needed.
<answer>-1650*z</answer>


Question:
Simplify this expression: (4*y**3 + 19*y**2)*(-8*y**3 - 13*y**2 + 30*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -32*y**6 - 204*y**5 - 127*y**4 + 570*y**3


Question:
Simplify this expression: (31*x**3 + 73*x)*(-40*x**3 - 6*x**2 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1240*x**6 - 186*x**5 - 2920*x**4 - 1957*x**3 - 3577*x


Question:
Simplify this expression: (43*x - 41)*(15*x**3 - 19*x**2 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x - 41)*(15*x**3 - 19*x**2 - 31)
Expanding the part (43*x - 41) using the distributive property, and we got: (43*x)*(15*x**3 - 19*x**2 - 31) - 41*(15*x**3 - 19*x**2 - 31)
<replace-#Step 1>#Step 2:
Current expression: (43*x)*(15*x**3 - 19*x**2 - 31) - 41*(15*x**3 - 19*x**2 - 31)</replace>
Simplifying the partial expression: -41*(15*x**3 - 19*x**2 - 31)
Expanding the part (15*x**3 - 19*x**2 - 31) using the distributive property, and we got: -19*x**2*(-41) + (15*x**3)*(-41) - 31*(-41)
Replacing -41*(15*x**3 - 19*x**2 - 31) with -19*x**2*(-41) + (15*x**3)*(-41) - 31*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(15*x**3 - 19*x**2 - 31) - 19*x**2*(-41) + (15*x**3)*(-41) + 1271</replace>
Simplifying the partial expression: (43*x)*(15*x**3 - 19*x**2 - 31)
Expanding the part (15*x**3 - 19*x**2 - 31) using the distributive property, and we got: -1333*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3)
Replacing (43*x)*(15*x**3 - 19*x**2 - 31) with -1333*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -31*43*x + (43*x)*(-19*x**2) + (43*x)*(15*x**3) - 19*x**2*(-41) + (15*x**3)*(-41) + 1271</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**2)*-41 = 779*x**2
  (-19*x**2)*(43*x) = -817*x**3
  (15*x**3)*-41 = -615*x**3
  (15*x**3)*(43*x) = 645*x**4
  -31*43*x = -1333*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 645*x**4 - 817*x**3 - 615*x**3 + 779*x**2 - 1333*x + 1271</replace>
Combining like terms, got 645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271
<replace-#Step 5>#Step 6:
Current expression: 645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271</replace>
No more calculations needed.
<answer>645*x**4 - 1432*x**3 + 779*x**2 - 1333*x + 1271</answer>


Question:
Calculate the following: (-103*x**2 - 26*x)*(47*x**3 + 25*x**2 - 10*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -4841*x**5 - 3797*x**4 + 380*x**3 + 260*x**2


Question:
Simplify this expression: -68*z**2*(-34*z**2 - 26*z - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2312*z**4 + 1768*z**3 + 1156*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -68*z**2*(-34*z**2 - 26*z - 17)
Expanding the part (-34*z**2 - 26*z - 17) using the distributive property, and we got: (-26*z)*(-68*z**2) - (-1)*1156*z**2 + (-68*z**2)*(-34*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-26*z)*(-68*z**2) - (-1)*1156*z**2 + (-68*z**2)*(-34*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -17*(-68*z**2) = 1156*z**2
  (-34*z**2)*(-68*z**2) = 2312*z**4
  (-26*z)*(-68*z**2) = 1768*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2312*z**4 + 1768*z**3 + 1156*z**2</replace>
No more calculations needed.
<answer>2312*z**4 + 1768*z**3 + 1156*z**2</answer>


Question:
Simplify this expression: (43*x**3 - 31*x)*(15*x**3 - 11*x + 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x**3 - 31*x)*(15*x**3 - 11*x + 23)
Expanding the part (43*x**3 - 31*x) using the distributive property, and we got: (-31*x)*(15*x**3 - 11*x + 23) + (43*x**3)*(15*x**3 - 11*x + 23)
<replace-#Step 1>#Step 2:
Current expression: (-31*x)*(15*x**3 - 11*x + 23) + (43*x**3)*(15*x**3 - 11*x + 23)</replace>
Simplifying the partial expression: (-31*x)*(15*x**3 - 11*x + 23)
Expanding the part (15*x**3 - 11*x + 23) using the distributive property, and we got: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31*x)
Replacing (-31*x)*(15*x**3 - 11*x + 23) with (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31*x) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + 23*(-31)*x + (43*x**3)*(15*x**3 - 11*x + 23)</replace>
Simplifying the partial expression: (43*x**3)*(15*x**3 - 11*x + 23)
Expanding the part (15*x**3 - 11*x + 23) using the distributive property, and we got: (-11*x)*(43*x**3) + 23*(43*x**3) + (15*x**3)*(43*x**3)
Replacing (43*x**3)*(15*x**3 - 11*x + 23) with (-11*x)*(43*x**3) + 23*(43*x**3) + (15*x**3)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*x)*(-11*x) + (-31*x)*(15*x**3) + (-11*x)*(43*x**3) + 23*43*x**3 + 23*(-31)*x + (15*x**3)*(43*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x)*(-31*x) = 341*x**2
  (-11*x)*(43*x**3) = -473*x**4
  (15*x**3)*(-31*x) = -465*x**4
  (15*x**3)*(43*x**3) = 645*x**6
  23*-31*x = -713*x
  23*43*x**3 = 989*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 645*x**6 - 473*x**4 - 465*x**4 + 989*x**3 + 341*x**2 - 713*x</replace>
Combining like terms, got 645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x
<replace-#Step 5>#Step 6:
Current expression: 645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x</replace>
No more calculations needed.
<answer>645*x**6 - 938*x**4 + 989*x**3 + 341*x**2 - 713*x</answer>


Question:
Simplify this expression: (48*x**2 - 46*x)*(32*x**3 - 62)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (48*x**2 - 46*x)*(32*x**3 - 62)
Expanding the part (32*x**3 - 62) using the distributive property, and we got: (32*x**3)*(48*x**2 - 46*x) - 62*(48*x**2 - 46*x)
<replace-#Step 1>#Step 2:
Current expression: (32*x**3)*(48*x**2 - 46*x) - 62*(48*x**2 - 46*x)</replace>
Simplifying the partial expression: -62*(48*x**2 - 46*x)
Expanding the part (48*x**2 - 46*x) using the distributive property, and we got: -46*x*(-62) + (48*x**2)*(-62)
Replacing -62*(48*x**2 - 46*x) with -46*x*(-62) + (48*x**2)*(-62) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*x*(-62) + (48*x**2)*(-62) + (32*x**3)*(48*x**2 - 46*x)</replace>
Simplifying the partial expression: (32*x**3)*(48*x**2 - 46*x)
Expanding the part (48*x**2 - 46*x) using the distributive property, and we got: (-46*x)*(32*x**3) + (48*x**2)*(32*x**3)
Replacing (32*x**3)*(48*x**2 - 46*x) with (-46*x)*(32*x**3) + (48*x**2)*(32*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*x)*(32*x**3) - 46*x*(-62) + (48*x**2)*(32*x**3) + (48*x**2)*(-62)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*x)*-62 = 2852*x
  (-46*x)*(32*x**3) = -1472*x**4
  (48*x**2)*-62 = -2976*x**2
  (48*x**2)*(32*x**3) = 1536*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x</replace>
No more calculations needed.
<answer>1536*x**5 - 1472*x**4 - 2976*x**2 + 2852*x</answer>


Question:
Simplify this expression: (32*x**2 + 43*x - 7)*(13*x**3 + 10*x - 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 416*x**5 + 559*x**4 + 229*x**3 - 1074*x**2 - 2091*x + 329


Question:
Calculate the following: (43*x + 44)*(-8*x**2 - 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -344*x**3 - 352*x**2 - 258*x - 264

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x + 44)*(-8*x**2 - 6)
Expanding the part (-8*x**2 - 6) using the distributive property, and we got: (-8*x**2)*(43*x + 44) - 6*(43*x + 44)
<replace-#Step 1>#Step 2:
Current expression: (-8*x**2)*(43*x + 44) - 6*(43*x + 44)</replace>
Simplifying the partial expression: -6*(43*x + 44)
Expanding the part (43*x + 44) using the distributive property, and we got: (43*x)*(-6) + 44*(-6)
Replacing -6*(43*x + 44) with (43*x)*(-6) + 44*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(-6) + (-8*x**2)*(43*x + 44) - 264</replace>
Simplifying the partial expression: (-8*x**2)*(43*x + 44)
Expanding the part (43*x + 44) using the distributive property, and we got: 44*(-8*x**2) + (43*x)*(-8*x**2)
Replacing (-8*x**2)*(43*x + 44) with 44*(-8*x**2) + (43*x)*(-8*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 44*(-8)*x**2 + (43*x)*(-8*x**2) + (43*x)*(-6) - 264</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x)*-6 = -258*x
  (43*x)*(-8*x**2) = -344*x**3
  44*-8*x**2 = -352*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -344*x**3 - 352*x**2 - 258*x - 264</replace>
No more calculations needed.
<answer>-344*x**3 - 352*x**2 - 258*x - 264</answer>


Question:
Simplify this expression: -56*z**3*(-48*z**2 - 40*z + 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2688*z**5 + 2240*z**4 - 504*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -56*z**3*(-48*z**2 - 40*z + 9)
Expanding the part (-48*z**2 - 40*z + 9) using the distributive property, and we got: (-40*z)*(-56*z**3) + 9*(-56*z**3) + (-48*z**2)*(-56*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-40*z)*(-56*z**3) + 9*(-56*z**3) + (-48*z**2)*(-56*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  9*(-56*z**3) = -504*z**3
  (-48*z**2)*(-56*z**3) = 2688*z**5
  (-40*z)*(-56*z**3) = 2240*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2688*z**5 + 2240*z**4 - 504*z**3</replace>
No more calculations needed.
<answer>2688*z**5 + 2240*z**4 - 504*z**3</answer>


Question:
Simplify this expression: -z*(29*z - 52)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -29*z**2 + 52*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -z*(29*z - 52)
Expanding the part (29*z - 52) using the distributive property, and we got: (-z)*(29*z) - (-1)*52*z
<replace-#Step 1>#Step 2:
Current expression: (-z)*(29*z) - (-1)*52*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -52*(-z) = 52*z
  (29*z)*(-z) = -29*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -29*z**2 + 52*z</replace>
No more calculations needed.
<answer>-29*z**2 + 52*z</answer>


Question:
Calculate the following: -612*x**3 + 90*x**2 + 486
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -612*x**3 + 90*x**2 + 486

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -612*x**3 + 90*x**2 + 486
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -612*x**3 + 90*x**2 + 486</replace>
No more calculations needed.
<answer>-612*x**3 + 90*x**2 + 486</answer>


Question:
Calculate the following: (57 - x)*(49*x + 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -49*x**2 + 2768*x + 1425

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (57 - x)*(49*x + 25)
Expanding the part (49*x + 25) using the distributive property, and we got: (49*x)*(57 - x) + 25*(57 - x)
<replace-#Step 1>#Step 2:
Current expression: (49*x)*(57 - x) + 25*(57 - x)</replace>
Simplifying the partial expression: 25*(57 - x)
Expanding the part (57 - x) using the distributive property, and we got: -x*25 + 57*25
Replacing 25*(57 - x) with -x*25 + 57*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -x*25 + (49*x)*(57 - x) + 1425</replace>
Simplifying the partial expression: (49*x)*(57 - x)
Expanding the part (57 - x) using the distributive property, and we got: (-x)*(49*x) + 57*(49*x)
Replacing (49*x)*(57 - x) with (-x)*(49*x) + 57*(49*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(49*x) - x*25 + 57*49*x + 1425</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x)*25 = -25*x
  (-x)*(49*x) = -49*x**2
  57*49*x = 2793*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -49*x**2 - 25*x + 2793*x + 1425</replace>
Combining like terms, got -49*x**2 + 2768*x + 1425
<replace-#Step 5>#Step 6:
Current expression: -49*x**2 + 2768*x + 1425</replace>
No more calculations needed.
<answer>-49*x**2 + 2768*x + 1425</answer>


Question:
Calculate the following: (22*z**3 - 25*z)*(-49*z**3 + 13*z**2 - 92)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1078*z**6 + 286*z**5 + 1225*z**4 - 2349*z**3 + 2300*z


Question:
Simplify this expression: (-49*x**2 + 46*x)*(-25*x**3 - 90*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-49*x**2 + 46*x)*(-25*x**3 - 90*x)
Expanding the part (-25*x**3 - 90*x) using the distributive property, and we got: (-90*x)*(-49*x**2 + 46*x) + (-25*x**3)*(-49*x**2 + 46*x)
<replace-#Step 1>#Step 2:
Current expression: (-90*x)*(-49*x**2 + 46*x) + (-25*x**3)*(-49*x**2 + 46*x)</replace>
Simplifying the partial expression: (-90*x)*(-49*x**2 + 46*x)
Expanding the part (-49*x**2 + 46*x) using the distributive property, and we got: (-90*x)*(46*x) + (-90*x)*(-49*x**2)
Replacing (-90*x)*(-49*x**2 + 46*x) with (-90*x)*(46*x) + (-90*x)*(-49*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-90*x)*(46*x) + (-90*x)*(-49*x**2) + (-25*x**3)*(-49*x**2 + 46*x)</replace>
Simplifying the partial expression: (-25*x**3)*(-49*x**2 + 46*x)
Expanding the part (-49*x**2 + 46*x) using the distributive property, and we got: (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3)
Replacing (-25*x**3)*(-49*x**2 + 46*x) with (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-90*x)*(46*x) + (-90*x)*(-49*x**2) + (46*x)*(-25*x**3) + (-49*x**2)*(-25*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**2)*(-90*x) = 4410*x**3
  (-49*x**2)*(-25*x**3) = 1225*x**5
  (46*x)*(-90*x) = -4140*x**2
  (46*x)*(-25*x**3) = -1150*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2</replace>
No more calculations needed.
<answer>1225*x**5 - 1150*x**4 + 4410*x**3 - 4140*x**2</answer>


Question:
Calculate the following: (-20*x**3 - 23)*(-16*x**3 - 39*x**2 - 43*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 320*x**6 + 780*x**5 + 860*x**4 + 368*x**3 + 897*x**2 + 989*x


Question:
Simplify this expression: -71*y**2*(-13*y**3 - 39*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 923*y**5 + 2769*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -71*y**2*(-13*y**3 - 39*y)
Expanding the part (-13*y**3 - 39*y) using the distributive property, and we got: (-39*y)*(-71*y**2) + (-71*y**2)*(-13*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-39*y)*(-71*y**2) + (-71*y**2)*(-13*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y)*(-71*y**2) = 2769*y**3
  (-13*y**3)*(-71*y**2) = 923*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 923*y**5 + 2769*y**3</replace>
No more calculations needed.
<answer>923*y**5 + 2769*y**3</answer>


Question:
Calculate the following: (-47*y**3 + 47*y)*(-2*y**3 - 13*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 94*y**6 + 611*y**5 - 94*y**4 - 611*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-47*y**3 + 47*y)*(-2*y**3 - 13*y**2)
Expanding the part (-47*y**3 + 47*y) using the distributive property, and we got: (47*y)*(-2*y**3 - 13*y**2) + (-47*y**3)*(-2*y**3 - 13*y**2)
<replace-#Step 1>#Step 2:
Current expression: (47*y)*(-2*y**3 - 13*y**2) + (-47*y**3)*(-2*y**3 - 13*y**2)</replace>
Simplifying the partial expression: (-47*y**3)*(-2*y**3 - 13*y**2)
Expanding the part (-2*y**3 - 13*y**2) using the distributive property, and we got: (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)
Replacing (-47*y**3)*(-2*y**3 - 13*y**2) with (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (47*y)*(-2*y**3 - 13*y**2) + (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)</replace>
Simplifying the partial expression: (47*y)*(-2*y**3 - 13*y**2)
Expanding the part (-2*y**3 - 13*y**2) using the distributive property, and we got: (47*y)*(-13*y**2) + (47*y)*(-2*y**3)
Replacing (47*y)*(-2*y**3 - 13*y**2) with (47*y)*(-13*y**2) + (47*y)*(-2*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (47*y)*(-13*y**2) + (47*y)*(-2*y**3) + (-13*y**2)*(-47*y**3) + (-47*y**3)*(-2*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*y**2)*(-47*y**3) = 611*y**5
  (-13*y**2)*(47*y) = -611*y**3
  (-2*y**3)*(-47*y**3) = 94*y**6
  (-2*y**3)*(47*y) = -94*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 94*y**6 + 611*y**5 - 94*y**4 - 611*y**3</replace>
No more calculations needed.
<answer>94*y**6 + 611*y**5 - 94*y**4 - 611*y**3</answer>


Question:
Calculate the following: (-47*x - 23)*(44*x**2 - 10*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2068*x**3 - 542*x**2 + 230*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-47*x - 23)*(44*x**2 - 10*x)
Expanding the part (-47*x - 23) using the distributive property, and we got: (-47*x)*(44*x**2 - 10*x) - 23*(44*x**2 - 10*x)
<replace-#Step 1>#Step 2:
Current expression: (-47*x)*(44*x**2 - 10*x) - 23*(44*x**2 - 10*x)</replace>
Simplifying the partial expression: -23*(44*x**2 - 10*x)
Expanding the part (44*x**2 - 10*x) using the distributive property, and we got: -10*x*(-23) + (44*x**2)*(-23)
Replacing -23*(44*x**2 - 10*x) with -10*x*(-23) + (44*x**2)*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*x)*(44*x**2 - 10*x) - 10*x*(-23) + (44*x**2)*(-23)</replace>
Simplifying the partial expression: (-47*x)*(44*x**2 - 10*x)
Expanding the part (44*x**2 - 10*x) using the distributive property, and we got: (-47*x)*(-10*x) + (-47*x)*(44*x**2)
Replacing (-47*x)*(44*x**2 - 10*x) with (-47*x)*(-10*x) + (-47*x)*(44*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*x)*(-10*x) + (-47*x)*(44*x**2) - 10*x*(-23) + (44*x**2)*(-23)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*x)*-23 = 230*x
  (-10*x)*(-47*x) = 470*x**2
  (44*x**2)*-23 = -1012*x**2
  (44*x**2)*(-47*x) = -2068*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2068*x**3 - 1012*x**2 + 470*x**2 + 230*x</replace>
Combining like terms, got -2068*x**3 - 542*x**2 + 230*x
<replace-#Step 5>#Step 6:
Current expression: -2068*x**3 - 542*x**2 + 230*x</replace>
No more calculations needed.
<answer>-2068*x**3 - 542*x**2 + 230*x</answer>


Question:
Simplify this expression: (5*y**3 + 62)*(19*y**3 + 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 95*y**6 + 1363*y**3 + 2294

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (5*y**3 + 62)*(19*y**3 + 37)
Expanding the part (19*y**3 + 37) using the distributive property, and we got: (19*y**3)*(5*y**3 + 62) + 37*(5*y**3 + 62)
<replace-#Step 1>#Step 2:
Current expression: (19*y**3)*(5*y**3 + 62) + 37*(5*y**3 + 62)</replace>
Simplifying the partial expression: 37*(5*y**3 + 62)
Expanding the part (5*y**3 + 62) using the distributive property, and we got: (5*y**3)*37 + 62*37
Replacing 37*(5*y**3 + 62) with (5*y**3)*37 + 62*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*y**3)*37 + (19*y**3)*(5*y**3 + 62) + 2294</replace>
Simplifying the partial expression: (19*y**3)*(5*y**3 + 62)
Expanding the part (5*y**3 + 62) using the distributive property, and we got: 62*(19*y**3) + (5*y**3)*(19*y**3)
Replacing (19*y**3)*(5*y**3 + 62) with 62*(19*y**3) + (5*y**3)*(19*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 62*19*y**3 + (5*y**3)*(19*y**3) + (5*y**3)*37 + 2294</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y**3)*37 = 185*y**3
  (5*y**3)*(19*y**3) = 95*y**6
  62*19*y**3 = 1178*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 95*y**6 + 185*y**3 + 1178*y**3 + 2294</replace>
Combining like terms, got 95*y**6 + 1363*y**3 + 2294
<replace-#Step 5>#Step 6:
Current expression: 95*y**6 + 1363*y**3 + 2294</replace>
No more calculations needed.
<answer>95*y**6 + 1363*y**3 + 2294</answer>


Question:
Calculate the following: (30*x**3 + 6)*(-14*x**3 - 38*x**2 - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (30*x**3 + 6)*(-14*x**3 - 38*x**2 - 16)
Expanding the part (30*x**3 + 6) using the distributive property, and we got: (30*x**3)*(-14*x**3 - 38*x**2 - 16) + 6*(-14*x**3 - 38*x**2 - 16)
<replace-#Step 1>#Step 2:
Current expression: (30*x**3)*(-14*x**3 - 38*x**2 - 16) + 6*(-14*x**3 - 38*x**2 - 16)</replace>
Simplifying the partial expression: 6*(-14*x**3 - 38*x**2 - 16)
Expanding the part (-14*x**3 - 38*x**2 - 16) using the distributive property, and we got: -38*x**2*6 - 14*x**3*6 - 16*6
Replacing 6*(-14*x**3 - 38*x**2 - 16) with -38*x**2*6 - 14*x**3*6 - 16*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -38*x**2*6 - 14*x**3*6 + (30*x**3)*(-14*x**3 - 38*x**2 - 16) - 96</replace>
Simplifying the partial expression: (30*x**3)*(-14*x**3 - 38*x**2 - 16)
Expanding the part (-14*x**3 - 38*x**2 - 16) using the distributive property, and we got: -480*x**3 + (-38*x**2)*(30*x**3) + (-14*x**3)*(30*x**3)
Replacing (30*x**3)*(-14*x**3 - 38*x**2 - 16) with -480*x**3 + (-38*x**2)*(30*x**3) + (-14*x**3)*(30*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -16*30*x**3 + (-38*x**2)*(30*x**3) - 38*x**2*6 + (-14*x**3)*(30*x**3) - 14*x**3*6 - 96</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**2)*6 = -228*x**2
  (-38*x**2)*(30*x**3) = -1140*x**5
  (-14*x**3)*6 = -84*x**3
  (-14*x**3)*(30*x**3) = -420*x**6
  -16*30*x**3 = -480*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -420*x**6 - 1140*x**5 - 480*x**3 - 84*x**3 - 228*x**2 - 96</replace>
Combining like terms, got -420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96
<replace-#Step 5>#Step 6:
Current expression: -420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96</replace>
No more calculations needed.
<answer>-420*x**6 - 1140*x**5 - 564*x**3 - 228*x**2 - 96</answer>


Question:
Calculate the following: (11 - 57*x)*(-28*x**3 + 16*x**2 + 78*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11 - 57*x)*(-28*x**3 + 16*x**2 + 78*x)
Expanding the part (11 - 57*x) using the distributive property, and we got: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + 11*(-28*x**3 + 16*x**2 + 78*x)
<replace-#Step 1>#Step 2:
Current expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + 11*(-28*x**3 + 16*x**2 + 78*x)</replace>
Simplifying the partial expression: 11*(-28*x**3 + 16*x**2 + 78*x)
Expanding the part (-28*x**3 + 16*x**2 + 78*x) using the distributive property, and we got: (78*x)*11 + (16*x**2)*11 - 28*x**3*11
Replacing 11*(-28*x**3 + 16*x**2 + 78*x) with (78*x)*11 + (16*x**2)*11 - 28*x**3*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x) + (78*x)*11 + (16*x**2)*11 - 28*x**3*11</replace>
Simplifying the partial expression: (-57*x)*(-28*x**3 + 16*x**2 + 78*x)
Expanding the part (-28*x**3 + 16*x**2 + 78*x) using the distributive property, and we got: (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3)
Replacing (-57*x)*(-28*x**3 + 16*x**2 + 78*x) with (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-57*x)*(78*x) + (-57*x)*(16*x**2) + (-57*x)*(-28*x**3) + (78*x)*11 + (16*x**2)*11 - 28*x**3*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*x**3)*11 = -308*x**3
  (-28*x**3)*(-57*x) = 1596*x**4
  (16*x**2)*11 = 176*x**2
  (16*x**2)*(-57*x) = -912*x**3
  (78*x)*11 = 858*x
  (78*x)*(-57*x) = -4446*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1596*x**4 - 912*x**3 - 308*x**3 - 4446*x**2 + 176*x**2 + 858*x</replace>
Combining like terms, got 1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x
<replace-#Step 5>#Step 6:
Current expression: 1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x</replace>
No more calculations needed.
<answer>1596*x**4 - 1220*x**3 - 4270*x**2 + 858*x</answer>


Question:
Calculate the following: (81*y + 14)*(32*y**2 + 35*y - 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2592*y**3 + 3283*y**2 - 2264*y - 476

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (81*y + 14)*(32*y**2 + 35*y - 34)
Expanding the part (81*y + 14) using the distributive property, and we got: (81*y)*(32*y**2 + 35*y - 34) + 14*(32*y**2 + 35*y - 34)
<replace-#Step 1>#Step 2:
Current expression: (81*y)*(32*y**2 + 35*y - 34) + 14*(32*y**2 + 35*y - 34)</replace>
Simplifying the partial expression: 14*(32*y**2 + 35*y - 34)
Expanding the part (32*y**2 + 35*y - 34) using the distributive property, and we got: (35*y)*14 + (32*y**2)*14 - 34*14
Replacing 14*(32*y**2 + 35*y - 34) with (35*y)*14 + (32*y**2)*14 - 34*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*y)*14 + (81*y)*(32*y**2 + 35*y - 34) + (32*y**2)*14 - 476</replace>
Simplifying the partial expression: (81*y)*(32*y**2 + 35*y - 34)
Expanding the part (32*y**2 + 35*y - 34) using the distributive property, and we got: -2754*y + (35*y)*(81*y) + (81*y)*(32*y**2)
Replacing (81*y)*(32*y**2 + 35*y - 34) with -2754*y + (35*y)*(81*y) + (81*y)*(32*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -34*81*y + (35*y)*(81*y) + (35*y)*14 + (81*y)*(32*y**2) + (32*y**2)*14 - 476</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*y**2)*14 = 448*y**2
  (32*y**2)*(81*y) = 2592*y**3
  (35*y)*14 = 490*y
  (35*y)*(81*y) = 2835*y**2
  -34*81*y = -2754*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2592*y**3 + 448*y**2 + 2835*y**2 - 2754*y + 490*y - 476</replace>
Combining like terms, got 2592*y**3 + 3283*y**2 - 2264*y - 476
<replace-#Step 5>#Step 6:
Current expression: 2592*y**3 + 3283*y**2 - 2264*y - 476</replace>
No more calculations needed.
<answer>2592*y**3 + 3283*y**2 - 2264*y - 476</answer>


Question:
Calculate the following: (17 - 45*x**3)*(43 - 40*x**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1800*x**6 - 2615*x**3 + 731

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17 - 45*x**3)*(43 - 40*x**3)
Expanding the part (17 - 45*x**3) using the distributive property, and we got: (-45*x**3)*(43 - 40*x**3) + 17*(43 - 40*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-45*x**3)*(43 - 40*x**3) + 17*(43 - 40*x**3)</replace>
Simplifying the partial expression: 17*(43 - 40*x**3)
Expanding the part (43 - 40*x**3) using the distributive property, and we got: -40*x**3*17 + 43*17
Replacing 17*(43 - 40*x**3) with -40*x**3*17 + 43*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-45*x**3)*(43 - 40*x**3) - 40*x**3*17 + 731</replace>
Simplifying the partial expression: (-45*x**3)*(43 - 40*x**3)
Expanding the part (43 - 40*x**3) using the distributive property, and we got: 43*(-45*x**3) + (-45*x**3)*(-40*x**3)
Replacing (-45*x**3)*(43 - 40*x**3) with 43*(-45*x**3) + (-45*x**3)*(-40*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 43*(-45)*x**3 + (-45*x**3)*(-40*x**3) - 40*x**3*17 + 731</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*x**3)*17 = -680*x**3
  (-40*x**3)*(-45*x**3) = 1800*x**6
  43*-45*x**3 = -1935*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1800*x**6 - 1935*x**3 - 680*x**3 + 731</replace>
Combining like terms, got 1800*x**6 - 2615*x**3 + 731
<replace-#Step 5>#Step 6:
Current expression: 1800*x**6 - 2615*x**3 + 731</replace>
No more calculations needed.
<answer>1800*x**6 - 2615*x**3 + 731</answer>


Question:
Simplify this expression: (-20*z**3 - 6)*(-38*z**3 - 7*z**2 + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-20*z**3 - 6)*(-38*z**3 - 7*z**2 + 19)
Expanding the part (-20*z**3 - 6) using the distributive property, and we got: (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 6*(-38*z**3 - 7*z**2 + 19)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 6*(-38*z**3 - 7*z**2 + 19)</replace>
Simplifying the partial expression: -6*(-38*z**3 - 7*z**2 + 19)
Expanding the part (-38*z**3 - 7*z**2 + 19) using the distributive property, and we got: -7*z**2*(-6) - 38*z**3*(-6) + 19*(-6)
Replacing -6*(-38*z**3 - 7*z**2 + 19) with -7*z**2*(-6) - 38*z**3*(-6) + 19*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -7*z**2*(-6) - 38*z**3*(-6) + (-20*z**3)*(-38*z**3 - 7*z**2 + 19) - 114</replace>
Simplifying the partial expression: (-20*z**3)*(-38*z**3 - 7*z**2 + 19)
Expanding the part (-38*z**3 - 7*z**2 + 19) using the distributive property, and we got: 19*(-20*z**3) + (-7*z**2)*(-20*z**3) + (-38*z**3)*(-20*z**3)
Replacing (-20*z**3)*(-38*z**3 - 7*z**2 + 19) with 19*(-20*z**3) + (-7*z**2)*(-20*z**3) + (-38*z**3)*(-20*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 19*(-20)*z**3 + (-7*z**2)*(-20*z**3) - 7*z**2*(-6) + (-38*z**3)*(-20*z**3) - 38*z**3*(-6) - 114</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*z**3)*-6 = 228*z**3
  (-38*z**3)*(-20*z**3) = 760*z**6
  (-7*z**2)*-6 = 42*z**2
  (-7*z**2)*(-20*z**3) = 140*z**5
  19*-20*z**3 = -380*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 760*z**6 + 140*z**5 - 380*z**3 + 228*z**3 + 42*z**2 - 114</replace>
Combining like terms, got 760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114
<replace-#Step 5>#Step 6:
Current expression: 760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114</replace>
No more calculations needed.
<answer>760*z**6 + 140*z**5 - 152*z**3 + 42*z**2 - 114</answer>


Question:
Simplify this expression: (18 - 33*x**2)*(22*x**3 + 12*x**2 - 33*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -726*x**5 - 396*x**4 + 1485*x**3 + 216*x**2 - 594*x


Question:
Simplify this expression: (64*x**3 + x)*(-73*x**3 + 22*x - 2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (64*x**3 + x)*(-73*x**3 + 22*x - 2)
Expanding the part (64*x**3 + x) using the distributive property, and we got: x*(-73*x**3 + 22*x - 2) + (64*x**3)*(-73*x**3 + 22*x - 2)
<replace-#Step 1>#Step 2:
Current expression: x*(-73*x**3 + 22*x - 2) + (64*x**3)*(-73*x**3 + 22*x - 2)</replace>
Simplifying the partial expression: x*(-73*x**3 + 22*x - 2)
Expanding the part (-73*x**3 + 22*x - 2) using the distributive property, and we got: x*(22*x) + x*(-73*x**3) - 2*x
Replacing x*(-73*x**3 + 22*x - 2) with x*(22*x) + x*(-73*x**3) - 2*x in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x*(22*x) + x*(-73*x**3) - 2*x + (64*x**3)*(-73*x**3 + 22*x - 2)</replace>
Simplifying the partial expression: (64*x**3)*(-73*x**3 + 22*x - 2)
Expanding the part (-73*x**3 + 22*x - 2) using the distributive property, and we got: -128*x**3 + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3)
Replacing (64*x**3)*(-73*x**3 + 22*x - 2) with -128*x**3 + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -2*64*x**3 + x*(22*x) + x*(-73*x**3) - 2*x + (22*x)*(64*x**3) + (-73*x**3)*(64*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-73*x**3)*x = -73*x**4
  (-73*x**3)*(64*x**3) = -4672*x**6
  (22*x)*x = 22*x**2
  (22*x)*(64*x**3) = 1408*x**4
  -2*64*x**3 = -128*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -4672*x**6 - 73*x**4 + 1408*x**4 - 128*x**3 + 22*x**2 - 2*x</replace>
Combining like terms, got -4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x
<replace-#Step 5>#Step 6:
Current expression: -4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x</replace>
No more calculations needed.
<answer>-4672*x**6 + 1335*x**4 - 128*x**3 + 22*x**2 - 2*x</answer>


Question:
Simplify this expression: (14*x**2 - 48*x)*(43*x**3 + 33*x**2 - 41*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 602*x**5 - 1602*x**4 - 2158*x**3 + 1968*x**2


Question:
Simplify this expression: (63 - 41*x**3)*(-10*x**3 - 40*x**2 + 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (63 - 41*x**3)*(-10*x**3 - 40*x**2 + 38)
Expanding the part (63 - 41*x**3) using the distributive property, and we got: (-41*x**3)*(-10*x**3 - 40*x**2 + 38) + 63*(-10*x**3 - 40*x**2 + 38)
<replace-#Step 1>#Step 2:
Current expression: (-41*x**3)*(-10*x**3 - 40*x**2 + 38) + 63*(-10*x**3 - 40*x**2 + 38)</replace>
Simplifying the partial expression: 63*(-10*x**3 - 40*x**2 + 38)
Expanding the part (-10*x**3 - 40*x**2 + 38) using the distributive property, and we got: -40*x**2*63 - 10*x**3*63 + 38*63
Replacing 63*(-10*x**3 - 40*x**2 + 38) with -40*x**2*63 - 10*x**3*63 + 38*63 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -40*x**2*63 + (-41*x**3)*(-10*x**3 - 40*x**2 + 38) - 10*x**3*63 + 2394</replace>
Simplifying the partial expression: (-41*x**3)*(-10*x**3 - 40*x**2 + 38)
Expanding the part (-10*x**3 - 40*x**2 + 38) using the distributive property, and we got: 38*(-41*x**3) + (-40*x**2)*(-41*x**3) + (-41*x**3)*(-10*x**3)
Replacing (-41*x**3)*(-10*x**3 - 40*x**2 + 38) with 38*(-41*x**3) + (-40*x**2)*(-41*x**3) + (-41*x**3)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 38*(-41)*x**3 + (-40*x**2)*(-41*x**3) - 40*x**2*63 + (-41*x**3)*(-10*x**3) - 10*x**3*63 + 2394</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*x**2)*63 = -2520*x**2
  (-40*x**2)*(-41*x**3) = 1640*x**5
  (-10*x**3)*63 = -630*x**3
  (-10*x**3)*(-41*x**3) = 410*x**6
  38*-41*x**3 = -1558*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 410*x**6 + 1640*x**5 - 1558*x**3 - 630*x**3 - 2520*x**2 + 2394</replace>
Combining like terms, got 410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394
<replace-#Step 5>#Step 6:
Current expression: 410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394</replace>
No more calculations needed.
<answer>410*x**6 + 1640*x**5 - 2188*x**3 - 2520*x**2 + 2394</answer>


Question:
Simplify this expression: (40*y + 46)*(-14*y**3 - y + 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (40*y + 46)*(-14*y**3 - y + 27)
Expanding the part (40*y + 46) using the distributive property, and we got: (40*y)*(-14*y**3 - y + 27) + 46*(-14*y**3 - y + 27)
<replace-#Step 1>#Step 2:
Current expression: (40*y)*(-14*y**3 - y + 27) + 46*(-14*y**3 - y + 27)</replace>
Simplifying the partial expression: 46*(-14*y**3 - y + 27)
Expanding the part (-14*y**3 - y + 27) using the distributive property, and we got: -y*46 - 14*y**3*46 + 27*46
Replacing 46*(-14*y**3 - y + 27) with -y*46 - 14*y**3*46 + 27*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -y*46 + (40*y)*(-14*y**3 - y + 27) - 14*y**3*46 + 1242</replace>
Simplifying the partial expression: (40*y)*(-14*y**3 - y + 27)
Expanding the part (-14*y**3 - y + 27) using the distributive property, and we got: (-y)*(40*y) + 27*(40*y) + (40*y)*(-14*y**3)
Replacing (40*y)*(-14*y**3 - y + 27) with (-y)*(40*y) + 27*(40*y) + (40*y)*(-14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y)*(40*y) - y*46 + 27*40*y + (40*y)*(-14*y**3) - 14*y**3*46 + 1242</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y)*46 = -46*y
  (-y)*(40*y) = -40*y**2
  (-14*y**3)*46 = -644*y**3
  (-14*y**3)*(40*y) = -560*y**4
  27*40*y = 1080*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -560*y**4 - 644*y**3 - 40*y**2 - 46*y + 1080*y + 1242</replace>
Combining like terms, got -560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242
<replace-#Step 5>#Step 6:
Current expression: -560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242</replace>
No more calculations needed.
<answer>-560*y**4 - 644*y**3 - 40*y**2 + 1034*y + 1242</answer>


Question:
Simplify this expression: (21*x + 23)*(3*x**2 + 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 63*x**3 + 69*x**2 + 462*x + 506

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*x + 23)*(3*x**2 + 22)
Expanding the part (3*x**2 + 22) using the distributive property, and we got: (3*x**2)*(21*x + 23) + 22*(21*x + 23)
<replace-#Step 1>#Step 2:
Current expression: (3*x**2)*(21*x + 23) + 22*(21*x + 23)</replace>
Simplifying the partial expression: 22*(21*x + 23)
Expanding the part (21*x + 23) using the distributive property, and we got: (21*x)*22 + 23*22
Replacing 22*(21*x + 23) with (21*x)*22 + 23*22 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*x)*22 + (3*x**2)*(21*x + 23) + 506</replace>
Simplifying the partial expression: (3*x**2)*(21*x + 23)
Expanding the part (21*x + 23) using the distributive property, and we got: 23*(3*x**2) + (21*x)*(3*x**2)
Replacing (3*x**2)*(21*x + 23) with 23*(3*x**2) + (21*x)*(3*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 23*3*x**2 + (21*x)*(3*x**2) + (21*x)*22 + 506</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (21*x)*22 = 462*x
  (21*x)*(3*x**2) = 63*x**3
  23*3*x**2 = 69*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 63*x**3 + 69*x**2 + 462*x + 506</replace>
No more calculations needed.
<answer>63*x**3 + 69*x**2 + 462*x + 506</answer>


Question:
Calculate the following: (-15*z**2 - 42*z)*(18*z**3 + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -270*z**5 - 756*z**4 - 90*z**2 - 252*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*z**2 - 42*z)*(18*z**3 + 6)
Expanding the part (18*z**3 + 6) using the distributive property, and we got: (18*z**3)*(-15*z**2 - 42*z) + 6*(-15*z**2 - 42*z)
<replace-#Step 1>#Step 2:
Current expression: (18*z**3)*(-15*z**2 - 42*z) + 6*(-15*z**2 - 42*z)</replace>
Simplifying the partial expression: 6*(-15*z**2 - 42*z)
Expanding the part (-15*z**2 - 42*z) using the distributive property, and we got: -42*z*6 - 15*z**2*6
Replacing 6*(-15*z**2 - 42*z) with -42*z*6 - 15*z**2*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*z*6 - 15*z**2*6 + (18*z**3)*(-15*z**2 - 42*z)</replace>
Simplifying the partial expression: (18*z**3)*(-15*z**2 - 42*z)
Expanding the part (-15*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(18*z**3) + (-15*z**2)*(18*z**3)
Replacing (18*z**3)*(-15*z**2 - 42*z) with (-42*z)*(18*z**3) + (-15*z**2)*(18*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*z)*(18*z**3) - 42*z*6 + (-15*z**2)*(18*z**3) - 15*z**2*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z)*6 = -252*z
  (-42*z)*(18*z**3) = -756*z**4
  (-15*z**2)*6 = -90*z**2
  (-15*z**2)*(18*z**3) = -270*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -270*z**5 - 756*z**4 - 90*z**2 - 252*z</replace>
No more calculations needed.
<answer>-270*z**5 - 756*z**4 - 90*z**2 - 252*z</answer>


Question:
Calculate the following: (-19*z**3 - 45)*(35*z**3 - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -665*z**6 - 1119*z**3 + 1080

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-19*z**3 - 45)*(35*z**3 - 24)
Expanding the part (-19*z**3 - 45) using the distributive property, and we got: (-19*z**3)*(35*z**3 - 24) - 45*(35*z**3 - 24)
<replace-#Step 1>#Step 2:
Current expression: (-19*z**3)*(35*z**3 - 24) - 45*(35*z**3 - 24)</replace>
Simplifying the partial expression: -45*(35*z**3 - 24)
Expanding the part (35*z**3 - 24) using the distributive property, and we got: (35*z**3)*(-45) - 24*(-45)
Replacing -45*(35*z**3 - 24) with (35*z**3)*(-45) - 24*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-19*z**3)*(35*z**3 - 24) + (35*z**3)*(-45) + 1080</replace>
Simplifying the partial expression: (-19*z**3)*(35*z**3 - 24)
Expanding the part (35*z**3 - 24) using the distributive property, and we got: -(-1)*456*z**3 + (-19*z**3)*(35*z**3)
Replacing (-19*z**3)*(35*z**3 - 24) with -(-1)*456*z**3 + (-19*z**3)*(35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -24*(-19)*z**3 + (-19*z**3)*(35*z**3) + (35*z**3)*(-45) + 1080</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*z**3)*-45 = -1575*z**3
  (35*z**3)*(-19*z**3) = -665*z**6
  -24*-19*z**3 = 456*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -665*z**6 - 1575*z**3 + 456*z**3 + 1080</replace>
Combining like terms, got -665*z**6 - 1119*z**3 + 1080
<replace-#Step 5>#Step 6:
Current expression: -665*z**6 - 1119*z**3 + 1080</replace>
No more calculations needed.
<answer>-665*z**6 - 1119*z**3 + 1080</answer>


Question:
Calculate the following: (49 - 34*x**2)*(x - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -34*x**3 + 476*x**2 + 49*x - 686

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49 - 34*x**2)*(x - 14)
Expanding the part (x - 14) using the distributive property, and we got: x*(49 - 34*x**2) - 14*(49 - 34*x**2)
<replace-#Step 1>#Step 2:
Current expression: x*(49 - 34*x**2) - 14*(49 - 34*x**2)</replace>
Simplifying the partial expression: -14*(49 - 34*x**2)
Expanding the part (49 - 34*x**2) using the distributive property, and we got: -34*x**2*(-14) + 49*(-14)
Replacing -14*(49 - 34*x**2) with -34*x**2*(-14) + 49*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x*(49 - 34*x**2) - 34*x**2*(-14) - 686</replace>
Simplifying the partial expression: x*(49 - 34*x**2)
Expanding the part (49 - 34*x**2) using the distributive property, and we got: x*(-34*x**2) + 49*x
Replacing x*(49 - 34*x**2) with x*(-34*x**2) + 49*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: x*(-34*x**2) + 49*x - 34*x**2*(-14) - 686</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**2)*-14 = 476*x**2
  (-34*x**2)*x = -34*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -34*x**3 + 476*x**2 + 49*x - 686</replace>
No more calculations needed.
<answer>-34*x**3 + 476*x**2 + 49*x - 686</answer>


Question:
Simplify this expression: (12*z**3 + 19*z**2 + 62)*(34*z**3 - 26*z**2 + 16*z + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 408*z**6 + 334*z**5 - 302*z**4 + 2952*z**3 - 757*z**2 + 992*z + 2790


Question:
Simplify this expression: (-6*y**3 - 27*y)*(18*y**3 - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -108*y**6 - 486*y**4 + 72*y**3 + 324*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-6*y**3 - 27*y)*(18*y**3 - 12)
Expanding the part (18*y**3 - 12) using the distributive property, and we got: (18*y**3)*(-6*y**3 - 27*y) - 12*(-6*y**3 - 27*y)
<replace-#Step 1>#Step 2:
Current expression: (18*y**3)*(-6*y**3 - 27*y) - 12*(-6*y**3 - 27*y)</replace>
Simplifying the partial expression: -12*(-6*y**3 - 27*y)
Expanding the part (-6*y**3 - 27*y) using the distributive property, and we got: -27*y*(-12) - 6*y**3*(-12)
Replacing -12*(-6*y**3 - 27*y) with -27*y*(-12) - 6*y**3*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -27*y*(-12) - 6*y**3*(-12) + (18*y**3)*(-6*y**3 - 27*y)</replace>
Simplifying the partial expression: (18*y**3)*(-6*y**3 - 27*y)
Expanding the part (-6*y**3 - 27*y) using the distributive property, and we got: (-27*y)*(18*y**3) + (-6*y**3)*(18*y**3)
Replacing (18*y**3)*(-6*y**3 - 27*y) with (-27*y)*(18*y**3) + (-6*y**3)*(18*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-27*y)*(18*y**3) - 27*y*(-12) + (-6*y**3)*(18*y**3) - 6*y**3*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y)*-12 = 324*y
  (-27*y)*(18*y**3) = -486*y**4
  (-6*y**3)*-12 = 72*y**3
  (-6*y**3)*(18*y**3) = -108*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -108*y**6 - 486*y**4 + 72*y**3 + 324*y</replace>
No more calculations needed.
<answer>-108*y**6 - 486*y**4 + 72*y**3 + 324*y</answer>


Question:
Simplify this expression: (15 - 16*y**2)*(-61*y**3 + 32*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 976*y**5 - 1427*y**3 + 480*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (15 - 16*y**2)*(-61*y**3 + 32*y)
Expanding the part (15 - 16*y**2) using the distributive property, and we got: (-16*y**2)*(-61*y**3 + 32*y) + 15*(-61*y**3 + 32*y)
<replace-#Step 1>#Step 2:
Current expression: (-16*y**2)*(-61*y**3 + 32*y) + 15*(-61*y**3 + 32*y)</replace>
Simplifying the partial expression: 15*(-61*y**3 + 32*y)
Expanding the part (-61*y**3 + 32*y) using the distributive property, and we got: (32*y)*15 - 61*y**3*15
Replacing 15*(-61*y**3 + 32*y) with (32*y)*15 - 61*y**3*15 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (32*y)*15 + (-16*y**2)*(-61*y**3 + 32*y) - 61*y**3*15</replace>
Simplifying the partial expression: (-16*y**2)*(-61*y**3 + 32*y)
Expanding the part (-61*y**3 + 32*y) using the distributive property, and we got: (32*y)*(-16*y**2) + (-16*y**2)*(-61*y**3)
Replacing (-16*y**2)*(-61*y**3 + 32*y) with (32*y)*(-16*y**2) + (-16*y**2)*(-61*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (32*y)*(-16*y**2) + (32*y)*15 + (-16*y**2)*(-61*y**3) - 61*y**3*15</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-61*y**3)*15 = -915*y**3
  (-61*y**3)*(-16*y**2) = 976*y**5
  (32*y)*15 = 480*y
  (32*y)*(-16*y**2) = -512*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 976*y**5 - 915*y**3 - 512*y**3 + 480*y</replace>
Combining like terms, got 976*y**5 - 1427*y**3 + 480*y
<replace-#Step 5>#Step 6:
Current expression: 976*y**5 - 1427*y**3 + 480*y</replace>
No more calculations needed.
<answer>976*y**5 - 1427*y**3 + 480*y</answer>


Question:
Simplify this expression: (44*z**3 + 25*z**2)*(15*z**3 - 46*z**2 - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 660*z**6 - 1649*z**5 - 1150*z**4 - 1760*z**3 - 1000*z**2


Question:
Simplify this expression: (44*z**2 - 13)*(17*z**3 - 35*z**2 + 49*z - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 748*z**5 - 1540*z**4 + 1935*z**3 - 1305*z**2 - 637*z + 520


Question:
Calculate the following: (-42*y**3 - 47*y**2 - 27*y)*(-39*y**3 + 3*y**2 + 51)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1638*y**6 + 1707*y**5 + 912*y**4 - 2223*y**3 - 2397*y**2 - 1377*y


Question:
Simplify this expression: 16*z**3 - 44*z - 92
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 16*z**3 - 44*z - 92

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 16*z**3 - 44*z - 92
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 16*z**3 - 44*z - 92</replace>
No more calculations needed.
<answer>16*z**3 - 44*z - 92</answer>


Question:
Calculate the following: (-9*y**3 - y**2)*(-y**3 - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 9*y**6 + y**5 + 324*y**3 + 36*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-9*y**3 - y**2)*(-y**3 - 36)
Expanding the part (-y**3 - 36) using the distributive property, and we got: (-y**3)*(-9*y**3 - y**2) - 36*(-9*y**3 - y**2)
<replace-#Step 1>#Step 2:
Current expression: (-y**3)*(-9*y**3 - y**2) - 36*(-9*y**3 - y**2)</replace>
Simplifying the partial expression: -36*(-9*y**3 - y**2)
Expanding the part (-9*y**3 - y**2) using the distributive property, and we got: -y**2*(-36) - 9*y**3*(-36)
Replacing -36*(-9*y**3 - y**2) with -y**2*(-36) - 9*y**3*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -y**2*(-36) - 9*y**3*(-36) + (-y**3)*(-9*y**3 - y**2)</replace>
Simplifying the partial expression: (-y**3)*(-9*y**3 - y**2)
Expanding the part (-9*y**3 - y**2) using the distributive property, and we got: (-y**2)*(-y**3) + (-9*y**3)*(-y**3)
Replacing (-y**3)*(-9*y**3 - y**2) with (-y**2)*(-y**3) + (-9*y**3)*(-y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y**2)*(-y**3) - y**2*(-36) + (-9*y**3)*(-y**3) - 9*y**3*(-36)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y**2)*-36 = 36*y**2
  (-y**2)*(-y**3) = y**5
  (-9*y**3)*-36 = 324*y**3
  (-9*y**3)*(-y**3) = 9*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 9*y**6 + y**5 + 324*y**3 + 36*y**2</replace>
No more calculations needed.
<answer>9*y**6 + y**5 + 324*y**3 + 36*y**2</answer>


Question:
Calculate the following: (36*x**3 + 40*x - 24)*(41*x**3 - 22*x**2 - 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1476*x**6 - 792*x**5 + 1640*x**4 - 3484*x**3 + 528*x**2 - 1800*x + 1080


Question:
Calculate the following: (11*y**2 + 44*y)*(-9*y**3 + 49*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11*y**2 + 44*y)*(-9*y**3 + 49*y)
Expanding the part (-9*y**3 + 49*y) using the distributive property, and we got: (49*y)*(11*y**2 + 44*y) + (-9*y**3)*(11*y**2 + 44*y)
<replace-#Step 1>#Step 2:
Current expression: (49*y)*(11*y**2 + 44*y) + (-9*y**3)*(11*y**2 + 44*y)</replace>
Simplifying the partial expression: (-9*y**3)*(11*y**2 + 44*y)
Expanding the part (11*y**2 + 44*y) using the distributive property, and we got: (44*y)*(-9*y**3) + (11*y**2)*(-9*y**3)
Replacing (-9*y**3)*(11*y**2 + 44*y) with (44*y)*(-9*y**3) + (11*y**2)*(-9*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (44*y)*(-9*y**3) + (49*y)*(11*y**2 + 44*y) + (11*y**2)*(-9*y**3)</replace>
Simplifying the partial expression: (49*y)*(11*y**2 + 44*y)
Expanding the part (11*y**2 + 44*y) using the distributive property, and we got: (44*y)*(49*y) + (49*y)*(11*y**2)
Replacing (49*y)*(11*y**2 + 44*y) with (44*y)*(49*y) + (49*y)*(11*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (44*y)*(49*y) + (44*y)*(-9*y**3) + (49*y)*(11*y**2) + (11*y**2)*(-9*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*y**2)*(-9*y**3) = -99*y**5
  (11*y**2)*(49*y) = 539*y**3
  (44*y)*(-9*y**3) = -396*y**4
  (44*y)*(49*y) = 2156*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2</replace>
No more calculations needed.
<answer>-99*y**5 - 396*y**4 + 539*y**3 + 2156*y**2</answer>


Question:
Calculate the following: (-19*x**2 - 31)*(6*x**3 + 39*x**2 - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -114*x**5 - 741*x**4 - 186*x**3 - 886*x**2 + 527


Question:
Calculate the following: (66*x**3 - 47*x**2)*(-26*x**3 + 30*x - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1716*x**6 + 1222*x**5 + 1980*x**4 - 3918*x**3 + 1786*x**2


Question:
Simplify this expression: (46 - 39*y**2)*(27*y**2 - 31*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46 - 39*y**2)*(27*y**2 - 31*y)
Expanding the part (46 - 39*y**2) using the distributive property, and we got: (-39*y**2)*(27*y**2 - 31*y) + 46*(27*y**2 - 31*y)
<replace-#Step 1>#Step 2:
Current expression: (-39*y**2)*(27*y**2 - 31*y) + 46*(27*y**2 - 31*y)</replace>
Simplifying the partial expression: 46*(27*y**2 - 31*y)
Expanding the part (27*y**2 - 31*y) using the distributive property, and we got: -31*y*46 + (27*y**2)*46
Replacing 46*(27*y**2 - 31*y) with -31*y*46 + (27*y**2)*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -31*y*46 + (-39*y**2)*(27*y**2 - 31*y) + (27*y**2)*46</replace>
Simplifying the partial expression: (-39*y**2)*(27*y**2 - 31*y)
Expanding the part (27*y**2 - 31*y) using the distributive property, and we got: (-31*y)*(-39*y**2) + (-39*y**2)*(27*y**2)
Replacing (-39*y**2)*(27*y**2 - 31*y) with (-31*y)*(-39*y**2) + (-39*y**2)*(27*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*y)*(-39*y**2) - 31*y*46 + (-39*y**2)*(27*y**2) + (27*y**2)*46</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*y)*46 = -1426*y
  (-31*y)*(-39*y**2) = 1209*y**3
  (27*y**2)*46 = 1242*y**2
  (27*y**2)*(-39*y**2) = -1053*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y</replace>
No more calculations needed.
<answer>-1053*y**4 + 1209*y**3 + 1242*y**2 - 1426*y</answer>


Question:
Simplify this expression: (39*x**3 + 50*x)*(-16*x**3 + 75*x + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*x**3 + 50*x)*(-16*x**3 + 75*x + 7)
Expanding the part (39*x**3 + 50*x) using the distributive property, and we got: (50*x)*(-16*x**3 + 75*x + 7) + (39*x**3)*(-16*x**3 + 75*x + 7)
<replace-#Step 1>#Step 2:
Current expression: (50*x)*(-16*x**3 + 75*x + 7) + (39*x**3)*(-16*x**3 + 75*x + 7)</replace>
Simplifying the partial expression: (39*x**3)*(-16*x**3 + 75*x + 7)
Expanding the part (-16*x**3 + 75*x + 7) using the distributive property, and we got: 7*(39*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)
Replacing (39*x**3)*(-16*x**3 + 75*x + 7) with 7*(39*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 7*39*x**3 + (50*x)*(-16*x**3 + 75*x + 7) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)</replace>
Simplifying the partial expression: (50*x)*(-16*x**3 + 75*x + 7)
Expanding the part (-16*x**3 + 75*x + 7) using the distributive property, and we got: 7*(50*x) + (50*x)*(75*x) + (50*x)*(-16*x**3)
Replacing (50*x)*(-16*x**3 + 75*x + 7) with 7*(50*x) + (50*x)*(75*x) + (50*x)*(-16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 7*39*x**3 + 7*50*x + (50*x)*(75*x) + (50*x)*(-16*x**3) + (75*x)*(39*x**3) + (-16*x**3)*(39*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*x**3)*(39*x**3) = -624*x**6
  (-16*x**3)*(50*x) = -800*x**4
  (75*x)*(39*x**3) = 2925*x**4
  (75*x)*(50*x) = 3750*x**2
  7*39*x**3 = 273*x**3
  7*50*x = 350*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -624*x**6 - 800*x**4 + 2925*x**4 + 273*x**3 + 3750*x**2 + 350*x</replace>
Combining like terms, got -624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x
<replace-#Step 5>#Step 6:
Current expression: -624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x</replace>
No more calculations needed.
<answer>-624*x**6 + 2125*x**4 + 273*x**3 + 3750*x**2 + 350*x</answer>


Question:
Simplify this expression: 67*y**2*(-19*y**2 + 36*y + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1273*y**4 + 2412*y**3 + 1876*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 67*y**2*(-19*y**2 + 36*y + 28)
Expanding the part (-19*y**2 + 36*y + 28) using the distributive property, and we got: 28*(67*y**2) + (36*y)*(67*y**2) + (-19*y**2)*(67*y**2)
<replace-#Step 1>#Step 2:
Current expression: 28*(67*y**2) + (36*y)*(67*y**2) + (-19*y**2)*(67*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  28*(67*y**2) = 1876*y**2
  (-19*y**2)*(67*y**2) = -1273*y**4
  (36*y)*(67*y**2) = 2412*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1273*y**4 + 2412*y**3 + 1876*y**2</replace>
No more calculations needed.
<answer>-1273*y**4 + 2412*y**3 + 1876*y**2</answer>


Question:
Simplify this expression: (-61*y**2 - 21)*(61*y**3 + y**2 - 5*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-61*y**2 - 21)*(61*y**3 + y**2 - 5*y)
Expanding the part (-61*y**2 - 21) using the distributive property, and we got: (-61*y**2)*(61*y**3 + y**2 - 5*y) - 21*(61*y**3 + y**2 - 5*y)
<replace-#Step 1>#Step 2:
Current expression: (-61*y**2)*(61*y**3 + y**2 - 5*y) - 21*(61*y**3 + y**2 - 5*y)</replace>
Simplifying the partial expression: -21*(61*y**3 + y**2 - 5*y)
Expanding the part (61*y**3 + y**2 - 5*y) using the distributive property, and we got: -5*y*(-21) + y**2*(-21) + (61*y**3)*(-21)
Replacing -21*(61*y**3 + y**2 - 5*y) with -5*y*(-21) + y**2*(-21) + (61*y**3)*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -5*y*(-21) + y**2*(-21) + (-61*y**2)*(61*y**3 + y**2 - 5*y) + (61*y**3)*(-21)</replace>
Simplifying the partial expression: (-61*y**2)*(61*y**3 + y**2 - 5*y)
Expanding the part (61*y**3 + y**2 - 5*y) using the distributive property, and we got: (-5*y)*(-61*y**2) + (-61*y**2)*y**2 + (-61*y**2)*(61*y**3)
Replacing (-61*y**2)*(61*y**3 + y**2 - 5*y) with (-5*y)*(-61*y**2) + (-61*y**2)*y**2 + (-61*y**2)*(61*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*y)*(-61*y**2) - 5*y*(-21) + (-61*y**2)*y**2 + y**2*(-21) + (-61*y**2)*(61*y**3) + (61*y**3)*(-21)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**2*-21 = -21*y**2
  y**2*(-61*y**2) = -61*y**4
  (-5*y)*-21 = 105*y
  (-5*y)*(-61*y**2) = 305*y**3
  (61*y**3)*-21 = -1281*y**3
  (61*y**3)*(-61*y**2) = -3721*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3721*y**5 - 61*y**4 - 1281*y**3 + 305*y**3 - 21*y**2 + 105*y</replace>
Combining like terms, got -3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y
<replace-#Step 5>#Step 6:
Current expression: -3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y</replace>
No more calculations needed.
<answer>-3721*y**5 - 61*y**4 - 976*y**3 - 21*y**2 + 105*y</answer>


Question:
Calculate the following: (-109*y**2 - 26)*(-10*y**2 - 49*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-109*y**2 - 26)*(-10*y**2 - 49*y)
Expanding the part (-109*y**2 - 26) using the distributive property, and we got: (-109*y**2)*(-10*y**2 - 49*y) - 26*(-10*y**2 - 49*y)
<replace-#Step 1>#Step 2:
Current expression: (-109*y**2)*(-10*y**2 - 49*y) - 26*(-10*y**2 - 49*y)</replace>
Simplifying the partial expression: -26*(-10*y**2 - 49*y)
Expanding the part (-10*y**2 - 49*y) using the distributive property, and we got: -49*y*(-26) - 10*y**2*(-26)
Replacing -26*(-10*y**2 - 49*y) with -49*y*(-26) - 10*y**2*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*y*(-26) + (-109*y**2)*(-10*y**2 - 49*y) - 10*y**2*(-26)</replace>
Simplifying the partial expression: (-109*y**2)*(-10*y**2 - 49*y)
Expanding the part (-10*y**2 - 49*y) using the distributive property, and we got: (-49*y)*(-109*y**2) + (-109*y**2)*(-10*y**2)
Replacing (-109*y**2)*(-10*y**2 - 49*y) with (-49*y)*(-109*y**2) + (-109*y**2)*(-10*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(-109*y**2) - 49*y*(-26) + (-109*y**2)*(-10*y**2) - 10*y**2*(-26)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*y)*-26 = 1274*y
  (-49*y)*(-109*y**2) = 5341*y**3
  (-10*y**2)*-26 = 260*y**2
  (-10*y**2)*(-109*y**2) = 1090*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y</replace>
No more calculations needed.
<answer>1090*y**4 + 5341*y**3 + 260*y**2 + 1274*y</answer>


Question:
Simplify this expression: (-47*x**3 + 11*x**2)*(12*x**3 + 8*x**2 - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -564*x**6 - 244*x**5 + 88*x**4 + 470*x**3 - 110*x**2


Question:
Simplify this expression: (1 - 2*x**3)*(-7*x**2 + 34*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 14*x**5 - 68*x**4 - 7*x**2 + 34*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (1 - 2*x**3)*(-7*x**2 + 34*x)
Expanding the part (1 - 2*x**3) using the distributive property, and we got: (-2*x**3)*(-7*x**2 + 34*x) + 1*(-7*x**2 + 34*x)
<replace-#Step 1>#Step 2:
Current expression: (-2*x**3)*(-7*x**2 + 34*x) + 1*(-7*x**2 + 34*x)</replace>
Simplifying the partial expression: 1*(-7*x**2 + 34*x)
Expanding the part (-7*x**2 + 34*x) using the distributive property, and we got: (34*x)*1 - 7*x**2*1
Replacing 1*(-7*x**2 + 34*x) with (34*x)*1 - 7*x**2*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*x)*1 - 7*x**2*1 + (-2*x**3)*(-7*x**2 + 34*x)</replace>
Simplifying the partial expression: (-2*x**3)*(-7*x**2 + 34*x)
Expanding the part (-7*x**2 + 34*x) using the distributive property, and we got: (34*x)*(-2*x**3) + (-7*x**2)*(-2*x**3)
Replacing (-2*x**3)*(-7*x**2 + 34*x) with (34*x)*(-2*x**3) + (-7*x**2)*(-2*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*x)*(-2*x**3) + (34*x)*1 + (-7*x**2)*(-2*x**3) - 7*x**2*1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*x**2)*1 = -7*x**2
  (-7*x**2)*(-2*x**3) = 14*x**5
  (34*x)*1 = 34*x
  (34*x)*(-2*x**3) = -68*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 14*x**5 - 68*x**4 - 7*x**2 + 34*x</replace>
No more calculations needed.
<answer>14*x**5 - 68*x**4 - 7*x**2 + 34*x</answer>


Question:
Simplify this expression: (34*x**3 - 68*x**2)*(47*x**3 - 25*x**2 + 45*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1598*x**6 - 4046*x**5 + 3230*x**4 - 3060*x**3