Question:
Simplify this expression: (43*x**3 + 12)*(-33*x**3 + 35*x - 30)
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: -1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360

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 + 12)*(-33*x**3 + 35*x - 30)
Expanding the part (43*x**3 + 12) using the distributive property, and we got: (43*x**3)*(-33*x**3 + 35*x - 30) + 12*(-33*x**3 + 35*x - 30)
<replace-#Step 1>#Step 2:
Current expression: (43*x**3)*(-33*x**3 + 35*x - 30) + 12*(-33*x**3 + 35*x - 30)</replace>
Simplifying the partial expression: 12*(-33*x**3 + 35*x - 30)
Expanding the part (-33*x**3 + 35*x - 30) using the distributive property, and we got: (35*x)*12 - 33*x**3*12 - 30*12
Replacing 12*(-33*x**3 + 35*x - 30) with (35*x)*12 - 33*x**3*12 - 30*12 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*x)*12 - 33*x**3*12 + (43*x**3)*(-33*x**3 + 35*x - 30) - 360</replace>
Simplifying the partial expression: (43*x**3)*(-33*x**3 + 35*x - 30)
Expanding the part (-33*x**3 + 35*x - 30) using the distributive property, and we got: -1290*x**3 + (35*x)*(43*x**3) + (-33*x**3)*(43*x**3)
Replacing (43*x**3)*(-33*x**3 + 35*x - 30) with -1290*x**3 + (35*x)*(43*x**3) + (-33*x**3)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -30*43*x**3 + (35*x)*(43*x**3) + (35*x)*12 + (-33*x**3)*(43*x**3) - 33*x**3*12 - 360</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*x**3)*12 = -396*x**3
  (-33*x**3)*(43*x**3) = -1419*x**6
  (35*x)*12 = 420*x
  (35*x)*(43*x**3) = 1505*x**4
  -30*43*x**3 = -1290*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1419*x**6 + 1505*x**4 - 1290*x**3 - 396*x**3 + 420*x - 360</replace>
Combining like terms, got -1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360
<replace-#Step 5>#Step 6:
Current expression: -1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360</replace>
No more calculations needed.
<answer>-1419*x**6 + 1505*x**4 - 1686*x**3 + 420*x - 360</answer>


Question:
Simplify this expression: (9*y**2 - 38)*(-34*y**3 + 49*y**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: -306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836

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**2 - 38)*(-34*y**3 + 49*y**2 - 22)
Expanding the part (9*y**2 - 38) using the distributive property, and we got: (9*y**2)*(-34*y**3 + 49*y**2 - 22) - 38*(-34*y**3 + 49*y**2 - 22)
<replace-#Step 1>#Step 2:
Current expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22) - 38*(-34*y**3 + 49*y**2 - 22)</replace>
Simplifying the partial expression: -38*(-34*y**3 + 49*y**2 - 22)
Expanding the part (-34*y**3 + 49*y**2 - 22) using the distributive property, and we got: (49*y**2)*(-38) - 34*y**3*(-38) - 22*(-38)
Replacing -38*(-34*y**3 + 49*y**2 - 22) with (49*y**2)*(-38) - 34*y**3*(-38) - 22*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22) + (49*y**2)*(-38) - 34*y**3*(-38) + 836</replace>
Simplifying the partial expression: (9*y**2)*(-34*y**3 + 49*y**2 - 22)
Expanding the part (-34*y**3 + 49*y**2 - 22) using the distributive property, and we got: -198*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3)
Replacing (9*y**2)*(-34*y**3 + 49*y**2 - 22) with -198*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -22*9*y**2 + (9*y**2)*(49*y**2) + (9*y**2)*(-34*y**3) + (49*y**2)*(-38) - 34*y**3*(-38) + 836</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*y**3)*-38 = 1292*y**3
  (-34*y**3)*(9*y**2) = -306*y**5
  (49*y**2)*-38 = -1862*y**2
  (49*y**2)*(9*y**2) = 441*y**4
  -22*9*y**2 = -198*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -306*y**5 + 441*y**4 + 1292*y**3 - 1862*y**2 - 198*y**2 + 836</replace>
Combining like terms, got -306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836
<replace-#Step 5>#Step 6:
Current expression: -306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836</replace>
No more calculations needed.
<answer>-306*y**5 + 441*y**4 + 1292*y**3 - 2060*y**2 + 836</answer>


Question:
Simplify this expression: (-42*x - 36)*(41*x**3 + 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: -1722*x**4 - 1476*x**3 - 672*x - 576

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: (-42*x - 36)*(41*x**3 + 16)
Expanding the part (-42*x - 36) using the distributive property, and we got: (-42*x)*(41*x**3 + 16) - 36*(41*x**3 + 16)
<replace-#Step 1>#Step 2:
Current expression: (-42*x)*(41*x**3 + 16) - 36*(41*x**3 + 16)</replace>
Simplifying the partial expression: -36*(41*x**3 + 16)
Expanding the part (41*x**3 + 16) using the distributive property, and we got: (41*x**3)*(-36) + 16*(-36)
Replacing -36*(41*x**3 + 16) with (41*x**3)*(-36) + 16*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-42*x)*(41*x**3 + 16) + (41*x**3)*(-36) - 576</replace>
Simplifying the partial expression: (-42*x)*(41*x**3 + 16)
Expanding the part (41*x**3 + 16) using the distributive property, and we got: (-42*x)*(41*x**3) + 16*(-42*x)
Replacing (-42*x)*(41*x**3 + 16) with (-42*x)*(41*x**3) + 16*(-42*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*x)*(41*x**3) + 16*(-42)*x + (41*x**3)*(-36) - 576</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (41*x**3)*-36 = -1476*x**3
  (41*x**3)*(-42*x) = -1722*x**4
  16*-42*x = -672*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1722*x**4 - 1476*x**3 - 672*x - 576</replace>
No more calculations needed.
<answer>-1722*x**4 - 1476*x**3 - 672*x - 576</answer>


Question:
Simplify this expression: (19*x**2 - 10*x)*(15*x**3 - 46*x**2 + 13)
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: 285*x**5 - 1024*x**4 + 460*x**3 + 247*x**2 - 130*x


Question:
Simplify this expression: (-15*y**2 - 7)*(22*y**3 + 7*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: -330*y**5 - 259*y**3 - 49*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*y**2 - 7)*(22*y**3 + 7*y)
Expanding the part (-15*y**2 - 7) using the distributive property, and we got: (-15*y**2)*(22*y**3 + 7*y) - 7*(22*y**3 + 7*y)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**2)*(22*y**3 + 7*y) - 7*(22*y**3 + 7*y)</replace>
Simplifying the partial expression: -7*(22*y**3 + 7*y)
Expanding the part (22*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-7) + (22*y**3)*(-7)
Replacing -7*(22*y**3 + 7*y) with (7*y)*(-7) + (22*y**3)*(-7) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*y)*(-7) + (-15*y**2)*(22*y**3 + 7*y) + (22*y**3)*(-7)</replace>
Simplifying the partial expression: (-15*y**2)*(22*y**3 + 7*y)
Expanding the part (22*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-15*y**2) + (-15*y**2)*(22*y**3)
Replacing (-15*y**2)*(22*y**3 + 7*y) with (7*y)*(-15*y**2) + (-15*y**2)*(22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*y)*(-15*y**2) + (7*y)*(-7) + (-15*y**2)*(22*y**3) + (22*y**3)*(-7)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*y)*-7 = -49*y
  (7*y)*(-15*y**2) = -105*y**3
  (22*y**3)*-7 = -154*y**3
  (22*y**3)*(-15*y**2) = -330*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -330*y**5 - 154*y**3 - 105*y**3 - 49*y</replace>
Combining like terms, got -330*y**5 - 259*y**3 - 49*y
<replace-#Step 5>#Step 6:
Current expression: -330*y**5 - 259*y**3 - 49*y</replace>
No more calculations needed.
<answer>-330*y**5 - 259*y**3 - 49*y</answer>


Question:
Calculate the following: (-42*x**3 - 38*x)*(30*x**3 + 19*x - 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: -1260*x**6 - 1938*x**4 + 2058*x**3 - 722*x**2 + 1862*x


Question:
Calculate the following: (41*y**2 + 13*y)*(-59*y**3 + 17*y**2 - 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: -2419*y**5 - 70*y**4 + 221*y**3 - 1394*y**2 - 442*y


Question:
Simplify this expression: 54*x**3*(-48*x**2 + 21*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: -2592*x**5 + 1134*x**4

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: 54*x**3*(-48*x**2 + 21*x)
Expanding the part (-48*x**2 + 21*x) using the distributive property, and we got: (21*x)*(54*x**3) + (-48*x**2)*(54*x**3)
<replace-#Step 1>#Step 2:
Current expression: (21*x)*(54*x**3) + (-48*x**2)*(54*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**2)*(54*x**3) = -2592*x**5
  (21*x)*(54*x**3) = 1134*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2592*x**5 + 1134*x**4</replace>
No more calculations needed.
<answer>-2592*x**5 + 1134*x**4</answer>


Question:
Simplify this expression: (-46*z**3 + 20*z**2 + 4*z + 23)*(17*z**3 - 28*z**2 + 14*z - 18)
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: -782*z**6 + 1628*z**5 - 1136*z**4 + 1387*z**3 - 948*z**2 + 250*z - 414


Question:
Calculate the following: (8*x**2 - 20)*(8*x**3 + 10*x**2 + 30*x + 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: 64*x**5 + 80*x**4 + 80*x**3 - 120*x**2 - 600*x - 200


Question:
Calculate the following: -46*y*(38*y**2 - 12*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: -1748*y**3 + 552*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: -46*y*(38*y**2 - 12*y)
Expanding the part (38*y**2 - 12*y) using the distributive property, and we got: (-46*y)*(-12*y) + (-46*y)*(38*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-46*y)*(-12*y) + (-46*y)*(38*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*y)*(-46*y) = 552*y**2
  (38*y**2)*(-46*y) = -1748*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1748*y**3 + 552*y**2</replace>
No more calculations needed.
<answer>-1748*y**3 + 552*y**2</answer>


Question:
Calculate the following: (3 - 16*x)*(33*x**2 - 11*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: -528*x**3 + 275*x**2 - 33*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: (3 - 16*x)*(33*x**2 - 11*x)
Expanding the part (3 - 16*x) using the distributive property, and we got: (-16*x)*(33*x**2 - 11*x) + 3*(33*x**2 - 11*x)
<replace-#Step 1>#Step 2:
Current expression: (-16*x)*(33*x**2 - 11*x) + 3*(33*x**2 - 11*x)</replace>
Simplifying the partial expression: 3*(33*x**2 - 11*x)
Expanding the part (33*x**2 - 11*x) using the distributive property, and we got: -11*x*3 + (33*x**2)*3
Replacing 3*(33*x**2 - 11*x) with -11*x*3 + (33*x**2)*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-16*x)*(33*x**2 - 11*x) - 11*x*3 + (33*x**2)*3</replace>
Simplifying the partial expression: (-16*x)*(33*x**2 - 11*x)
Expanding the part (33*x**2 - 11*x) using the distributive property, and we got: (-16*x)*(-11*x) + (-16*x)*(33*x**2)
Replacing (-16*x)*(33*x**2 - 11*x) with (-16*x)*(-11*x) + (-16*x)*(33*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*x)*(-11*x) + (-16*x)*(33*x**2) - 11*x*3 + (33*x**2)*3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x)*3 = -33*x
  (-11*x)*(-16*x) = 176*x**2
  (33*x**2)*3 = 99*x**2
  (33*x**2)*(-16*x) = -528*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -528*x**3 + 99*x**2 + 176*x**2 - 33*x</replace>
Combining like terms, got -528*x**3 + 275*x**2 - 33*x
<replace-#Step 5>#Step 6:
Current expression: -528*x**3 + 275*x**2 - 33*x</replace>
No more calculations needed.
<answer>-528*x**3 + 275*x**2 - 33*x</answer>


Question:
Simplify this expression: (21*x**2 + 23*x)*(36*x**3 + 43*x**2 - 17*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: 756*x**5 + 1731*x**4 + 632*x**3 - 391*x**2


Question:
Calculate the following: (62*y**2 + 39*y)*(-21*y**2 - 38*y + 44)
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: -1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*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: (62*y**2 + 39*y)*(-21*y**2 - 38*y + 44)
Expanding the part (62*y**2 + 39*y) using the distributive property, and we got: (39*y)*(-21*y**2 - 38*y + 44) + (62*y**2)*(-21*y**2 - 38*y + 44)
<replace-#Step 1>#Step 2:
Current expression: (39*y)*(-21*y**2 - 38*y + 44) + (62*y**2)*(-21*y**2 - 38*y + 44)</replace>
Simplifying the partial expression: (39*y)*(-21*y**2 - 38*y + 44)
Expanding the part (-21*y**2 - 38*y + 44) using the distributive property, and we got: (-38*y)*(39*y) + 44*(39*y) + (39*y)*(-21*y**2)
Replacing (39*y)*(-21*y**2 - 38*y + 44) with (-38*y)*(39*y) + 44*(39*y) + (39*y)*(-21*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-38*y)*(39*y) + 44*39*y + (39*y)*(-21*y**2) + (62*y**2)*(-21*y**2 - 38*y + 44)</replace>
Simplifying the partial expression: (62*y**2)*(-21*y**2 - 38*y + 44)
Expanding the part (-21*y**2 - 38*y + 44) using the distributive property, and we got: (-38*y)*(62*y**2) + 44*(62*y**2) + (-21*y**2)*(62*y**2)
Replacing (62*y**2)*(-21*y**2 - 38*y + 44) with (-38*y)*(62*y**2) + 44*(62*y**2) + (-21*y**2)*(62*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-38*y)*(39*y) + (-38*y)*(62*y**2) + 44*62*y**2 + 44*39*y + (39*y)*(-21*y**2) + (-21*y**2)*(62*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*y)*(39*y) = -1482*y**2
  (-38*y)*(62*y**2) = -2356*y**3
  (-21*y**2)*(39*y) = -819*y**3
  (-21*y**2)*(62*y**2) = -1302*y**4
  44*39*y = 1716*y
  44*62*y**2 = 2728*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1302*y**4 - 2356*y**3 - 819*y**3 - 1482*y**2 + 2728*y**2 + 1716*y</replace>
Combining like terms, got -1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y
<replace-#Step 5>#Step 6:
Current expression: -1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y</replace>
No more calculations needed.
<answer>-1302*y**4 - 3175*y**3 + 1246*y**2 + 1716*y</answer>


Question:
Simplify this expression: 203*z**2 + 133
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: 203*z**2 + 133

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: 203*z**2 + 133
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: 203*z**2 + 133</replace>
No more calculations needed.
<answer>203*z**2 + 133</answer>


Question:
Simplify this expression: -13*y**3*(-49*y**3 - 24*y**2 + 20*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: 637*y**6 + 312*y**5 - 260*y**4

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: -13*y**3*(-49*y**3 - 24*y**2 + 20*y)
Expanding the part (-49*y**3 - 24*y**2 + 20*y) using the distributive property, and we got: (20*y)*(-13*y**3) + (-24*y**2)*(-13*y**3) + (-49*y**3)*(-13*y**3)
<replace-#Step 1>#Step 2:
Current expression: (20*y)*(-13*y**3) + (-24*y**2)*(-13*y**3) + (-49*y**3)*(-13*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*y**3)*(-13*y**3) = 637*y**6
  (-24*y**2)*(-13*y**3) = 312*y**5
  (20*y)*(-13*y**3) = -260*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 637*y**6 + 312*y**5 - 260*y**4</replace>
No more calculations needed.
<answer>637*y**6 + 312*y**5 - 260*y**4</answer>


Question:
Calculate the following: (42*y**2 + 38*y)*(42*y**3 - 145)
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: 1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*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: (42*y**2 + 38*y)*(42*y**3 - 145)
Expanding the part (42*y**3 - 145) using the distributive property, and we got: (42*y**3)*(42*y**2 + 38*y) - 145*(42*y**2 + 38*y)
<replace-#Step 1>#Step 2:
Current expression: (42*y**3)*(42*y**2 + 38*y) - 145*(42*y**2 + 38*y)</replace>
Simplifying the partial expression: -145*(42*y**2 + 38*y)
Expanding the part (42*y**2 + 38*y) using the distributive property, and we got: (38*y)*(-145) + (42*y**2)*(-145)
Replacing -145*(42*y**2 + 38*y) with (38*y)*(-145) + (42*y**2)*(-145) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (38*y)*(-145) + (42*y**2)*(-145) + (42*y**3)*(42*y**2 + 38*y)</replace>
Simplifying the partial expression: (42*y**3)*(42*y**2 + 38*y)
Expanding the part (42*y**2 + 38*y) using the distributive property, and we got: (38*y)*(42*y**3) + (42*y**2)*(42*y**3)
Replacing (42*y**3)*(42*y**2 + 38*y) with (38*y)*(42*y**3) + (42*y**2)*(42*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (38*y)*(42*y**3) + (38*y)*(-145) + (42*y**2)*(42*y**3) + (42*y**2)*(-145)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (38*y)*-145 = -5510*y
  (38*y)*(42*y**3) = 1596*y**4
  (42*y**2)*-145 = -6090*y**2
  (42*y**2)*(42*y**3) = 1764*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y</replace>
No more calculations needed.
<answer>1764*y**5 + 1596*y**4 - 6090*y**2 - 5510*y</answer>


Question:
Simplify this expression: -30*y**3*(-43*y**2 + 44*y - 30)
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: 1290*y**5 - 1320*y**4 + 900*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: -30*y**3*(-43*y**2 + 44*y - 30)
Expanding the part (-43*y**2 + 44*y - 30) using the distributive property, and we got: -(-1)*900*y**3 + (44*y)*(-30*y**3) + (-43*y**2)*(-30*y**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*900*y**3 + (44*y)*(-30*y**3) + (-43*y**2)*(-30*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -30*(-30*y**3) = 900*y**3
  (-43*y**2)*(-30*y**3) = 1290*y**5
  (44*y)*(-30*y**3) = -1320*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1290*y**5 - 1320*y**4 + 900*y**3</replace>
No more calculations needed.
<answer>1290*y**5 - 1320*y**4 + 900*y**3</answer>


Question:
Calculate the following: (-20*z**2 - 18*z)*(20*z**2 - 8*z - 43)
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: -400*z**4 - 200*z**3 + 1004*z**2 + 774*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: (-20*z**2 - 18*z)*(20*z**2 - 8*z - 43)
Expanding the part (-20*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(20*z**2 - 8*z - 43) + (-20*z**2)*(20*z**2 - 8*z - 43)
<replace-#Step 1>#Step 2:
Current expression: (-18*z)*(20*z**2 - 8*z - 43) + (-20*z**2)*(20*z**2 - 8*z - 43)</replace>
Simplifying the partial expression: (-20*z**2)*(20*z**2 - 8*z - 43)
Expanding the part (20*z**2 - 8*z - 43) using the distributive property, and we got: (-8*z)*(-20*z**2) - (-1)*860*z**2 + (-20*z**2)*(20*z**2)
Replacing (-20*z**2)*(20*z**2 - 8*z - 43) with (-8*z)*(-20*z**2) - (-1)*860*z**2 + (-20*z**2)*(20*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*z)*(20*z**2 - 8*z - 43) + (-8*z)*(-20*z**2) - 43*(-20)*z**2 + (-20*z**2)*(20*z**2)</replace>
Simplifying the partial expression: (-18*z)*(20*z**2 - 8*z - 43)
Expanding the part (20*z**2 - 8*z - 43) using the distributive property, and we got: (-18*z)*(-8*z) + (-18*z)*(20*z**2) - (-1)*774*z
Replacing (-18*z)*(20*z**2 - 8*z - 43) with (-18*z)*(-8*z) + (-18*z)*(20*z**2) - (-1)*774*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*z)*(-8*z) + (-18*z)*(20*z**2) + (-8*z)*(-20*z**2) - 43*(-20)*z**2 - 43*(-18)*z + (-20*z**2)*(20*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*z)*(-20*z**2) = 160*z**3
  (-8*z)*(-18*z) = 144*z**2
  (20*z**2)*(-20*z**2) = -400*z**4
  (20*z**2)*(-18*z) = -360*z**3
  -43*-20*z**2 = 860*z**2
  -43*-18*z = 774*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -400*z**4 - 360*z**3 + 160*z**3 + 144*z**2 + 860*z**2 + 774*z</replace>
Combining like terms, got -400*z**4 - 200*z**3 + 1004*z**2 + 774*z
<replace-#Step 5>#Step 6:
Current expression: -400*z**4 - 200*z**3 + 1004*z**2 + 774*z</replace>
No more calculations needed.
<answer>-400*z**4 - 200*z**3 + 1004*z**2 + 774*z</answer>


Question:
Calculate the following: -3*z*(42*z**3 - 35*z - 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: -126*z**4 + 105*z**2 + 114*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: -3*z*(42*z**3 - 35*z - 38)
Expanding the part (42*z**3 - 35*z - 38) using the distributive property, and we got: (-35*z)*(-3*z) + (-3*z)*(42*z**3) - (-1)*114*z
<replace-#Step 1>#Step 2:
Current expression: (-35*z)*(-3*z) + (-3*z)*(42*z**3) - (-1)*114*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -38*(-3*z) = 114*z
  (-35*z)*(-3*z) = 105*z**2
  (42*z**3)*(-3*z) = -126*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -126*z**4 + 105*z**2 + 114*z</replace>
No more calculations needed.
<answer>-126*z**4 + 105*z**2 + 114*z</answer>


Question:
Simplify this expression: (-6*z**3 - 24)*(20*z**3 + 19*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: -120*z**6 - 114*z**4 - 480*z**3 - 456*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: (-6*z**3 - 24)*(20*z**3 + 19*z)
Expanding the part (-6*z**3 - 24) using the distributive property, and we got: (-6*z**3)*(20*z**3 + 19*z) - 24*(20*z**3 + 19*z)
<replace-#Step 1>#Step 2:
Current expression: (-6*z**3)*(20*z**3 + 19*z) - 24*(20*z**3 + 19*z)</replace>
Simplifying the partial expression: -24*(20*z**3 + 19*z)
Expanding the part (20*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-24) + (20*z**3)*(-24)
Replacing -24*(20*z**3 + 19*z) with (19*z)*(-24) + (20*z**3)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*z)*(-24) + (-6*z**3)*(20*z**3 + 19*z) + (20*z**3)*(-24)</replace>
Simplifying the partial expression: (-6*z**3)*(20*z**3 + 19*z)
Expanding the part (20*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-6*z**3) + (-6*z**3)*(20*z**3)
Replacing (-6*z**3)*(20*z**3 + 19*z) with (19*z)*(-6*z**3) + (-6*z**3)*(20*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (19*z)*(-6*z**3) + (19*z)*(-24) + (-6*z**3)*(20*z**3) + (20*z**3)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*z)*-24 = -456*z
  (19*z)*(-6*z**3) = -114*z**4
  (20*z**3)*-24 = -480*z**3
  (20*z**3)*(-6*z**3) = -120*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -120*z**6 - 114*z**4 - 480*z**3 - 456*z</replace>
No more calculations needed.
<answer>-120*z**6 - 114*z**4 - 480*z**3 - 456*z</answer>


Question:
Calculate the following: (-36*z**2 - 26)*(21*z**3 + 43*z + 30)
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: -756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780

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: (-36*z**2 - 26)*(21*z**3 + 43*z + 30)
Expanding the part (-36*z**2 - 26) using the distributive property, and we got: (-36*z**2)*(21*z**3 + 43*z + 30) - 26*(21*z**3 + 43*z + 30)
<replace-#Step 1>#Step 2:
Current expression: (-36*z**2)*(21*z**3 + 43*z + 30) - 26*(21*z**3 + 43*z + 30)</replace>
Simplifying the partial expression: -26*(21*z**3 + 43*z + 30)
Expanding the part (21*z**3 + 43*z + 30) using the distributive property, and we got: (43*z)*(-26) + (21*z**3)*(-26) + 30*(-26)
Replacing -26*(21*z**3 + 43*z + 30) with (43*z)*(-26) + (21*z**3)*(-26) + 30*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*z)*(-26) + (-36*z**2)*(21*z**3 + 43*z + 30) + (21*z**3)*(-26) - 780</replace>
Simplifying the partial expression: (-36*z**2)*(21*z**3 + 43*z + 30)
Expanding the part (21*z**3 + 43*z + 30) using the distributive property, and we got: 30*(-36*z**2) + (43*z)*(-36*z**2) + (-36*z**2)*(21*z**3)
Replacing (-36*z**2)*(21*z**3 + 43*z + 30) with 30*(-36*z**2) + (43*z)*(-36*z**2) + (-36*z**2)*(21*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 30*(-36)*z**2 + (43*z)*(-36*z**2) + (43*z)*(-26) + (-36*z**2)*(21*z**3) + (21*z**3)*(-26) - 780</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (21*z**3)*-26 = -546*z**3
  (21*z**3)*(-36*z**2) = -756*z**5
  (43*z)*-26 = -1118*z
  (43*z)*(-36*z**2) = -1548*z**3
  30*-36*z**2 = -1080*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -756*z**5 - 1548*z**3 - 546*z**3 - 1080*z**2 - 1118*z - 780</replace>
Combining like terms, got -756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780
<replace-#Step 5>#Step 6:
Current expression: -756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780</replace>
No more calculations needed.
<answer>-756*z**5 - 2094*z**3 - 1080*z**2 - 1118*z - 780</answer>


Question:
Calculate the following: (50*x - 12)*(31*x**3 - 31*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: 1550*x**4 - 1922*x**3 + 372*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: (50*x - 12)*(31*x**3 - 31*x**2)
Expanding the part (50*x - 12) using the distributive property, and we got: (50*x)*(31*x**3 - 31*x**2) - 12*(31*x**3 - 31*x**2)
<replace-#Step 1>#Step 2:
Current expression: (50*x)*(31*x**3 - 31*x**2) - 12*(31*x**3 - 31*x**2)</replace>
Simplifying the partial expression: -12*(31*x**3 - 31*x**2)
Expanding the part (31*x**3 - 31*x**2) using the distributive property, and we got: -31*x**2*(-12) + (31*x**3)*(-12)
Replacing -12*(31*x**3 - 31*x**2) with -31*x**2*(-12) + (31*x**3)*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*x)*(31*x**3 - 31*x**2) - 31*x**2*(-12) + (31*x**3)*(-12)</replace>
Simplifying the partial expression: (50*x)*(31*x**3 - 31*x**2)
Expanding the part (31*x**3 - 31*x**2) using the distributive property, and we got: (50*x)*(-31*x**2) + (50*x)*(31*x**3)
Replacing (50*x)*(31*x**3 - 31*x**2) with (50*x)*(-31*x**2) + (50*x)*(31*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (50*x)*(-31*x**2) + (50*x)*(31*x**3) - 31*x**2*(-12) + (31*x**3)*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*x**2)*-12 = 372*x**2
  (-31*x**2)*(50*x) = -1550*x**3
  (31*x**3)*-12 = -372*x**3
  (31*x**3)*(50*x) = 1550*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1550*x**4 - 1550*x**3 - 372*x**3 + 372*x**2</replace>
Combining like terms, got 1550*x**4 - 1922*x**3 + 372*x**2
<replace-#Step 5>#Step 6:
Current expression: 1550*x**4 - 1922*x**3 + 372*x**2</replace>
No more calculations needed.
<answer>1550*x**4 - 1922*x**3 + 372*x**2</answer>


Question:
Simplify this expression: (-64*x**2 - 17)*(6*x**3 - 23*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: -384*x**5 + 1472*x**4 - 102*x**3 + 391*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: (-64*x**2 - 17)*(6*x**3 - 23*x**2)
Expanding the part (-64*x**2 - 17) using the distributive property, and we got: (-64*x**2)*(6*x**3 - 23*x**2) - 17*(6*x**3 - 23*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-64*x**2)*(6*x**3 - 23*x**2) - 17*(6*x**3 - 23*x**2)</replace>
Simplifying the partial expression: -17*(6*x**3 - 23*x**2)
Expanding the part (6*x**3 - 23*x**2) using the distributive property, and we got: -23*x**2*(-17) + (6*x**3)*(-17)
Replacing -17*(6*x**3 - 23*x**2) with -23*x**2*(-17) + (6*x**3)*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-64*x**2)*(6*x**3 - 23*x**2) - 23*x**2*(-17) + (6*x**3)*(-17)</replace>
Simplifying the partial expression: (-64*x**2)*(6*x**3 - 23*x**2)
Expanding the part (6*x**3 - 23*x**2) using the distributive property, and we got: (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3)
Replacing (-64*x**2)*(6*x**3 - 23*x**2) with (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-64*x**2)*(-23*x**2) + (-64*x**2)*(6*x**3) - 23*x**2*(-17) + (6*x**3)*(-17)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*x**2)*-17 = 391*x**2
  (-23*x**2)*(-64*x**2) = 1472*x**4
  (6*x**3)*-17 = -102*x**3
  (6*x**3)*(-64*x**2) = -384*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2</replace>
No more calculations needed.
<answer>-384*x**5 + 1472*x**4 - 102*x**3 + 391*x**2</answer>


Question:
Calculate the following: (18 - 21*z**2)*(-14*z**3 + 14*z + 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: 294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288

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: (18 - 21*z**2)*(-14*z**3 + 14*z + 16)
Expanding the part (18 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(-14*z**3 + 14*z + 16) + 18*(-14*z**3 + 14*z + 16)
<replace-#Step 1>#Step 2:
Current expression: (-21*z**2)*(-14*z**3 + 14*z + 16) + 18*(-14*z**3 + 14*z + 16)</replace>
Simplifying the partial expression: 18*(-14*z**3 + 14*z + 16)
Expanding the part (-14*z**3 + 14*z + 16) using the distributive property, and we got: (14*z)*18 - 14*z**3*18 + 16*18
Replacing 18*(-14*z**3 + 14*z + 16) with (14*z)*18 - 14*z**3*18 + 16*18 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*18 + (-21*z**2)*(-14*z**3 + 14*z + 16) - 14*z**3*18 + 288</replace>
Simplifying the partial expression: (-21*z**2)*(-14*z**3 + 14*z + 16)
Expanding the part (-14*z**3 + 14*z + 16) using the distributive property, and we got: 16*(-21*z**2) + (14*z)*(-21*z**2) + (-21*z**2)*(-14*z**3)
Replacing (-21*z**2)*(-14*z**3 + 14*z + 16) with 16*(-21*z**2) + (14*z)*(-21*z**2) + (-21*z**2)*(-14*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 16*(-21)*z**2 + (14*z)*(-21*z**2) + (14*z)*18 + (-21*z**2)*(-14*z**3) - 14*z**3*18 + 288</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**3)*18 = -252*z**3
  (-14*z**3)*(-21*z**2) = 294*z**5
  (14*z)*18 = 252*z
  (14*z)*(-21*z**2) = -294*z**3
  16*-21*z**2 = -336*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 294*z**5 - 294*z**3 - 252*z**3 - 336*z**2 + 252*z + 288</replace>
Combining like terms, got 294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288
<replace-#Step 5>#Step 6:
Current expression: 294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288</replace>
No more calculations needed.
<answer>294*z**5 - 546*z**3 - 336*z**2 + 252*z + 288</answer>


Question:
Simplify this expression: (19*x**2 - 18*x - 40)*(-37*x**3 - 25*x**2 + 17*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: -703*x**5 + 191*x**4 + 2253*x**3 + 694*x**2 - 680*x


Question:
Simplify this expression: (x**3 + 48*x)*(6*x**3 + 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: 6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*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: (x**3 + 48*x)*(6*x**3 + x - 14)
Expanding the part (x**3 + 48*x) using the distributive property, and we got: x**3*(6*x**3 + x - 14) + (48*x)*(6*x**3 + x - 14)
<replace-#Step 1>#Step 2:
Current expression: x**3*(6*x**3 + x - 14) + (48*x)*(6*x**3 + x - 14)</replace>
Simplifying the partial expression: x**3*(6*x**3 + x - 14)
Expanding the part (6*x**3 + x - 14) using the distributive property, and we got: x**3*(6*x**3) - 14*x**3 + x*x**3
Replacing x**3*(6*x**3 + x - 14) with x**3*(6*x**3) - 14*x**3 + x*x**3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x**3*(6*x**3) - 14*x**3 + x*x**3 + (48*x)*(6*x**3 + x - 14)</replace>
Simplifying the partial expression: (48*x)*(6*x**3 + x - 14)
Expanding the part (6*x**3 + x - 14) using the distributive property, and we got: x*(48*x) - 672*x + (48*x)*(6*x**3)
Replacing (48*x)*(6*x**3 + x - 14) with x*(48*x) - 672*x + (48*x)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: x**3*(6*x**3) - 14*x**3 + x*x**3 + x*(48*x) - 14*48*x + (48*x)*(6*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x*x**3 = x**4
  x*(48*x) = 48*x**2
  (6*x**3)*x**3 = 6*x**6
  (6*x**3)*(48*x) = 288*x**4
  -14*48*x = -672*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 6*x**6 + x**4 + 288*x**4 - 14*x**3 + 48*x**2 - 672*x</replace>
Combining like terms, got 6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x
<replace-#Step 5>#Step 6:
Current expression: 6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x</replace>
No more calculations needed.
<answer>6*x**6 + 289*x**4 - 14*x**3 + 48*x**2 - 672*x</answer>


Question:
Calculate the following: (9*z**3 - 4)*(31*z**3 - 61*z**2 - 41*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: 279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*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: (9*z**3 - 4)*(31*z**3 - 61*z**2 - 41*z)
Expanding the part (9*z**3 - 4) using the distributive property, and we got: (9*z**3)*(31*z**3 - 61*z**2 - 41*z) - 4*(31*z**3 - 61*z**2 - 41*z)
<replace-#Step 1>#Step 2:
Current expression: (9*z**3)*(31*z**3 - 61*z**2 - 41*z) - 4*(31*z**3 - 61*z**2 - 41*z)</replace>
Simplifying the partial expression: -4*(31*z**3 - 61*z**2 - 41*z)
Expanding the part (31*z**3 - 61*z**2 - 41*z) using the distributive property, and we got: -41*z*(-4) - 61*z**2*(-4) + (31*z**3)*(-4)
Replacing -4*(31*z**3 - 61*z**2 - 41*z) with -41*z*(-4) - 61*z**2*(-4) + (31*z**3)*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*z*(-4) - 61*z**2*(-4) + (9*z**3)*(31*z**3 - 61*z**2 - 41*z) + (31*z**3)*(-4)</replace>
Simplifying the partial expression: (9*z**3)*(31*z**3 - 61*z**2 - 41*z)
Expanding the part (31*z**3 - 61*z**2 - 41*z) using the distributive property, and we got: (-41*z)*(9*z**3) + (-61*z**2)*(9*z**3) + (9*z**3)*(31*z**3)
Replacing (9*z**3)*(31*z**3 - 61*z**2 - 41*z) with (-41*z)*(9*z**3) + (-61*z**2)*(9*z**3) + (9*z**3)*(31*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*z)*(9*z**3) - 41*z*(-4) + (-61*z**2)*(9*z**3) - 61*z**2*(-4) + (9*z**3)*(31*z**3) + (31*z**3)*(-4)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-61*z**2)*-4 = 244*z**2
  (-61*z**2)*(9*z**3) = -549*z**5
  (-41*z)*-4 = 164*z
  (-41*z)*(9*z**3) = -369*z**4
  (31*z**3)*-4 = -124*z**3
  (31*z**3)*(9*z**3) = 279*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z</replace>
No more calculations needed.
<answer>279*z**6 - 549*z**5 - 369*z**4 - 124*z**3 + 244*z**2 + 164*z</answer>


Question:
Simplify this expression: (-49*y - 1)*(-24*y**3 - 5*y + 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: 1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38

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 - 1)*(-24*y**3 - 5*y + 38)
Expanding the part (-49*y - 1) using the distributive property, and we got: (-49*y)*(-24*y**3 - 5*y + 38) - (-24*y**3 - 5*y + 38)
<replace-#Step 1>#Step 2:
Current expression: (-49*y)*(-24*y**3 - 5*y + 38) - (-24*y**3 - 5*y + 38)</replace>
Simplifying the partial expression: -(-24*y**3 - 5*y + 38)
Expanding the part (-24*y**3 - 5*y + 38) using the distributive property, and we got: -5*y*(-1) - 24*y**3*(-1) + 38*(-1)
Replacing -(-24*y**3 - 5*y + 38) with -5*y*(-1) - 24*y**3*(-1) + 38*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*y)*(-24*y**3 - 5*y + 38) - 5*y*(-1) - 24*y**3*(-1) - 38</replace>
Simplifying the partial expression: (-49*y)*(-24*y**3 - 5*y + 38)
Expanding the part (-24*y**3 - 5*y + 38) using the distributive property, and we got: (-49*y)*(-5*y) + (-49*y)*(-24*y**3) + 38*(-49*y)
Replacing (-49*y)*(-24*y**3 - 5*y + 38) with (-49*y)*(-5*y) + (-49*y)*(-24*y**3) + 38*(-49*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(-5*y) + (-49*y)*(-24*y**3) - 5*y*(-1) + 38*(-49)*y - 24*y**3*(-1) - 38</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*y**3)*-1 = 24*y**3
  (-24*y**3)*(-49*y) = 1176*y**4
  (-5*y)*-1 = 5*y
  (-5*y)*(-49*y) = 245*y**2
  38*-49*y = -1862*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1176*y**4 + 24*y**3 + 245*y**2 - 1862*y + 5*y - 38</replace>
Combining like terms, got 1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38
<replace-#Step 5>#Step 6:
Current expression: 1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38</replace>
No more calculations needed.
<answer>1176*y**4 + 24*y**3 + 245*y**2 - 1857*y - 38</answer>


Question:
Calculate the following: (-38*z**3 - 1)*(-4*z**3 + 4*z - 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: 152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19

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: (-38*z**3 - 1)*(-4*z**3 + 4*z - 19)
Expanding the part (-38*z**3 - 1) using the distributive property, and we got: (-38*z**3)*(-4*z**3 + 4*z - 19) - (-4*z**3 + 4*z - 19)
<replace-#Step 1>#Step 2:
Current expression: (-38*z**3)*(-4*z**3 + 4*z - 19) - (-4*z**3 + 4*z - 19)</replace>
Simplifying the partial expression: -(-4*z**3 + 4*z - 19)
Expanding the part (-4*z**3 + 4*z - 19) using the distributive property, and we got: (4*z)*(-1) - 4*z**3*(-1) - 19*(-1)
Replacing -(-4*z**3 + 4*z - 19) with (4*z)*(-1) - 4*z**3*(-1) - 19*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*z)*(-1) + (-38*z**3)*(-4*z**3 + 4*z - 19) - 4*z**3*(-1) + 19</replace>
Simplifying the partial expression: (-38*z**3)*(-4*z**3 + 4*z - 19)
Expanding the part (-4*z**3 + 4*z - 19) using the distributive property, and we got: -(-1)*722*z**3 + (4*z)*(-38*z**3) + (-38*z**3)*(-4*z**3)
Replacing (-38*z**3)*(-4*z**3 + 4*z - 19) with -(-1)*722*z**3 + (4*z)*(-38*z**3) + (-38*z**3)*(-4*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -19*(-38)*z**3 + (4*z)*(-38*z**3) + (4*z)*(-1) + (-38*z**3)*(-4*z**3) - 4*z**3*(-1) + 19</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*z**3)*-1 = 4*z**3
  (-4*z**3)*(-38*z**3) = 152*z**6
  (4*z)*-1 = -4*z
  (4*z)*(-38*z**3) = -152*z**4
  -19*-38*z**3 = 722*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 152*z**6 - 152*z**4 + 4*z**3 + 722*z**3 - 4*z + 19</replace>
Combining like terms, got 152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19
<replace-#Step 5>#Step 6:
Current expression: 152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19</replace>
No more calculations needed.
<answer>152*z**6 - 152*z**4 + 726*z**3 - 4*z + 19</answer>


Question:
Calculate the following: 20*y*(40*y**3 + 33*y**2 - 58)
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: 800*y**4 + 660*y**3 - 1160*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: 20*y*(40*y**3 + 33*y**2 - 58)
Expanding the part (40*y**3 + 33*y**2 - 58) using the distributive property, and we got: -1160*y + (20*y)*(33*y**2) + (20*y)*(40*y**3)
<replace-#Step 1>#Step 2:
Current expression: -1160*y + (20*y)*(33*y**2) + (20*y)*(40*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -58*(20*y) = -1160*y
  (33*y**2)*(20*y) = 660*y**3
  (40*y**3)*(20*y) = 800*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 800*y**4 + 660*y**3 - 1160*y</replace>
No more calculations needed.
<answer>800*y**4 + 660*y**3 - 1160*y</answer>


Question:
Calculate the following: 380*z**4
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: 380*z**4

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: 380*z**4
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: 380*z**4</replace>
No more calculations needed.
<answer>380*z**4</answer>


Question:
Calculate the following: (35*z**3 + 14*z)*(49*z**3 - 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: 1715*z**6 + 686*z**4 - 70*z**3 - 28*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: (35*z**3 + 14*z)*(49*z**3 - 2)
Expanding the part (49*z**3 - 2) using the distributive property, and we got: (49*z**3)*(35*z**3 + 14*z) - 2*(35*z**3 + 14*z)
<replace-#Step 1>#Step 2:
Current expression: (49*z**3)*(35*z**3 + 14*z) - 2*(35*z**3 + 14*z)</replace>
Simplifying the partial expression: -2*(35*z**3 + 14*z)
Expanding the part (35*z**3 + 14*z) using the distributive property, and we got: (14*z)*(-2) + (35*z**3)*(-2)
Replacing -2*(35*z**3 + 14*z) with (14*z)*(-2) + (35*z**3)*(-2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*(-2) + (35*z**3)*(-2) + (49*z**3)*(35*z**3 + 14*z)</replace>
Simplifying the partial expression: (49*z**3)*(35*z**3 + 14*z)
Expanding the part (35*z**3 + 14*z) using the distributive property, and we got: (14*z)*(49*z**3) + (35*z**3)*(49*z**3)
Replacing (49*z**3)*(35*z**3 + 14*z) with (14*z)*(49*z**3) + (35*z**3)*(49*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*z)*(49*z**3) + (14*z)*(-2) + (35*z**3)*(49*z**3) + (35*z**3)*(-2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*z)*-2 = -28*z
  (14*z)*(49*z**3) = 686*z**4
  (35*z**3)*-2 = -70*z**3
  (35*z**3)*(49*z**3) = 1715*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1715*z**6 + 686*z**4 - 70*z**3 - 28*z</replace>
No more calculations needed.
<answer>1715*z**6 + 686*z**4 - 70*z**3 - 28*z</answer>


Question:
Calculate the following: (8*z + 64)*(-45*z**3 - 21*z**2 + 49*z + 15)
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: -360*z**4 - 3048*z**3 - 952*z**2 + 3256*z + 960


Question:
Simplify this expression: (-9*y**3 - 7*y**2)*(7*y**3 + 7*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: -63*y**6 - 49*y**5 - 63*y**4 - 49*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: (-9*y**3 - 7*y**2)*(7*y**3 + 7*y)
Expanding the part (-9*y**3 - 7*y**2) using the distributive property, and we got: (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3 + 7*y)
<replace-#Step 1>#Step 2:
Current expression: (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3 + 7*y)</replace>
Simplifying the partial expression: (-9*y**3)*(7*y**3 + 7*y)
Expanding the part (7*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-9*y**3) + (-9*y**3)*(7*y**3)
Replacing (-9*y**3)*(7*y**3 + 7*y) with (7*y)*(-9*y**3) + (-9*y**3)*(7*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*y)*(-9*y**3) + (-7*y**2)*(7*y**3 + 7*y) + (-9*y**3)*(7*y**3)</replace>
Simplifying the partial expression: (-7*y**2)*(7*y**3 + 7*y)
Expanding the part (7*y**3 + 7*y) using the distributive property, and we got: (7*y)*(-7*y**2) + (-7*y**2)*(7*y**3)
Replacing (-7*y**2)*(7*y**3 + 7*y) with (7*y)*(-7*y**2) + (-7*y**2)*(7*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*y)*(-7*y**2) + (7*y)*(-9*y**3) + (-7*y**2)*(7*y**3) + (-9*y**3)*(7*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*y)*(-9*y**3) = -63*y**4
  (7*y)*(-7*y**2) = -49*y**3
  (7*y**3)*(-9*y**3) = -63*y**6
  (7*y**3)*(-7*y**2) = -49*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -63*y**6 - 49*y**5 - 63*y**4 - 49*y**3</replace>
No more calculations needed.
<answer>-63*y**6 - 49*y**5 - 63*y**4 - 49*y**3</answer>


Question:
Simplify this expression: (-45*y**2 - 24)*(25*y**3 + 39*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: -1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672

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*y**2 - 24)*(25*y**3 + 39*y + 28)
Expanding the part (-45*y**2 - 24) using the distributive property, and we got: (-45*y**2)*(25*y**3 + 39*y + 28) - 24*(25*y**3 + 39*y + 28)
<replace-#Step 1>#Step 2:
Current expression: (-45*y**2)*(25*y**3 + 39*y + 28) - 24*(25*y**3 + 39*y + 28)</replace>
Simplifying the partial expression: -24*(25*y**3 + 39*y + 28)
Expanding the part (25*y**3 + 39*y + 28) using the distributive property, and we got: (39*y)*(-24) + (25*y**3)*(-24) + 28*(-24)
Replacing -24*(25*y**3 + 39*y + 28) with (39*y)*(-24) + (25*y**3)*(-24) + 28*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*y)*(-24) + (-45*y**2)*(25*y**3 + 39*y + 28) + (25*y**3)*(-24) - 672</replace>
Simplifying the partial expression: (-45*y**2)*(25*y**3 + 39*y + 28)
Expanding the part (25*y**3 + 39*y + 28) using the distributive property, and we got: 28*(-45*y**2) + (39*y)*(-45*y**2) + (-45*y**2)*(25*y**3)
Replacing (-45*y**2)*(25*y**3 + 39*y + 28) with 28*(-45*y**2) + (39*y)*(-45*y**2) + (-45*y**2)*(25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 28*(-45)*y**2 + (39*y)*(-45*y**2) + (39*y)*(-24) + (-45*y**2)*(25*y**3) + (25*y**3)*(-24) - 672</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*y**3)*-24 = -600*y**3
  (25*y**3)*(-45*y**2) = -1125*y**5
  (39*y)*-24 = -936*y
  (39*y)*(-45*y**2) = -1755*y**3
  28*-45*y**2 = -1260*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1125*y**5 - 1755*y**3 - 600*y**3 - 1260*y**2 - 936*y - 672</replace>
Combining like terms, got -1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672
<replace-#Step 5>#Step 6:
Current expression: -1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672</replace>
No more calculations needed.
<answer>-1125*y**5 - 2355*y**3 - 1260*y**2 - 936*y - 672</answer>


Question:
Simplify this expression: (29*x**2 + 6)*(-20*x**3 + 20*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: -580*x**5 + 580*x**4 - 120*x**3 + 120*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: (29*x**2 + 6)*(-20*x**3 + 20*x**2)
Expanding the part (29*x**2 + 6) using the distributive property, and we got: (29*x**2)*(-20*x**3 + 20*x**2) + 6*(-20*x**3 + 20*x**2)
<replace-#Step 1>#Step 2:
Current expression: (29*x**2)*(-20*x**3 + 20*x**2) + 6*(-20*x**3 + 20*x**2)</replace>
Simplifying the partial expression: 6*(-20*x**3 + 20*x**2)
Expanding the part (-20*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*6 - 20*x**3*6
Replacing 6*(-20*x**3 + 20*x**2) with (20*x**2)*6 - 20*x**3*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*x**2)*6 + (29*x**2)*(-20*x**3 + 20*x**2) - 20*x**3*6</replace>
Simplifying the partial expression: (29*x**2)*(-20*x**3 + 20*x**2)
Expanding the part (-20*x**3 + 20*x**2) using the distributive property, and we got: (20*x**2)*(29*x**2) + (29*x**2)*(-20*x**3)
Replacing (29*x**2)*(-20*x**3 + 20*x**2) with (20*x**2)*(29*x**2) + (29*x**2)*(-20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*x**2)*(29*x**2) + (20*x**2)*6 + (29*x**2)*(-20*x**3) - 20*x**3*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x**3)*6 = -120*x**3
  (-20*x**3)*(29*x**2) = -580*x**5
  (20*x**2)*6 = 120*x**2
  (20*x**2)*(29*x**2) = 580*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -580*x**5 + 580*x**4 - 120*x**3 + 120*x**2</replace>
No more calculations needed.
<answer>-580*x**5 + 580*x**4 - 120*x**3 + 120*x**2</answer>


Question:
Calculate the following: (-48*y**3 - 41*y**2 + 7*y)*(-4*y**3 + 15*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: 192*y**6 - 556*y**5 + 1277*y**4 + 1745*y**3 - 280*y**2


Question:
Simplify this expression: (-47*z**2 + 10*z + 23)*(-30*z**3 - 13*z**2 - 2*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: 1410*z**5 + 311*z**4 - 726*z**3 - 319*z**2 - 46*z


Question:
Simplify this expression: 34*z**3*(41*z + 48)
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: 1394*z**4 + 1632*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: 34*z**3*(41*z + 48)
Expanding the part (41*z + 48) using the distributive property, and we got: 48*(34*z**3) + (41*z)*(34*z**3)
<replace-#Step 1>#Step 2:
Current expression: 48*(34*z**3) + (41*z)*(34*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  48*(34*z**3) = 1632*z**3
  (41*z)*(34*z**3) = 1394*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1394*z**4 + 1632*z**3</replace>
No more calculations needed.
<answer>1394*z**4 + 1632*z**3</answer>


Question:
Calculate the following: (-37*x - 47)*(-48*x**3 + 47*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: 1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*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: (-37*x - 47)*(-48*x**3 + 47*x)
Expanding the part (-37*x - 47) using the distributive property, and we got: (-37*x)*(-48*x**3 + 47*x) - 47*(-48*x**3 + 47*x)
<replace-#Step 1>#Step 2:
Current expression: (-37*x)*(-48*x**3 + 47*x) - 47*(-48*x**3 + 47*x)</replace>
Simplifying the partial expression: -47*(-48*x**3 + 47*x)
Expanding the part (-48*x**3 + 47*x) using the distributive property, and we got: (47*x)*(-47) - 48*x**3*(-47)
Replacing -47*(-48*x**3 + 47*x) with (47*x)*(-47) - 48*x**3*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*x)*(-48*x**3 + 47*x) + (47*x)*(-47) - 48*x**3*(-47)</replace>
Simplifying the partial expression: (-37*x)*(-48*x**3 + 47*x)
Expanding the part (-48*x**3 + 47*x) using the distributive property, and we got: (-37*x)*(47*x) + (-37*x)*(-48*x**3)
Replacing (-37*x)*(-48*x**3 + 47*x) with (-37*x)*(47*x) + (-37*x)*(-48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*x)*(47*x) + (-37*x)*(-48*x**3) + (47*x)*(-47) - 48*x**3*(-47)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**3)*-47 = 2256*x**3
  (-48*x**3)*(-37*x) = 1776*x**4
  (47*x)*-47 = -2209*x
  (47*x)*(-37*x) = -1739*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x</replace>
No more calculations needed.
<answer>1776*x**4 + 2256*x**3 - 1739*x**2 - 2209*x</answer>


Question:
Calculate the following: (12*y - 49)*(44*y**3 - 16*y**2 - 37*y + 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: 528*y**4 - 2348*y**3 + 340*y**2 + 1933*y - 490


Question:
Calculate the following: (40*x**3 - x**2)*(-22*x**3 - 2*x**2 + 61*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: -880*x**6 - 58*x**5 + 2442*x**4 - 61*x**3


Question:
Simplify this expression: (7*y**3 - 25)*(37*y**2 + 28*y + 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: 259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400

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: (7*y**3 - 25)*(37*y**2 + 28*y + 16)
Expanding the part (7*y**3 - 25) using the distributive property, and we got: (7*y**3)*(37*y**2 + 28*y + 16) - 25*(37*y**2 + 28*y + 16)
<replace-#Step 1>#Step 2:
Current expression: (7*y**3)*(37*y**2 + 28*y + 16) - 25*(37*y**2 + 28*y + 16)</replace>
Simplifying the partial expression: -25*(37*y**2 + 28*y + 16)
Expanding the part (37*y**2 + 28*y + 16) using the distributive property, and we got: (28*y)*(-25) + (37*y**2)*(-25) + 16*(-25)
Replacing -25*(37*y**2 + 28*y + 16) with (28*y)*(-25) + (37*y**2)*(-25) + 16*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*y)*(-25) + (37*y**2)*(-25) + (7*y**3)*(37*y**2 + 28*y + 16) - 400</replace>
Simplifying the partial expression: (7*y**3)*(37*y**2 + 28*y + 16)
Expanding the part (37*y**2 + 28*y + 16) using the distributive property, and we got: 16*(7*y**3) + (28*y)*(7*y**3) + (37*y**2)*(7*y**3)
Replacing (7*y**3)*(37*y**2 + 28*y + 16) with 16*(7*y**3) + (28*y)*(7*y**3) + (37*y**2)*(7*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 16*7*y**3 + (28*y)*(7*y**3) + (28*y)*(-25) + (37*y**2)*(7*y**3) + (37*y**2)*(-25) - 400</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*y)*-25 = -700*y
  (28*y)*(7*y**3) = 196*y**4
  (37*y**2)*-25 = -925*y**2
  (37*y**2)*(7*y**3) = 259*y**5
  16*7*y**3 = 112*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400</replace>
No more calculations needed.
<answer>259*y**5 + 196*y**4 + 112*y**3 - 925*y**2 - 700*y - 400</answer>


Question:
Calculate the following: 93 - 1302*y**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: 93 - 1302*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: 93 - 1302*y**3
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: 93 - 1302*y**3</replace>
No more calculations needed.
<answer>93 - 1302*y**3</answer>


Question:
Simplify this expression: (-48*z**2 - 46*z)*(38*z**3 + 34*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: -1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*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: (-48*z**2 - 46*z)*(38*z**3 + 34*z)
Expanding the part (-48*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(38*z**3 + 34*z) + (-48*z**2)*(38*z**3 + 34*z)
<replace-#Step 1>#Step 2:
Current expression: (-46*z)*(38*z**3 + 34*z) + (-48*z**2)*(38*z**3 + 34*z)</replace>
Simplifying the partial expression: (-48*z**2)*(38*z**3 + 34*z)
Expanding the part (38*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)
Replacing (-48*z**2)*(38*z**3 + 34*z) with (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-46*z)*(38*z**3 + 34*z) + (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)</replace>
Simplifying the partial expression: (-46*z)*(38*z**3 + 34*z)
Expanding the part (38*z**3 + 34*z) using the distributive property, and we got: (-46*z)*(34*z) + (-46*z)*(38*z**3)
Replacing (-46*z)*(38*z**3 + 34*z) with (-46*z)*(34*z) + (-46*z)*(38*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(34*z) + (-46*z)*(38*z**3) + (34*z)*(-48*z**2) + (-48*z**2)*(38*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*z)*(-48*z**2) = -1632*z**3
  (34*z)*(-46*z) = -1564*z**2
  (38*z**3)*(-48*z**2) = -1824*z**5
  (38*z**3)*(-46*z) = -1748*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2</replace>
No more calculations needed.
<answer>-1824*z**5 - 1748*z**4 - 1632*z**3 - 1564*z**2</answer>


Question:
Calculate the following: (-18*z - 11)*(-21*z**3 - 38*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: 378*z**4 + 231*z**3 + 684*z**2 + 418*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: (-18*z - 11)*(-21*z**3 - 38*z)
Expanding the part (-18*z - 11) using the distributive property, and we got: (-18*z)*(-21*z**3 - 38*z) - 11*(-21*z**3 - 38*z)
<replace-#Step 1>#Step 2:
Current expression: (-18*z)*(-21*z**3 - 38*z) - 11*(-21*z**3 - 38*z)</replace>
Simplifying the partial expression: -11*(-21*z**3 - 38*z)
Expanding the part (-21*z**3 - 38*z) using the distributive property, and we got: -38*z*(-11) - 21*z**3*(-11)
Replacing -11*(-21*z**3 - 38*z) with -38*z*(-11) - 21*z**3*(-11) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -38*z*(-11) + (-18*z)*(-21*z**3 - 38*z) - 21*z**3*(-11)</replace>
Simplifying the partial expression: (-18*z)*(-21*z**3 - 38*z)
Expanding the part (-21*z**3 - 38*z) using the distributive property, and we got: (-38*z)*(-18*z) + (-18*z)*(-21*z**3)
Replacing (-18*z)*(-21*z**3 - 38*z) with (-38*z)*(-18*z) + (-18*z)*(-21*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-38*z)*(-18*z) - 38*z*(-11) + (-18*z)*(-21*z**3) - 21*z**3*(-11)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*z)*-11 = 418*z
  (-38*z)*(-18*z) = 684*z**2
  (-21*z**3)*-11 = 231*z**3
  (-21*z**3)*(-18*z) = 378*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 378*z**4 + 231*z**3 + 684*z**2 + 418*z</replace>
No more calculations needed.
<answer>378*z**4 + 231*z**3 + 684*z**2 + 418*z</answer>


Question:
Calculate the following: (24*z - 27)*(27*z**3 + 10*z + 41)
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: 648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107

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: (24*z - 27)*(27*z**3 + 10*z + 41)
Expanding the part (24*z - 27) using the distributive property, and we got: (24*z)*(27*z**3 + 10*z + 41) - 27*(27*z**3 + 10*z + 41)
<replace-#Step 1>#Step 2:
Current expression: (24*z)*(27*z**3 + 10*z + 41) - 27*(27*z**3 + 10*z + 41)</replace>
Simplifying the partial expression: -27*(27*z**3 + 10*z + 41)
Expanding the part (27*z**3 + 10*z + 41) using the distributive property, and we got: (10*z)*(-27) + (27*z**3)*(-27) + 41*(-27)
Replacing -27*(27*z**3 + 10*z + 41) with (10*z)*(-27) + (27*z**3)*(-27) + 41*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*z)*(-27) + (24*z)*(27*z**3 + 10*z + 41) + (27*z**3)*(-27) - 1107</replace>
Simplifying the partial expression: (24*z)*(27*z**3 + 10*z + 41)
Expanding the part (27*z**3 + 10*z + 41) using the distributive property, and we got: 41*(24*z) + (10*z)*(24*z) + (24*z)*(27*z**3)
Replacing (24*z)*(27*z**3 + 10*z + 41) with 41*(24*z) + (10*z)*(24*z) + (24*z)*(27*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 41*24*z + (10*z)*(24*z) + (10*z)*(-27) + (24*z)*(27*z**3) + (27*z**3)*(-27) - 1107</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*z)*-27 = -270*z
  (10*z)*(24*z) = 240*z**2
  (27*z**3)*-27 = -729*z**3
  (27*z**3)*(24*z) = 648*z**4
  41*24*z = 984*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 648*z**4 - 729*z**3 + 240*z**2 - 270*z + 984*z - 1107</replace>
Combining like terms, got 648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107
<replace-#Step 5>#Step 6:
Current expression: 648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107</replace>
No more calculations needed.
<answer>648*z**4 - 729*z**3 + 240*z**2 + 714*z - 1107</answer>


Question:
Calculate the following: 1470*x**3 + 70*x**2 + 280*x + 315
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: 1470*x**3 + 70*x**2 + 280*x + 315

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: 1470*x**3 + 70*x**2 + 280*x + 315
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: 1470*x**3 + 70*x**2 + 280*x + 315</replace>
No more calculations needed.
<answer>1470*x**3 + 70*x**2 + 280*x + 315</answer>


Question:
Calculate the following: 18*x**3*(-48*x - 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: -864*x**4 - 288*x**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: 18*x**3*(-48*x - 16)
Expanding the part (-48*x - 16) using the distributive property, and we got: (-48*x)*(18*x**3) - 288*x**3
<replace-#Step 1>#Step 2:
Current expression: (-48*x)*(18*x**3) - 288*x**3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(18*x**3) = -288*x**3
  (-48*x)*(18*x**3) = -864*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -864*x**4 - 288*x**3</replace>
No more calculations needed.
<answer>-864*x**4 - 288*x**3</answer>


Question:
Calculate the following: (40 - 38*x**2)*(50*x**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: -1900*x**5 + 2000*x**3 - 1406*x**2 + 1480

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 - 38*x**2)*(50*x**3 + 37)
Expanding the part (50*x**3 + 37) using the distributive property, and we got: (50*x**3)*(40 - 38*x**2) + 37*(40 - 38*x**2)
<replace-#Step 1>#Step 2:
Current expression: (50*x**3)*(40 - 38*x**2) + 37*(40 - 38*x**2)</replace>
Simplifying the partial expression: 37*(40 - 38*x**2)
Expanding the part (40 - 38*x**2) using the distributive property, and we got: -38*x**2*37 + 40*37
Replacing 37*(40 - 38*x**2) with -38*x**2*37 + 40*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -38*x**2*37 + (50*x**3)*(40 - 38*x**2) + 1480</replace>
Simplifying the partial expression: (50*x**3)*(40 - 38*x**2)
Expanding the part (40 - 38*x**2) using the distributive property, and we got: 40*(50*x**3) + (-38*x**2)*(50*x**3)
Replacing (50*x**3)*(40 - 38*x**2) with 40*(50*x**3) + (-38*x**2)*(50*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 40*50*x**3 + (-38*x**2)*(50*x**3) - 38*x**2*37 + 1480</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**2)*37 = -1406*x**2
  (-38*x**2)*(50*x**3) = -1900*x**5
  40*50*x**3 = 2000*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1900*x**5 + 2000*x**3 - 1406*x**2 + 1480</replace>
No more calculations needed.
<answer>-1900*x**5 + 2000*x**3 - 1406*x**2 + 1480</answer>


Question:
Simplify this expression: (44*y**3 - 7*y)*(21*y**2 - 64*y - 42)
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: 924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*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: (44*y**3 - 7*y)*(21*y**2 - 64*y - 42)
Expanding the part (44*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(21*y**2 - 64*y - 42) + (44*y**3)*(21*y**2 - 64*y - 42)
<replace-#Step 1>#Step 2:
Current expression: (-7*y)*(21*y**2 - 64*y - 42) + (44*y**3)*(21*y**2 - 64*y - 42)</replace>
Simplifying the partial expression: (-7*y)*(21*y**2 - 64*y - 42)
Expanding the part (21*y**2 - 64*y - 42) using the distributive property, and we got: (-64*y)*(-7*y) + (-7*y)*(21*y**2) - (-1)*294*y
Replacing (-7*y)*(21*y**2 - 64*y - 42) with (-64*y)*(-7*y) + (-7*y)*(21*y**2) - (-1)*294*y in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-64*y)*(-7*y) + (-7*y)*(21*y**2) - 42*(-7)*y + (44*y**3)*(21*y**2 - 64*y - 42)</replace>
Simplifying the partial expression: (44*y**3)*(21*y**2 - 64*y - 42)
Expanding the part (21*y**2 - 64*y - 42) using the distributive property, and we got: (-64*y)*(44*y**3) - 1848*y**3 + (21*y**2)*(44*y**3)
Replacing (44*y**3)*(21*y**2 - 64*y - 42) with (-64*y)*(44*y**3) - 1848*y**3 + (21*y**2)*(44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-64*y)*(-7*y) + (-64*y)*(44*y**3) + (-7*y)*(21*y**2) - 42*44*y**3 - 42*(-7)*y + (21*y**2)*(44*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-64*y)*(-7*y) = 448*y**2
  (-64*y)*(44*y**3) = -2816*y**4
  (21*y**2)*(-7*y) = -147*y**3
  (21*y**2)*(44*y**3) = 924*y**5
  -42*-7*y = 294*y
  -42*44*y**3 = -1848*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 924*y**5 - 2816*y**4 - 1848*y**3 - 147*y**3 + 448*y**2 + 294*y</replace>
Combining like terms, got 924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y
<replace-#Step 5>#Step 6:
Current expression: 924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y</replace>
No more calculations needed.
<answer>924*y**5 - 2816*y**4 - 1995*y**3 + 448*y**2 + 294*y</answer>


Question:
Simplify this expression: 11*x**3*(x**3 + 42*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: 11*x**6 + 462*x**4

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*x**3*(x**3 + 42*x)
Expanding the part (x**3 + 42*x) using the distributive property, and we got: x**3*(11*x**3) + (42*x)*(11*x**3)
<replace-#Step 1>#Step 2:
Current expression: x**3*(11*x**3) + (42*x)*(11*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x**3*(11*x**3) = 11*x**6
  (42*x)*(11*x**3) = 462*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 11*x**6 + 462*x**4</replace>
No more calculations needed.
<answer>11*x**6 + 462*x**4</answer>


Question:
Calculate the following: (-50*z**3 - 62*z)*(-10*z**3 - 6*z**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: 500*z**6 + 300*z**5 + 620*z**4 + 672*z**3 + 372*z


Question:
Calculate the following: (49*y**2 + 32*y)*(51*y**3 - 26*y**2 + 33*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: 2499*y**5 + 358*y**4 + 785*y**3 + 1056*y**2


Question:
Calculate the following: (13*y**2 + 37*y)*(-37*y**3 - 35*y**2 - 9*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: -481*y**5 - 1824*y**4 - 1412*y**3 - 333*y**2


Question:
Simplify this expression: 280*z**3 + 644*z**2 - 350
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: 280*z**3 + 644*z**2 - 350

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: 280*z**3 + 644*z**2 - 350
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: 280*z**3 + 644*z**2 - 350</replace>
No more calculations needed.
<answer>280*z**3 + 644*z**2 - 350</answer>


Question:
Calculate the following: (-17*x - 50)*(33*x**3 - 26)
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: -561*x**4 - 1650*x**3 + 442*x + 1300

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*x - 50)*(33*x**3 - 26)
Expanding the part (-17*x - 50) using the distributive property, and we got: (-17*x)*(33*x**3 - 26) - 50*(33*x**3 - 26)
<replace-#Step 1>#Step 2:
Current expression: (-17*x)*(33*x**3 - 26) - 50*(33*x**3 - 26)</replace>
Simplifying the partial expression: -50*(33*x**3 - 26)
Expanding the part (33*x**3 - 26) using the distributive property, and we got: (33*x**3)*(-50) - 26*(-50)
Replacing -50*(33*x**3 - 26) with (33*x**3)*(-50) - 26*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-17*x)*(33*x**3 - 26) + (33*x**3)*(-50) + 1300</replace>
Simplifying the partial expression: (-17*x)*(33*x**3 - 26)
Expanding the part (33*x**3 - 26) using the distributive property, and we got: (-17*x)*(33*x**3) - (-1)*442*x
Replacing (-17*x)*(33*x**3 - 26) with (-17*x)*(33*x**3) - (-1)*442*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-17*x)*(33*x**3) - 26*(-17)*x + (33*x**3)*(-50) + 1300</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*x**3)*-50 = -1650*x**3
  (33*x**3)*(-17*x) = -561*x**4
  -26*-17*x = 442*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -561*x**4 - 1650*x**3 + 442*x + 1300</replace>
No more calculations needed.
<answer>-561*x**4 - 1650*x**3 + 442*x + 1300</answer>


Question:
Calculate the following: (3*x**3 + 18*x**2 - 22)*(17*x**3 + 23*x + 50)
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: 51*x**6 + 306*x**5 + 69*x**4 + 190*x**3 + 900*x**2 - 506*x - 1100


Question:
Calculate the following: (6 - 2*x)*(16*x**3 + 37*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: -32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186

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 - 2*x)*(16*x**3 + 37*x**2 - 31)
Expanding the part (6 - 2*x) using the distributive property, and we got: (-2*x)*(16*x**3 + 37*x**2 - 31) + 6*(16*x**3 + 37*x**2 - 31)
<replace-#Step 1>#Step 2:
Current expression: (-2*x)*(16*x**3 + 37*x**2 - 31) + 6*(16*x**3 + 37*x**2 - 31)</replace>
Simplifying the partial expression: 6*(16*x**3 + 37*x**2 - 31)
Expanding the part (16*x**3 + 37*x**2 - 31) using the distributive property, and we got: (37*x**2)*6 + (16*x**3)*6 - 31*6
Replacing 6*(16*x**3 + 37*x**2 - 31) with (37*x**2)*6 + (16*x**3)*6 - 31*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*x)*(16*x**3 + 37*x**2 - 31) + (37*x**2)*6 + (16*x**3)*6 - 186</replace>
Simplifying the partial expression: (-2*x)*(16*x**3 + 37*x**2 - 31)
Expanding the part (16*x**3 + 37*x**2 - 31) using the distributive property, and we got: (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - (-1)*62*x
Replacing (-2*x)*(16*x**3 + 37*x**2 - 31) with (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - (-1)*62*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*x)*(37*x**2) + (-2*x)*(16*x**3) - 31*(-2)*x + (37*x**2)*6 + (16*x**3)*6 - 186</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*x**3)*6 = 96*x**3
  (16*x**3)*(-2*x) = -32*x**4
  (37*x**2)*6 = 222*x**2
  (37*x**2)*(-2*x) = -74*x**3
  -31*-2*x = 62*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -32*x**4 - 74*x**3 + 96*x**3 + 222*x**2 + 62*x - 186</replace>
Combining like terms, got -32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186
<replace-#Step 5>#Step 6:
Current expression: -32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186</replace>
No more calculations needed.
<answer>-32*x**4 + 22*x**3 + 222*x**2 + 62*x - 186</answer>


Question:
Calculate the following: 1584*z**3 - 2904*z**2 + 1100
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: 1584*z**3 - 2904*z**2 + 1100

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: 1584*z**3 - 2904*z**2 + 1100
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: 1584*z**3 - 2904*z**2 + 1100</replace>
No more calculations needed.
<answer>1584*z**3 - 2904*z**2 + 1100</answer>