Question:
Simplify this expression: (43*x - 30)*(46*x**3 - 9*x**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: 1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740

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 - 30)*(46*x**3 - 9*x**2 - 58)
Expanding the part (43*x - 30) using the distributive property, and we got: (43*x)*(46*x**3 - 9*x**2 - 58) - 30*(46*x**3 - 9*x**2 - 58)
<replace-#Step 1>#Step 2:
Current expression: (43*x)*(46*x**3 - 9*x**2 - 58) - 30*(46*x**3 - 9*x**2 - 58)</replace>
Simplifying the partial expression: -30*(46*x**3 - 9*x**2 - 58)
Expanding the part (46*x**3 - 9*x**2 - 58) using the distributive property, and we got: -9*x**2*(-30) + (46*x**3)*(-30) - 58*(-30)
Replacing -30*(46*x**3 - 9*x**2 - 58) with -9*x**2*(-30) + (46*x**3)*(-30) - 58*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(46*x**3 - 9*x**2 - 58) - 9*x**2*(-30) + (46*x**3)*(-30) + 1740</replace>
Simplifying the partial expression: (43*x)*(46*x**3 - 9*x**2 - 58)
Expanding the part (46*x**3 - 9*x**2 - 58) using the distributive property, and we got: -2494*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3)
Replacing (43*x)*(46*x**3 - 9*x**2 - 58) with -2494*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -58*43*x + (43*x)*(-9*x**2) + (43*x)*(46*x**3) - 9*x**2*(-30) + (46*x**3)*(-30) + 1740</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*x**2)*-30 = 270*x**2
  (-9*x**2)*(43*x) = -387*x**3
  (46*x**3)*-30 = -1380*x**3
  (46*x**3)*(43*x) = 1978*x**4
  -58*43*x = -2494*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1978*x**4 - 1380*x**3 - 387*x**3 + 270*x**2 - 2494*x + 1740</replace>
Combining like terms, got 1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740
<replace-#Step 5>#Step 6:
Current expression: 1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740</replace>
No more calculations needed.
<answer>1978*x**4 - 1767*x**3 + 270*x**2 - 2494*x + 1740</answer>


Question:
Simplify this expression: (3*z + 45)*(-42*z**3 + 33*z - 46)
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 - 1890*z**3 + 99*z**2 + 1347*z - 2070

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 + 45)*(-42*z**3 + 33*z - 46)
Expanding the part (3*z + 45) using the distributive property, and we got: (3*z)*(-42*z**3 + 33*z - 46) + 45*(-42*z**3 + 33*z - 46)
<replace-#Step 1>#Step 2:
Current expression: (3*z)*(-42*z**3 + 33*z - 46) + 45*(-42*z**3 + 33*z - 46)</replace>
Simplifying the partial expression: 45*(-42*z**3 + 33*z - 46)
Expanding the part (-42*z**3 + 33*z - 46) using the distributive property, and we got: (33*z)*45 - 42*z**3*45 - 46*45
Replacing 45*(-42*z**3 + 33*z - 46) with (33*z)*45 - 42*z**3*45 - 46*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*(-42*z**3 + 33*z - 46) + (33*z)*45 - 42*z**3*45 - 2070</replace>
Simplifying the partial expression: (3*z)*(-42*z**3 + 33*z - 46)
Expanding the part (-42*z**3 + 33*z - 46) using the distributive property, and we got: -138*z + (3*z)*(33*z) + (3*z)*(-42*z**3)
Replacing (3*z)*(-42*z**3 + 33*z - 46) with -138*z + (3*z)*(33*z) + (3*z)*(-42*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -46*3*z + (3*z)*(33*z) + (3*z)*(-42*z**3) + (33*z)*45 - 42*z**3*45 - 2070</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z**3)*45 = -1890*z**3
  (-42*z**3)*(3*z) = -126*z**4
  (33*z)*45 = 1485*z
  (33*z)*(3*z) = 99*z**2
  -46*3*z = -138*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -126*z**4 - 1890*z**3 + 99*z**2 - 138*z + 1485*z - 2070</replace>
Combining like terms, got -126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070
<replace-#Step 5>#Step 6:
Current expression: -126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070</replace>
No more calculations needed.
<answer>-126*z**4 - 1890*z**3 + 99*z**2 + 1347*z - 2070</answer>


Question:
Calculate the following: (38*z**2 + 16*z)*(-8*z**3 - 5*z**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: -304*z**5 - 318*z**4 - 80*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: (38*z**2 + 16*z)*(-8*z**3 - 5*z**2)
Expanding the part (-8*z**3 - 5*z**2) using the distributive property, and we got: (-5*z**2)*(38*z**2 + 16*z) + (-8*z**3)*(38*z**2 + 16*z)
<replace-#Step 1>#Step 2:
Current expression: (-5*z**2)*(38*z**2 + 16*z) + (-8*z**3)*(38*z**2 + 16*z)</replace>
Simplifying the partial expression: (-8*z**3)*(38*z**2 + 16*z)
Expanding the part (38*z**2 + 16*z) using the distributive property, and we got: (16*z)*(-8*z**3) + (38*z**2)*(-8*z**3)
Replacing (-8*z**3)*(38*z**2 + 16*z) with (16*z)*(-8*z**3) + (38*z**2)*(-8*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*z)*(-8*z**3) + (-5*z**2)*(38*z**2 + 16*z) + (38*z**2)*(-8*z**3)</replace>
Simplifying the partial expression: (-5*z**2)*(38*z**2 + 16*z)
Expanding the part (38*z**2 + 16*z) using the distributive property, and we got: (16*z)*(-5*z**2) + (-5*z**2)*(38*z**2)
Replacing (-5*z**2)*(38*z**2 + 16*z) with (16*z)*(-5*z**2) + (-5*z**2)*(38*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*z)*(-5*z**2) + (16*z)*(-8*z**3) + (-5*z**2)*(38*z**2) + (38*z**2)*(-8*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*z)*(-8*z**3) = -128*z**4
  (16*z)*(-5*z**2) = -80*z**3
  (38*z**2)*(-8*z**3) = -304*z**5
  (38*z**2)*(-5*z**2) = -190*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -304*z**5 - 190*z**4 - 128*z**4 - 80*z**3</replace>
Combining like terms, got -304*z**5 - 318*z**4 - 80*z**3
<replace-#Step 5>#Step 6:
Current expression: -304*z**5 - 318*z**4 - 80*z**3</replace>
No more calculations needed.
<answer>-304*z**5 - 318*z**4 - 80*z**3</answer>


Question:
Calculate the following: (-32*x**3 + 38*x)*(-11*x**3 - x**2 - 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: 352*x**6 + 32*x**5 - 418*x**4 + 1274*x**3 - 1558*x


Question:
Simplify this expression: (-50*z**2 - 49*z)*(-13*z**2 + 26*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: 650*z**4 - 663*z**3 - 1274*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: (-50*z**2 - 49*z)*(-13*z**2 + 26*z)
Expanding the part (-50*z**2 - 49*z) using the distributive property, and we got: (-49*z)*(-13*z**2 + 26*z) + (-50*z**2)*(-13*z**2 + 26*z)
<replace-#Step 1>#Step 2:
Current expression: (-49*z)*(-13*z**2 + 26*z) + (-50*z**2)*(-13*z**2 + 26*z)</replace>
Simplifying the partial expression: (-50*z**2)*(-13*z**2 + 26*z)
Expanding the part (-13*z**2 + 26*z) using the distributive property, and we got: (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)
Replacing (-50*z**2)*(-13*z**2 + 26*z) with (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*z)*(-13*z**2 + 26*z) + (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)</replace>
Simplifying the partial expression: (-49*z)*(-13*z**2 + 26*z)
Expanding the part (-13*z**2 + 26*z) using the distributive property, and we got: (-49*z)*(26*z) + (-49*z)*(-13*z**2)
Replacing (-49*z)*(-13*z**2 + 26*z) with (-49*z)*(26*z) + (-49*z)*(-13*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*z)*(26*z) + (-49*z)*(-13*z**2) + (26*z)*(-50*z**2) + (-50*z**2)*(-13*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z**2)*(-50*z**2) = 650*z**4
  (-13*z**2)*(-49*z) = 637*z**3
  (26*z)*(-50*z**2) = -1300*z**3
  (26*z)*(-49*z) = -1274*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 650*z**4 - 1300*z**3 + 637*z**3 - 1274*z**2</replace>
Combining like terms, got 650*z**4 - 663*z**3 - 1274*z**2
<replace-#Step 5>#Step 6:
Current expression: 650*z**4 - 663*z**3 - 1274*z**2</replace>
No more calculations needed.
<answer>650*z**4 - 663*z**3 - 1274*z**2</answer>


Question:
Calculate the following: (26 - 25*z**2)*(43*z**2 - 42*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: -1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*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: (26 - 25*z**2)*(43*z**2 - 42*z)
Expanding the part (26 - 25*z**2) using the distributive property, and we got: (-25*z**2)*(43*z**2 - 42*z) + 26*(43*z**2 - 42*z)
<replace-#Step 1>#Step 2:
Current expression: (-25*z**2)*(43*z**2 - 42*z) + 26*(43*z**2 - 42*z)</replace>
Simplifying the partial expression: 26*(43*z**2 - 42*z)
Expanding the part (43*z**2 - 42*z) using the distributive property, and we got: -42*z*26 + (43*z**2)*26
Replacing 26*(43*z**2 - 42*z) with -42*z*26 + (43*z**2)*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*z*26 + (-25*z**2)*(43*z**2 - 42*z) + (43*z**2)*26</replace>
Simplifying the partial expression: (-25*z**2)*(43*z**2 - 42*z)
Expanding the part (43*z**2 - 42*z) using the distributive property, and we got: (-42*z)*(-25*z**2) + (-25*z**2)*(43*z**2)
Replacing (-25*z**2)*(43*z**2 - 42*z) with (-42*z)*(-25*z**2) + (-25*z**2)*(43*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*z)*(-25*z**2) - 42*z*26 + (-25*z**2)*(43*z**2) + (43*z**2)*26</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*z)*26 = -1092*z
  (-42*z)*(-25*z**2) = 1050*z**3
  (43*z**2)*26 = 1118*z**2
  (43*z**2)*(-25*z**2) = -1075*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z</replace>
No more calculations needed.
<answer>-1075*z**4 + 1050*z**3 + 1118*z**2 - 1092*z</answer>


Question:
Calculate the following: 83*z**3*(83*z**3 - 49*z**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: 6889*z**6 - 4067*z**5

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: 83*z**3*(83*z**3 - 49*z**2)
Expanding the part (83*z**3 - 49*z**2) using the distributive property, and we got: (-49*z**2)*(83*z**3) + (83*z**3)*(83*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-49*z**2)*(83*z**3) + (83*z**3)*(83*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*z**2)*(83*z**3) = -4067*z**5
  (83*z**3)*(83*z**3) = 6889*z**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 6889*z**6 - 4067*z**5</replace>
No more calculations needed.
<answer>6889*z**6 - 4067*z**5</answer>


Question:
Simplify this expression: (-26*x**3 - 38*x)*(-41*x**3 + 20*x**2 + 32*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: 1066*x**6 - 520*x**5 + 726*x**4 - 760*x**3 - 1216*x**2


Question:
Simplify this expression: 3640*x**3 - 2632*x**2 + 1512*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: 3640*x**3 - 2632*x**2 + 1512*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: 3640*x**3 - 2632*x**2 + 1512*x
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: 3640*x**3 - 2632*x**2 + 1512*x</replace>
No more calculations needed.
<answer>3640*x**3 - 2632*x**2 + 1512*x</answer>


Question:
Calculate the following: (-34*z**3 - 23*z**2)*(13*z**3 + 8*z**2 - 17*z - 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: -442*z**6 - 571*z**5 + 394*z**4 + 595*z**3 + 138*z**2


Question:
Calculate the following: (-23*x**2 - 11*x - 3)*(21*x**3 + 8*x**2 + 49*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: -483*x**5 - 415*x**4 - 1278*x**3 - 563*x**2 - 147*x


Question:
Simplify this expression: 17*y**3*(16*y**3 + 32*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 272*y**6 + 544*y**5

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*y**3*(16*y**3 + 32*y**2)
Expanding the part (16*y**3 + 32*y**2) using the distributive property, and we got: (32*y**2)*(17*y**3) + (16*y**3)*(17*y**3)
<replace-#Step 1>#Step 2:
Current expression: (32*y**2)*(17*y**3) + (16*y**3)*(17*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*y**3)*(17*y**3) = 272*y**6
  (32*y**2)*(17*y**3) = 544*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 272*y**6 + 544*y**5</replace>
No more calculations needed.
<answer>272*y**6 + 544*y**5</answer>


Question:
Simplify this expression: (33*x**3 - 47*x**2)*(15*x**3 - x - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*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: (33*x**3 - 47*x**2)*(15*x**3 - x - 40)
Expanding the part (33*x**3 - 47*x**2) using the distributive property, and we got: (-47*x**2)*(15*x**3 - x - 40) + (33*x**3)*(15*x**3 - x - 40)
<replace-#Step 1>#Step 2:
Current expression: (-47*x**2)*(15*x**3 - x - 40) + (33*x**3)*(15*x**3 - x - 40)</replace>
Simplifying the partial expression: (-47*x**2)*(15*x**3 - x - 40)
Expanding the part (15*x**3 - x - 40) using the distributive property, and we got: (-x)*(-47*x**2) - (-1)*1880*x**2 + (-47*x**2)*(15*x**3)
Replacing (-47*x**2)*(15*x**3 - x - 40) with (-x)*(-47*x**2) - (-1)*1880*x**2 + (-47*x**2)*(15*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-x)*(-47*x**2) - 40*(-47)*x**2 + (-47*x**2)*(15*x**3) + (33*x**3)*(15*x**3 - x - 40)</replace>
Simplifying the partial expression: (33*x**3)*(15*x**3 - x - 40)
Expanding the part (15*x**3 - x - 40) using the distributive property, and we got: (-x)*(33*x**3) - 1320*x**3 + (15*x**3)*(33*x**3)
Replacing (33*x**3)*(15*x**3 - x - 40) with (-x)*(33*x**3) - 1320*x**3 + (15*x**3)*(33*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(-47*x**2) + (-x)*(33*x**3) - 40*33*x**3 - 40*(-47)*x**2 + (-47*x**2)*(15*x**3) + (15*x**3)*(33*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x)*(-47*x**2) = 47*x**3
  (-x)*(33*x**3) = -33*x**4
  (15*x**3)*(-47*x**2) = -705*x**5
  (15*x**3)*(33*x**3) = 495*x**6
  -40*-47*x**2 = 1880*x**2
  -40*33*x**3 = -1320*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 495*x**6 - 705*x**5 - 33*x**4 - 1320*x**3 + 47*x**3 + 1880*x**2</replace>
Combining like terms, got 495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2
<replace-#Step 5>#Step 6:
Current expression: 495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2</replace>
No more calculations needed.
<answer>495*x**6 - 705*x**5 - 33*x**4 - 1273*x**3 + 1880*x**2</answer>


Question:
Simplify this expression: (21 - 65*y**2)*(45 - 5*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 325*y**3 - 2925*y**2 - 105*y + 945

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21 - 65*y**2)*(45 - 5*y)
Expanding the part (21 - 65*y**2) using the distributive property, and we got: (-65*y**2)*(45 - 5*y) + 21*(45 - 5*y)
<replace-#Step 1>#Step 2:
Current expression: (-65*y**2)*(45 - 5*y) + 21*(45 - 5*y)</replace>
Simplifying the partial expression: 21*(45 - 5*y)
Expanding the part (45 - 5*y) using the distributive property, and we got: -5*y*21 + 45*21
Replacing 21*(45 - 5*y) with -5*y*21 + 45*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -5*y*21 + (-65*y**2)*(45 - 5*y) + 945</replace>
Simplifying the partial expression: (-65*y**2)*(45 - 5*y)
Expanding the part (45 - 5*y) using the distributive property, and we got: (-5*y)*(-65*y**2) + 45*(-65*y**2)
Replacing (-65*y**2)*(45 - 5*y) with (-5*y)*(-65*y**2) + 45*(-65*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*y)*(-65*y**2) - 5*y*21 + 45*(-65)*y**2 + 945</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-5*y)*21 = -105*y
  (-5*y)*(-65*y**2) = 325*y**3
  45*-65*y**2 = -2925*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 325*y**3 - 2925*y**2 - 105*y + 945</replace>
No more calculations needed.
<answer>325*y**3 - 2925*y**2 - 105*y + 945</answer>


Question:
Calculate the following: -1856*y**3 - 192*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: -1856*y**3 - 192*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: -1856*y**3 - 192*y
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: -1856*y**3 - 192*y</replace>
No more calculations needed.
<answer>-1856*y**3 - 192*y</answer>


Question:
Simplify this expression: (33*x**3 - 35*x**2)*(-39*x**3 - 18*x**2 + 28*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: -1287*x**6 + 771*x**5 + 1554*x**4 - 980*x**3


Question:
Calculate the following: (31*x**2 - 105*x)*(23*x**2 - 47*x + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 713*x**4 - 3872*x**3 + 5679*x**2 - 2520*x


Question:
Calculate the following: (-21*z**3 - 46*z)*(-17*z**3 + 8*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: 357*z**6 - 168*z**5 + 1643*z**4 - 368*z**3 + 1886*z**2


Question:
Simplify this expression: (-11*y**3 - 41*y - 47)*(64*y**3 - 7*y**2 + 29)
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: -704*y**6 + 77*y**5 - 2624*y**4 - 3040*y**3 + 329*y**2 - 1189*y - 1363


Question:
Calculate the following: (18*x**2 + 1)*(-30*x**3 - 3*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: -540*x**5 - 54*x**4 - 30*x**3 - 3*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: (18*x**2 + 1)*(-30*x**3 - 3*x**2)
Expanding the part (18*x**2 + 1) using the distributive property, and we got: (18*x**2)*(-30*x**3 - 3*x**2) + 1*(-30*x**3 - 3*x**2)
<replace-#Step 1>#Step 2:
Current expression: (18*x**2)*(-30*x**3 - 3*x**2) + 1*(-30*x**3 - 3*x**2)</replace>
Simplifying the partial expression: 1*(-30*x**3 - 3*x**2)
Expanding the part (-30*x**3 - 3*x**2) using the distributive property, and we got: -3*x**2*1 - 30*x**3*1
Replacing 1*(-30*x**3 - 3*x**2) with -3*x**2*1 - 30*x**3*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3*x**2*1 + (18*x**2)*(-30*x**3 - 3*x**2) - 30*x**3*1</replace>
Simplifying the partial expression: (18*x**2)*(-30*x**3 - 3*x**2)
Expanding the part (-30*x**3 - 3*x**2) using the distributive property, and we got: (-3*x**2)*(18*x**2) + (18*x**2)*(-30*x**3)
Replacing (18*x**2)*(-30*x**3 - 3*x**2) with (-3*x**2)*(18*x**2) + (18*x**2)*(-30*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*x**2)*(18*x**2) - 3*x**2*1 + (18*x**2)*(-30*x**3) - 30*x**3*1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*x**3)*1 = -30*x**3
  (-30*x**3)*(18*x**2) = -540*x**5
  (-3*x**2)*1 = -3*x**2
  (-3*x**2)*(18*x**2) = -54*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -540*x**5 - 54*x**4 - 30*x**3 - 3*x**2</replace>
No more calculations needed.
<answer>-540*x**5 - 54*x**4 - 30*x**3 - 3*x**2</answer>


Question:
Simplify this expression: (-40*y**2 + 42*y - 33)*(-7*y**3 - 39*y**2 - 34*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: 280*y**5 + 1266*y**4 - 47*y**3 - 141*y**2 + 1122*y


Question:
Calculate the following: 861*x**3 + 651*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: 861*x**3 + 651*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: 861*x**3 + 651*x
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: 861*x**3 + 651*x</replace>
No more calculations needed.
<answer>861*x**3 + 651*x</answer>


Question:
Calculate the following: 1755*x**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: 1755*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: 1755*x**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: 1755*x**4</replace>
No more calculations needed.
<answer>1755*x**4</answer>


Question:
Calculate the following: -59*x**3*(-19*x**3 - 32*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: 1121*x**6 + 1888*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: -59*x**3*(-19*x**3 - 32*x)
Expanding the part (-19*x**3 - 32*x) using the distributive property, and we got: (-32*x)*(-59*x**3) + (-59*x**3)*(-19*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-32*x)*(-59*x**3) + (-59*x**3)*(-19*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*x)*(-59*x**3) = 1888*x**4
  (-19*x**3)*(-59*x**3) = 1121*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1121*x**6 + 1888*x**4</replace>
No more calculations needed.
<answer>1121*x**6 + 1888*x**4</answer>


Question:
Simplify this expression: (-7*z**2 - 49*z)*(34*z**2 + 11)
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: -238*z**4 - 1666*z**3 - 77*z**2 - 539*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: (-7*z**2 - 49*z)*(34*z**2 + 11)
Expanding the part (34*z**2 + 11) using the distributive property, and we got: (34*z**2)*(-7*z**2 - 49*z) + 11*(-7*z**2 - 49*z)
<replace-#Step 1>#Step 2:
Current expression: (34*z**2)*(-7*z**2 - 49*z) + 11*(-7*z**2 - 49*z)</replace>
Simplifying the partial expression: 11*(-7*z**2 - 49*z)
Expanding the part (-7*z**2 - 49*z) using the distributive property, and we got: -49*z*11 - 7*z**2*11
Replacing 11*(-7*z**2 - 49*z) with -49*z*11 - 7*z**2*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*z*11 - 7*z**2*11 + (34*z**2)*(-7*z**2 - 49*z)</replace>
Simplifying the partial expression: (34*z**2)*(-7*z**2 - 49*z)
Expanding the part (-7*z**2 - 49*z) using the distributive property, and we got: (-49*z)*(34*z**2) + (-7*z**2)*(34*z**2)
Replacing (34*z**2)*(-7*z**2 - 49*z) with (-49*z)*(34*z**2) + (-7*z**2)*(34*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*z)*(34*z**2) - 49*z*11 + (-7*z**2)*(34*z**2) - 7*z**2*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*z)*11 = -539*z
  (-49*z)*(34*z**2) = -1666*z**3
  (-7*z**2)*11 = -77*z**2
  (-7*z**2)*(34*z**2) = -238*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -238*z**4 - 1666*z**3 - 77*z**2 - 539*z</replace>
No more calculations needed.
<answer>-238*z**4 - 1666*z**3 - 77*z**2 - 539*z</answer>


Question:
Simplify this expression: (11 - 9*z)*(26*z**3 + 29*z**2 - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297

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 - 9*z)*(26*z**3 + 29*z**2 - 27)
Expanding the part (11 - 9*z) using the distributive property, and we got: (-9*z)*(26*z**3 + 29*z**2 - 27) + 11*(26*z**3 + 29*z**2 - 27)
<replace-#Step 1>#Step 2:
Current expression: (-9*z)*(26*z**3 + 29*z**2 - 27) + 11*(26*z**3 + 29*z**2 - 27)</replace>
Simplifying the partial expression: 11*(26*z**3 + 29*z**2 - 27)
Expanding the part (26*z**3 + 29*z**2 - 27) using the distributive property, and we got: (29*z**2)*11 + (26*z**3)*11 - 27*11
Replacing 11*(26*z**3 + 29*z**2 - 27) with (29*z**2)*11 + (26*z**3)*11 - 27*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*z)*(26*z**3 + 29*z**2 - 27) + (29*z**2)*11 + (26*z**3)*11 - 297</replace>
Simplifying the partial expression: (-9*z)*(26*z**3 + 29*z**2 - 27)
Expanding the part (26*z**3 + 29*z**2 - 27) using the distributive property, and we got: (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - (-1)*243*z
Replacing (-9*z)*(26*z**3 + 29*z**2 - 27) with (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - (-1)*243*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*z)*(29*z**2) + (-9*z)*(26*z**3) - 27*(-9)*z + (29*z**2)*11 + (26*z**3)*11 - 297</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*z**3)*11 = 286*z**3
  (26*z**3)*(-9*z) = -234*z**4
  (29*z**2)*11 = 319*z**2
  (29*z**2)*(-9*z) = -261*z**3
  -27*-9*z = 243*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -234*z**4 - 261*z**3 + 286*z**3 + 319*z**2 + 243*z - 297</replace>
Combining like terms, got -234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297
<replace-#Step 5>#Step 6:
Current expression: -234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297</replace>
No more calculations needed.
<answer>-234*z**4 + 25*z**3 + 319*z**2 + 243*z - 297</answer>


Question:
Calculate the following: 49*x**3*(55*x**3 - 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: 2695*x**6 - 2107*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: 49*x**3*(55*x**3 - 43)
Expanding the part (55*x**3 - 43) using the distributive property, and we got: -2107*x**3 + (49*x**3)*(55*x**3)
<replace-#Step 1>#Step 2:
Current expression: -2107*x**3 + (49*x**3)*(55*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -43*(49*x**3) = -2107*x**3
  (55*x**3)*(49*x**3) = 2695*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2695*x**6 - 2107*x**3</replace>
No more calculations needed.
<answer>2695*x**6 - 2107*x**3</answer>


Question:
Simplify this expression: (11*z - 12)*(-10*z**3 - 30*z**2 - 11*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: -110*z**4 - 210*z**3 + 239*z**2 + 132*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: (11*z - 12)*(-10*z**3 - 30*z**2 - 11*z)
Expanding the part (11*z - 12) using the distributive property, and we got: (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 12*(-10*z**3 - 30*z**2 - 11*z)
<replace-#Step 1>#Step 2:
Current expression: (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 12*(-10*z**3 - 30*z**2 - 11*z)</replace>
Simplifying the partial expression: -12*(-10*z**3 - 30*z**2 - 11*z)
Expanding the part (-10*z**3 - 30*z**2 - 11*z) using the distributive property, and we got: -11*z*(-12) - 30*z**2*(-12) - 10*z**3*(-12)
Replacing -12*(-10*z**3 - 30*z**2 - 11*z) with -11*z*(-12) - 30*z**2*(-12) - 10*z**3*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*z*(-12) + (11*z)*(-10*z**3 - 30*z**2 - 11*z) - 30*z**2*(-12) - 10*z**3*(-12)</replace>
Simplifying the partial expression: (11*z)*(-10*z**3 - 30*z**2 - 11*z)
Expanding the part (-10*z**3 - 30*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(11*z) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3)
Replacing (11*z)*(-10*z**3 - 30*z**2 - 11*z) with (-11*z)*(11*z) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(11*z) - 11*z*(-12) + (11*z)*(-30*z**2) + (11*z)*(-10*z**3) - 30*z**2*(-12) - 10*z**3*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z**2)*-12 = 360*z**2
  (-30*z**2)*(11*z) = -330*z**3
  (-11*z)*-12 = 132*z
  (-11*z)*(11*z) = -121*z**2
  (-10*z**3)*-12 = 120*z**3
  (-10*z**3)*(11*z) = -110*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -110*z**4 - 330*z**3 + 120*z**3 - 121*z**2 + 360*z**2 + 132*z</replace>
Combining like terms, got -110*z**4 - 210*z**3 + 239*z**2 + 132*z
<replace-#Step 5>#Step 6:
Current expression: -110*z**4 - 210*z**3 + 239*z**2 + 132*z</replace>
No more calculations needed.
<answer>-110*z**4 - 210*z**3 + 239*z**2 + 132*z</answer>


Question:
Calculate the following: 0
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: 0

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: 0
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: 0</replace>
No more calculations needed.
<answer>0</answer>


Question:
Calculate the following: (-40*z**2 + 9*z - 74)*(-5*z**3 - 48*z**2 - 92)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 200*z**5 + 1875*z**4 - 62*z**3 + 7232*z**2 - 828*z + 6808


Question:
Calculate the following: (23*x**2 + 21*x + 39)*(33*x**2 + 50*x + 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: 759*x**4 + 1843*x**3 + 2682*x**2 + 2265*x + 585


Question:
Simplify this expression: -29*y**2*(31*y**3 + 50*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -899*y**5 - 1450*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: -29*y**2*(31*y**3 + 50*y**2)
Expanding the part (31*y**3 + 50*y**2) using the distributive property, and we got: (-29*y**2)*(50*y**2) + (-29*y**2)*(31*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-29*y**2)*(50*y**2) + (-29*y**2)*(31*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*y**3)*(-29*y**2) = -899*y**5
  (50*y**2)*(-29*y**2) = -1450*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -899*y**5 - 1450*y**4</replace>
No more calculations needed.
<answer>-899*y**5 - 1450*y**4</answer>


Question:
Simplify this expression: (-13*y**2 - 26*y)*(-8*y**3 - 71)
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: 104*y**5 + 208*y**4 + 923*y**2 + 1846*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: (-13*y**2 - 26*y)*(-8*y**3 - 71)
Expanding the part (-8*y**3 - 71) using the distributive property, and we got: (-8*y**3)*(-13*y**2 - 26*y) - 71*(-13*y**2 - 26*y)
<replace-#Step 1>#Step 2:
Current expression: (-8*y**3)*(-13*y**2 - 26*y) - 71*(-13*y**2 - 26*y)</replace>
Simplifying the partial expression: -71*(-13*y**2 - 26*y)
Expanding the part (-13*y**2 - 26*y) using the distributive property, and we got: -26*y*(-71) - 13*y**2*(-71)
Replacing -71*(-13*y**2 - 26*y) with -26*y*(-71) - 13*y**2*(-71) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -26*y*(-71) - 13*y**2*(-71) + (-8*y**3)*(-13*y**2 - 26*y)</replace>
Simplifying the partial expression: (-8*y**3)*(-13*y**2 - 26*y)
Expanding the part (-13*y**2 - 26*y) using the distributive property, and we got: (-26*y)*(-8*y**3) + (-13*y**2)*(-8*y**3)
Replacing (-8*y**3)*(-13*y**2 - 26*y) with (-26*y)*(-8*y**3) + (-13*y**2)*(-8*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*y)*(-8*y**3) - 26*y*(-71) + (-13*y**2)*(-8*y**3) - 13*y**2*(-71)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-26*y)*-71 = 1846*y
  (-26*y)*(-8*y**3) = 208*y**4
  (-13*y**2)*-71 = 923*y**2
  (-13*y**2)*(-8*y**3) = 104*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 104*y**5 + 208*y**4 + 923*y**2 + 1846*y</replace>
No more calculations needed.
<answer>104*y**5 + 208*y**4 + 923*y**2 + 1846*y</answer>


Question:
Simplify this expression: 49*x**2*(-19*x**2 - 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: -931*x**4 - 2107*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 49*x**2*(-19*x**2 - 43)
Expanding the part (-19*x**2 - 43) using the distributive property, and we got: -2107*x**2 + (-19*x**2)*(49*x**2)
<replace-#Step 1>#Step 2:
Current expression: -2107*x**2 + (-19*x**2)*(49*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -43*(49*x**2) = -2107*x**2
  (-19*x**2)*(49*x**2) = -931*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -931*x**4 - 2107*x**2</replace>
No more calculations needed.
<answer>-931*x**4 - 2107*x**2</answer>


Question:
Simplify this expression: (9*x**2 - 63)*(13*x**2 + 8*x + 39)
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: 117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457

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*x**2 - 63)*(13*x**2 + 8*x + 39)
Expanding the part (9*x**2 - 63) using the distributive property, and we got: (9*x**2)*(13*x**2 + 8*x + 39) - 63*(13*x**2 + 8*x + 39)
<replace-#Step 1>#Step 2:
Current expression: (9*x**2)*(13*x**2 + 8*x + 39) - 63*(13*x**2 + 8*x + 39)</replace>
Simplifying the partial expression: -63*(13*x**2 + 8*x + 39)
Expanding the part (13*x**2 + 8*x + 39) using the distributive property, and we got: (8*x)*(-63) + (13*x**2)*(-63) + 39*(-63)
Replacing -63*(13*x**2 + 8*x + 39) with (8*x)*(-63) + (13*x**2)*(-63) + 39*(-63) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*x)*(-63) + (9*x**2)*(13*x**2 + 8*x + 39) + (13*x**2)*(-63) - 2457</replace>
Simplifying the partial expression: (9*x**2)*(13*x**2 + 8*x + 39)
Expanding the part (13*x**2 + 8*x + 39) using the distributive property, and we got: 39*(9*x**2) + (8*x)*(9*x**2) + (9*x**2)*(13*x**2)
Replacing (9*x**2)*(13*x**2 + 8*x + 39) with 39*(9*x**2) + (8*x)*(9*x**2) + (9*x**2)*(13*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 39*9*x**2 + (8*x)*(9*x**2) + (8*x)*(-63) + (9*x**2)*(13*x**2) + (13*x**2)*(-63) - 2457</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*x)*-63 = -504*x
  (8*x)*(9*x**2) = 72*x**3
  (13*x**2)*-63 = -819*x**2
  (13*x**2)*(9*x**2) = 117*x**4
  39*9*x**2 = 351*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 117*x**4 + 72*x**3 - 819*x**2 + 351*x**2 - 504*x - 2457</replace>
Combining like terms, got 117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457
<replace-#Step 5>#Step 6:
Current expression: 117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457</replace>
No more calculations needed.
<answer>117*x**4 + 72*x**3 - 468*x**2 - 504*x - 2457</answer>


Question:
Simplify this expression: (-24*z - 29)*(40*z**2 - 9*z + 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -960*z**3 - 944*z**2 - 699*z - 1160

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 - 29)*(40*z**2 - 9*z + 40)
Expanding the part (-24*z - 29) using the distributive property, and we got: (-24*z)*(40*z**2 - 9*z + 40) - 29*(40*z**2 - 9*z + 40)
<replace-#Step 1>#Step 2:
Current expression: (-24*z)*(40*z**2 - 9*z + 40) - 29*(40*z**2 - 9*z + 40)</replace>
Simplifying the partial expression: -29*(40*z**2 - 9*z + 40)
Expanding the part (40*z**2 - 9*z + 40) using the distributive property, and we got: -9*z*(-29) + (40*z**2)*(-29) + 40*(-29)
Replacing -29*(40*z**2 - 9*z + 40) with -9*z*(-29) + (40*z**2)*(-29) + 40*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-24*z)*(40*z**2 - 9*z + 40) - 9*z*(-29) + (40*z**2)*(-29) - 1160</replace>
Simplifying the partial expression: (-24*z)*(40*z**2 - 9*z + 40)
Expanding the part (40*z**2 - 9*z + 40) using the distributive property, and we got: (-24*z)*(-9*z) + (-24*z)*(40*z**2) + 40*(-24*z)
Replacing (-24*z)*(40*z**2 - 9*z + 40) with (-24*z)*(-9*z) + (-24*z)*(40*z**2) + 40*(-24*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*z)*(-9*z) + (-24*z)*(40*z**2) - 9*z*(-29) + 40*(-24)*z + (40*z**2)*(-29) - 1160</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*z)*-29 = 261*z
  (-9*z)*(-24*z) = 216*z**2
  (40*z**2)*-29 = -1160*z**2
  (40*z**2)*(-24*z) = -960*z**3
  40*-24*z = -960*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -960*z**3 - 1160*z**2 + 216*z**2 - 960*z + 261*z - 1160</replace>
Combining like terms, got -960*z**3 - 944*z**2 - 699*z - 1160
<replace-#Step 5>#Step 6:
Current expression: -960*z**3 - 944*z**2 - 699*z - 1160</replace>
No more calculations needed.
<answer>-960*z**3 - 944*z**2 - 699*z - 1160</answer>


Question:
Calculate the following: -10*y*(45*y**3 + 19*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: -450*y**4 - 190*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: -10*y*(45*y**3 + 19*y)
Expanding the part (45*y**3 + 19*y) using the distributive property, and we got: (-10*y)*(19*y) + (-10*y)*(45*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(19*y) + (-10*y)*(45*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*y)*(-10*y) = -190*y**2
  (45*y**3)*(-10*y) = -450*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -450*y**4 - 190*y**2</replace>
No more calculations needed.
<answer>-450*y**4 - 190*y**2</answer>


Question:
Calculate the following: (-2*z**3 + 10*z**2)*(-30*z**3 - 21*z**2 + 22*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: 60*z**6 - 258*z**5 - 254*z**4 + 212*z**3 + 40*z**2


Question:
Calculate the following: (2 - 43*x)*(-58*x**3 + 31*x - 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: 2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8

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: (2 - 43*x)*(-58*x**3 + 31*x - 4)
Expanding the part (2 - 43*x) using the distributive property, and we got: (-43*x)*(-58*x**3 + 31*x - 4) + 2*(-58*x**3 + 31*x - 4)
<replace-#Step 1>#Step 2:
Current expression: (-43*x)*(-58*x**3 + 31*x - 4) + 2*(-58*x**3 + 31*x - 4)</replace>
Simplifying the partial expression: 2*(-58*x**3 + 31*x - 4)
Expanding the part (-58*x**3 + 31*x - 4) using the distributive property, and we got: (31*x)*2 - 58*x**3*2 - 4*2
Replacing 2*(-58*x**3 + 31*x - 4) with (31*x)*2 - 58*x**3*2 - 4*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*x)*(-58*x**3 + 31*x - 4) + (31*x)*2 - 58*x**3*2 - 8</replace>
Simplifying the partial expression: (-43*x)*(-58*x**3 + 31*x - 4)
Expanding the part (-58*x**3 + 31*x - 4) using the distributive property, and we got: (-43*x)*(31*x) + (-43*x)*(-58*x**3) - (-1)*172*x
Replacing (-43*x)*(-58*x**3 + 31*x - 4) with (-43*x)*(31*x) + (-43*x)*(-58*x**3) - (-1)*172*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*x)*(31*x) + (-43*x)*(-58*x**3) - 4*(-43)*x + (31*x)*2 - 58*x**3*2 - 8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-58*x**3)*2 = -116*x**3
  (-58*x**3)*(-43*x) = 2494*x**4
  (31*x)*2 = 62*x
  (31*x)*(-43*x) = -1333*x**2
  -4*-43*x = 172*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2494*x**4 - 116*x**3 - 1333*x**2 + 62*x + 172*x - 8</replace>
Combining like terms, got 2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8
<replace-#Step 5>#Step 6:
Current expression: 2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8</replace>
No more calculations needed.
<answer>2494*x**4 - 116*x**3 - 1333*x**2 + 234*x - 8</answer>


Question:
Calculate the following: (-67*y**2 + 26*y)*(34*y**3 - 46)
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: -2278*y**5 + 884*y**4 + 3082*y**2 - 1196*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: (-67*y**2 + 26*y)*(34*y**3 - 46)
Expanding the part (34*y**3 - 46) using the distributive property, and we got: (34*y**3)*(-67*y**2 + 26*y) - 46*(-67*y**2 + 26*y)
<replace-#Step 1>#Step 2:
Current expression: (34*y**3)*(-67*y**2 + 26*y) - 46*(-67*y**2 + 26*y)</replace>
Simplifying the partial expression: -46*(-67*y**2 + 26*y)
Expanding the part (-67*y**2 + 26*y) using the distributive property, and we got: (26*y)*(-46) - 67*y**2*(-46)
Replacing -46*(-67*y**2 + 26*y) with (26*y)*(-46) - 67*y**2*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (26*y)*(-46) - 67*y**2*(-46) + (34*y**3)*(-67*y**2 + 26*y)</replace>
Simplifying the partial expression: (34*y**3)*(-67*y**2 + 26*y)
Expanding the part (-67*y**2 + 26*y) using the distributive property, and we got: (26*y)*(34*y**3) + (-67*y**2)*(34*y**3)
Replacing (34*y**3)*(-67*y**2 + 26*y) with (26*y)*(34*y**3) + (-67*y**2)*(34*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (26*y)*(34*y**3) + (26*y)*(-46) + (-67*y**2)*(34*y**3) - 67*y**2*(-46)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-67*y**2)*-46 = 3082*y**2
  (-67*y**2)*(34*y**3) = -2278*y**5
  (26*y)*-46 = -1196*y
  (26*y)*(34*y**3) = 884*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y</replace>
No more calculations needed.
<answer>-2278*y**5 + 884*y**4 + 3082*y**2 - 1196*y</answer>


Question:
Simplify this expression: (39*y**2 - 68*y)*(60*y**3 - 32)
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: 2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*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: (39*y**2 - 68*y)*(60*y**3 - 32)
Expanding the part (60*y**3 - 32) using the distributive property, and we got: (60*y**3)*(39*y**2 - 68*y) - 32*(39*y**2 - 68*y)
<replace-#Step 1>#Step 2:
Current expression: (60*y**3)*(39*y**2 - 68*y) - 32*(39*y**2 - 68*y)</replace>
Simplifying the partial expression: -32*(39*y**2 - 68*y)
Expanding the part (39*y**2 - 68*y) using the distributive property, and we got: -68*y*(-32) + (39*y**2)*(-32)
Replacing -32*(39*y**2 - 68*y) with -68*y*(-32) + (39*y**2)*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -68*y*(-32) + (39*y**2)*(-32) + (60*y**3)*(39*y**2 - 68*y)</replace>
Simplifying the partial expression: (60*y**3)*(39*y**2 - 68*y)
Expanding the part (39*y**2 - 68*y) using the distributive property, and we got: (-68*y)*(60*y**3) + (39*y**2)*(60*y**3)
Replacing (60*y**3)*(39*y**2 - 68*y) with (-68*y)*(60*y**3) + (39*y**2)*(60*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-68*y)*(60*y**3) - 68*y*(-32) + (39*y**2)*(60*y**3) + (39*y**2)*(-32)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*y)*-32 = 2176*y
  (-68*y)*(60*y**3) = -4080*y**4
  (39*y**2)*-32 = -1248*y**2
  (39*y**2)*(60*y**3) = 2340*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y</replace>
No more calculations needed.
<answer>2340*y**5 - 4080*y**4 - 1248*y**2 + 2176*y</answer>


Question:
Simplify this expression: 12*x*(43*x**2 + 45*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 516*x**3 + 540*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: 12*x*(43*x**2 + 45*x)
Expanding the part (43*x**2 + 45*x) using the distributive property, and we got: (12*x)*(45*x) + (12*x)*(43*x**2)
<replace-#Step 1>#Step 2:
Current expression: (12*x)*(45*x) + (12*x)*(43*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x**2)*(12*x) = 516*x**3
  (45*x)*(12*x) = 540*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 516*x**3 + 540*x**2</replace>
No more calculations needed.
<answer>516*x**3 + 540*x**2</answer>


Question:
Simplify this expression: -4*x**2*(21*x**3 + 43*x**2 + 42*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: -84*x**5 - 172*x**4 - 168*x**3 - 200*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: -4*x**2*(21*x**3 + 43*x**2 + 42*x + 50)
Expanding the part (21*x**3 + 43*x**2 + 42*x + 50) using the distributive property, and we got: 50*(-4*x**2) + (42*x)*(-4*x**2) + (-4*x**2)*(43*x**2) + (-4*x**2)*(21*x**3)
<replace-#Step 1>#Step 2:
Current expression: 50*(-4*x**2) + (42*x)*(-4*x**2) + (-4*x**2)*(43*x**2) + (-4*x**2)*(21*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  50*(-4*x**2) = -200*x**2
  (21*x**3)*(-4*x**2) = -84*x**5
  (42*x)*(-4*x**2) = -168*x**3
  (43*x**2)*(-4*x**2) = -172*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -84*x**5 - 172*x**4 - 168*x**3 - 200*x**2</replace>
No more calculations needed.
<answer>-84*x**5 - 172*x**4 - 168*x**3 - 200*x**2</answer>


Question:
Simplify this expression: (-28*y**3 + 21*y**2 - 46*y)*(38*y**3 + 79*y**2 + 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: -1064*y**6 - 1414*y**5 - 89*y**4 - 4054*y**3 + 315*y**2 - 690*y


Question:
Calculate the following: (y**2 + 16*y)*(21*y**2 + 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: 21*y**4 + 336*y**3 + 2*y**2 + 32*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: (y**2 + 16*y)*(21*y**2 + 2)
Expanding the part (21*y**2 + 2) using the distributive property, and we got: (21*y**2)*(y**2 + 16*y) + 2*(y**2 + 16*y)
<replace-#Step 1>#Step 2:
Current expression: (21*y**2)*(y**2 + 16*y) + 2*(y**2 + 16*y)</replace>
Simplifying the partial expression: 2*(y**2 + 16*y)
Expanding the part (y**2 + 16*y) using the distributive property, and we got: y**2*2 + (16*y)*2
Replacing 2*(y**2 + 16*y) with y**2*2 + (16*y)*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*2 + (16*y)*2 + (21*y**2)*(y**2 + 16*y)</replace>
Simplifying the partial expression: (21*y**2)*(y**2 + 16*y)
Expanding the part (y**2 + 16*y) using the distributive property, and we got: y**2*(21*y**2) + (16*y)*(21*y**2)
Replacing (21*y**2)*(y**2 + 16*y) with y**2*(21*y**2) + (16*y)*(21*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: y**2*(21*y**2) + y**2*2 + (16*y)*(21*y**2) + (16*y)*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**2*2 = 2*y**2
  y**2*(21*y**2) = 21*y**4
  (16*y)*2 = 32*y
  (16*y)*(21*y**2) = 336*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 21*y**4 + 336*y**3 + 2*y**2 + 32*y</replace>
No more calculations needed.
<answer>21*y**4 + 336*y**3 + 2*y**2 + 32*y</answer>


Question:
Simplify this expression: (-15*y**3 - 27)*(35*y**2 + 34*y - 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: -525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296

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**3 - 27)*(35*y**2 + 34*y - 48)
Expanding the part (-15*y**3 - 27) using the distributive property, and we got: (-15*y**3)*(35*y**2 + 34*y - 48) - 27*(35*y**2 + 34*y - 48)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**3)*(35*y**2 + 34*y - 48) - 27*(35*y**2 + 34*y - 48)</replace>
Simplifying the partial expression: -27*(35*y**2 + 34*y - 48)
Expanding the part (35*y**2 + 34*y - 48) using the distributive property, and we got: (34*y)*(-27) + (35*y**2)*(-27) - 48*(-27)
Replacing -27*(35*y**2 + 34*y - 48) with (34*y)*(-27) + (35*y**2)*(-27) - 48*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y)*(-27) + (35*y**2)*(-27) + (-15*y**3)*(35*y**2 + 34*y - 48) + 1296</replace>
Simplifying the partial expression: (-15*y**3)*(35*y**2 + 34*y - 48)
Expanding the part (35*y**2 + 34*y - 48) using the distributive property, and we got: -(-1)*720*y**3 + (34*y)*(-15*y**3) + (35*y**2)*(-15*y**3)
Replacing (-15*y**3)*(35*y**2 + 34*y - 48) with -(-1)*720*y**3 + (34*y)*(-15*y**3) + (35*y**2)*(-15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -48*(-15)*y**3 + (34*y)*(-15*y**3) + (34*y)*(-27) + (35*y**2)*(-15*y**3) + (35*y**2)*(-27) + 1296</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*y)*-27 = -918*y
  (34*y)*(-15*y**3) = -510*y**4
  (35*y**2)*-27 = -945*y**2
  (35*y**2)*(-15*y**3) = -525*y**5
  -48*-15*y**3 = 720*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296</replace>
No more calculations needed.
<answer>-525*y**5 - 510*y**4 + 720*y**3 - 945*y**2 - 918*y + 1296</answer>


Question:
Calculate the following: (-20*y**2 - 30*y + 38)*(-36*y**3 + 11*y**2 + 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 720*y**5 + 860*y**4 - 1698*y**3 + 218*y**2 - 300*y + 380


Question:
Calculate the following: (x**3 - x)*(-38*x**2 + 48*x - 5)
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: -38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*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 - x)*(-38*x**2 + 48*x - 5)
Expanding the part (x**3 - x) using the distributive property, and we got: (-x)*(-38*x**2 + 48*x - 5) + x**3*(-38*x**2 + 48*x - 5)
<replace-#Step 1>#Step 2:
Current expression: (-x)*(-38*x**2 + 48*x - 5) + x**3*(-38*x**2 + 48*x - 5)</replace>
Simplifying the partial expression: x**3*(-38*x**2 + 48*x - 5)
Expanding the part (-38*x**2 + 48*x - 5) using the distributive property, and we got: (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3
Replacing x**3*(-38*x**2 + 48*x - 5) with (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-x)*(-38*x**2 + 48*x - 5) + (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3</replace>
Simplifying the partial expression: (-x)*(-38*x**2 + 48*x - 5)
Expanding the part (-38*x**2 + 48*x - 5) using the distributive property, and we got: (-x)*(48*x) + (-x)*(-38*x**2) - (-1)*5*x
Replacing (-x)*(-38*x**2 + 48*x - 5) with (-x)*(48*x) + (-x)*(-38*x**2) - (-1)*5*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(48*x) + (-x)*(-38*x**2) + (48*x)*x**3 + (-38*x**2)*x**3 - 5*x**3 - 5*(-1)*x</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**2)*x**3 = -38*x**5
  (-38*x**2)*(-x) = 38*x**3
  (48*x)*x**3 = 48*x**4
  (48*x)*(-x) = -48*x**2
  -5*-1*x = 5*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -38*x**5 + 48*x**4 - 5*x**3 + 38*x**3 - 48*x**2 + 5*x</replace>
Combining like terms, got -38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x
<replace-#Step 5>#Step 6:
Current expression: -38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x</replace>
No more calculations needed.
<answer>-38*x**5 + 48*x**4 + 33*x**3 - 48*x**2 + 5*x</answer>


Question:
Calculate the following: (14*y**2 + 33*y)*(25*y**2 - 6*y + 61)
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: 350*y**4 + 741*y**3 + 656*y**2 + 2013*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: (14*y**2 + 33*y)*(25*y**2 - 6*y + 61)
Expanding the part (14*y**2 + 33*y) using the distributive property, and we got: (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2 - 6*y + 61)
<replace-#Step 1>#Step 2:
Current expression: (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2 - 6*y + 61)</replace>
Simplifying the partial expression: (14*y**2)*(25*y**2 - 6*y + 61)
Expanding the part (25*y**2 - 6*y + 61) using the distributive property, and we got: (-6*y)*(14*y**2) + 61*(14*y**2) + (14*y**2)*(25*y**2)
Replacing (14*y**2)*(25*y**2 - 6*y + 61) with (-6*y)*(14*y**2) + 61*(14*y**2) + (14*y**2)*(25*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*y)*(14*y**2) + 61*14*y**2 + (33*y)*(25*y**2 - 6*y + 61) + (14*y**2)*(25*y**2)</replace>
Simplifying the partial expression: (33*y)*(25*y**2 - 6*y + 61)
Expanding the part (25*y**2 - 6*y + 61) using the distributive property, and we got: (-6*y)*(33*y) + 61*(33*y) + (33*y)*(25*y**2)
Replacing (33*y)*(25*y**2 - 6*y + 61) with (-6*y)*(33*y) + 61*(33*y) + (33*y)*(25*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*y)*(33*y) + (-6*y)*(14*y**2) + 61*14*y**2 + 61*33*y + (33*y)*(25*y**2) + (14*y**2)*(25*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-6*y)*(14*y**2) = -84*y**3
  (-6*y)*(33*y) = -198*y**2
  (25*y**2)*(14*y**2) = 350*y**4
  (25*y**2)*(33*y) = 825*y**3
  61*14*y**2 = 854*y**2
  61*33*y = 2013*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 350*y**4 - 84*y**3 + 825*y**3 - 198*y**2 + 854*y**2 + 2013*y</replace>
Combining like terms, got 350*y**4 + 741*y**3 + 656*y**2 + 2013*y
<replace-#Step 5>#Step 6:
Current expression: 350*y**4 + 741*y**3 + 656*y**2 + 2013*y</replace>
No more calculations needed.
<answer>350*y**4 + 741*y**3 + 656*y**2 + 2013*y</answer>


Question:
Calculate the following: -510*y**3 + 2856*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: -510*y**3 + 2856*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: -510*y**3 + 2856*y
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: -510*y**3 + 2856*y</replace>
No more calculations needed.
<answer>-510*y**3 + 2856*y</answer>


Question:
Calculate the following: (-40*y**3 + 26*y**2 - 42*y)*(-3*y**3 + 30*y**2 - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 120*y**6 - 1278*y**5 + 906*y**4 - 580*y**3 - 442*y**2 + 714*y


Question:
Calculate the following: (24 - 23*x)*(-49*x**3 - 6*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: 1127*x**4 - 1038*x**3 - 144*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: (24 - 23*x)*(-49*x**3 - 6*x**2)
Expanding the part (24 - 23*x) using the distributive property, and we got: (-23*x)*(-49*x**3 - 6*x**2) + 24*(-49*x**3 - 6*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-23*x)*(-49*x**3 - 6*x**2) + 24*(-49*x**3 - 6*x**2)</replace>
Simplifying the partial expression: 24*(-49*x**3 - 6*x**2)
Expanding the part (-49*x**3 - 6*x**2) using the distributive property, and we got: -6*x**2*24 - 49*x**3*24
Replacing 24*(-49*x**3 - 6*x**2) with -6*x**2*24 - 49*x**3*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-23*x)*(-49*x**3 - 6*x**2) - 6*x**2*24 - 49*x**3*24</replace>
Simplifying the partial expression: (-23*x)*(-49*x**3 - 6*x**2)
Expanding the part (-49*x**3 - 6*x**2) using the distributive property, and we got: (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3)
Replacing (-23*x)*(-49*x**3 - 6*x**2) with (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*x)*(-6*x**2) + (-23*x)*(-49*x**3) - 6*x**2*24 - 49*x**3*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**3)*24 = -1176*x**3
  (-49*x**3)*(-23*x) = 1127*x**4
  (-6*x**2)*24 = -144*x**2
  (-6*x**2)*(-23*x) = 138*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1127*x**4 - 1176*x**3 + 138*x**3 - 144*x**2</replace>
Combining like terms, got 1127*x**4 - 1038*x**3 - 144*x**2
<replace-#Step 5>#Step 6:
Current expression: 1127*x**4 - 1038*x**3 - 144*x**2</replace>
No more calculations needed.
<answer>1127*x**4 - 1038*x**3 - 144*x**2</answer>


Question:
Simplify this expression: -21*x**2*(25*x**2 + 48*x + 84)
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: -525*x**4 - 1008*x**3 - 1764*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: -21*x**2*(25*x**2 + 48*x + 84)
Expanding the part (25*x**2 + 48*x + 84) using the distributive property, and we got: 84*(-21*x**2) + (48*x)*(-21*x**2) + (-21*x**2)*(25*x**2)
<replace-#Step 1>#Step 2:
Current expression: 84*(-21*x**2) + (48*x)*(-21*x**2) + (-21*x**2)*(25*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  84*(-21*x**2) = -1764*x**2
  (25*x**2)*(-21*x**2) = -525*x**4
  (48*x)*(-21*x**2) = -1008*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -525*x**4 - 1008*x**3 - 1764*x**2</replace>
No more calculations needed.
<answer>-525*x**4 - 1008*x**3 - 1764*x**2</answer>


Question:
Calculate the following: -38*y*(42 - 13*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: 494*y**2 - 1596*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: -38*y*(42 - 13*y)
Expanding the part (42 - 13*y) using the distributive property, and we got: (-38*y)*(-13*y) + 42*(-38*y)
<replace-#Step 1>#Step 2:
Current expression: (-38*y)*(-13*y) + 42*(-38*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  42*(-38*y) = -1596*y
  (-13*y)*(-38*y) = 494*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 494*y**2 - 1596*y</replace>
No more calculations needed.
<answer>494*y**2 - 1596*y</answer>


Question:
Calculate the following: (-16*x - 10)*(-44*x**3 - 50*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: 704*x**4 + 1240*x**3 + 500*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: (-16*x - 10)*(-44*x**3 - 50*x**2)
Expanding the part (-16*x - 10) using the distributive property, and we got: (-16*x)*(-44*x**3 - 50*x**2) - 10*(-44*x**3 - 50*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-16*x)*(-44*x**3 - 50*x**2) - 10*(-44*x**3 - 50*x**2)</replace>
Simplifying the partial expression: -10*(-44*x**3 - 50*x**2)
Expanding the part (-44*x**3 - 50*x**2) using the distributive property, and we got: -50*x**2*(-10) - 44*x**3*(-10)
Replacing -10*(-44*x**3 - 50*x**2) with -50*x**2*(-10) - 44*x**3*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-16*x)*(-44*x**3 - 50*x**2) - 50*x**2*(-10) - 44*x**3*(-10)</replace>
Simplifying the partial expression: (-16*x)*(-44*x**3 - 50*x**2)
Expanding the part (-44*x**3 - 50*x**2) using the distributive property, and we got: (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3)
Replacing (-16*x)*(-44*x**3 - 50*x**2) with (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*x)*(-50*x**2) + (-16*x)*(-44*x**3) - 50*x**2*(-10) - 44*x**3*(-10)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*x**2)*-10 = 500*x**2
  (-50*x**2)*(-16*x) = 800*x**3
  (-44*x**3)*-10 = 440*x**3
  (-44*x**3)*(-16*x) = 704*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 704*x**4 + 440*x**3 + 800*x**3 + 500*x**2</replace>
Combining like terms, got 704*x**4 + 1240*x**3 + 500*x**2
<replace-#Step 5>#Step 6:
Current expression: 704*x**4 + 1240*x**3 + 500*x**2</replace>
No more calculations needed.
<answer>704*x**4 + 1240*x**3 + 500*x**2</answer>


Question:
Simplify this expression: (-53*y**3 - 46)*(25*y**3 + 78*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: -1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736

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: (-53*y**3 - 46)*(25*y**3 + 78*y + 16)
Expanding the part (-53*y**3 - 46) using the distributive property, and we got: (-53*y**3)*(25*y**3 + 78*y + 16) - 46*(25*y**3 + 78*y + 16)
<replace-#Step 1>#Step 2:
Current expression: (-53*y**3)*(25*y**3 + 78*y + 16) - 46*(25*y**3 + 78*y + 16)</replace>
Simplifying the partial expression: -46*(25*y**3 + 78*y + 16)
Expanding the part (25*y**3 + 78*y + 16) using the distributive property, and we got: (78*y)*(-46) + (25*y**3)*(-46) + 16*(-46)
Replacing -46*(25*y**3 + 78*y + 16) with (78*y)*(-46) + (25*y**3)*(-46) + 16*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (78*y)*(-46) + (-53*y**3)*(25*y**3 + 78*y + 16) + (25*y**3)*(-46) - 736</replace>
Simplifying the partial expression: (-53*y**3)*(25*y**3 + 78*y + 16)
Expanding the part (25*y**3 + 78*y + 16) using the distributive property, and we got: 16*(-53*y**3) + (78*y)*(-53*y**3) + (-53*y**3)*(25*y**3)
Replacing (-53*y**3)*(25*y**3 + 78*y + 16) with 16*(-53*y**3) + (78*y)*(-53*y**3) + (-53*y**3)*(25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 16*(-53)*y**3 + (78*y)*(-53*y**3) + (78*y)*(-46) + (-53*y**3)*(25*y**3) + (25*y**3)*(-46) - 736</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*y**3)*-46 = -1150*y**3
  (25*y**3)*(-53*y**3) = -1325*y**6
  (78*y)*-46 = -3588*y
  (78*y)*(-53*y**3) = -4134*y**4
  16*-53*y**3 = -848*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1325*y**6 - 4134*y**4 - 1150*y**3 - 848*y**3 - 3588*y - 736</replace>
Combining like terms, got -1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736
<replace-#Step 5>#Step 6:
Current expression: -1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736</replace>
No more calculations needed.
<answer>-1325*y**6 - 4134*y**4 - 1998*y**3 - 3588*y - 736</answer>


Question:
Simplify this expression: (50*z - 6)*(-46*z**2 - 46*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: -2300*z**3 - 2024*z**2 + 276*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: (50*z - 6)*(-46*z**2 - 46*z)
Expanding the part (50*z - 6) using the distributive property, and we got: (50*z)*(-46*z**2 - 46*z) - 6*(-46*z**2 - 46*z)
<replace-#Step 1>#Step 2:
Current expression: (50*z)*(-46*z**2 - 46*z) - 6*(-46*z**2 - 46*z)</replace>
Simplifying the partial expression: -6*(-46*z**2 - 46*z)
Expanding the part (-46*z**2 - 46*z) using the distributive property, and we got: -46*z*(-6) - 46*z**2*(-6)
Replacing -6*(-46*z**2 - 46*z) with -46*z*(-6) - 46*z**2*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*z*(-6) + (50*z)*(-46*z**2 - 46*z) - 46*z**2*(-6)</replace>
Simplifying the partial expression: (50*z)*(-46*z**2 - 46*z)
Expanding the part (-46*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(50*z) + (50*z)*(-46*z**2)
Replacing (50*z)*(-46*z**2 - 46*z) with (-46*z)*(50*z) + (50*z)*(-46*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(50*z) - 46*z*(-6) + (50*z)*(-46*z**2) - 46*z**2*(-6)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*z)*-6 = 276*z
  (-46*z)*(50*z) = -2300*z**2
  (-46*z**2)*-6 = 276*z**2
  (-46*z**2)*(50*z) = -2300*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2300*z**3 - 2300*z**2 + 276*z**2 + 276*z</replace>
Combining like terms, got -2300*z**3 - 2024*z**2 + 276*z
<replace-#Step 5>#Step 6:
Current expression: -2300*z**3 - 2024*z**2 + 276*z</replace>
No more calculations needed.
<answer>-2300*z**3 - 2024*z**2 + 276*z</answer>


Question:
Simplify this expression: (-33*z - 15)*(-13*z**2 + 2*z - 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: 429*z**3 + 129*z**2 + 168*z + 90

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: (-33*z - 15)*(-13*z**2 + 2*z - 6)
Expanding the part (-33*z - 15) using the distributive property, and we got: (-33*z)*(-13*z**2 + 2*z - 6) - 15*(-13*z**2 + 2*z - 6)
<replace-#Step 1>#Step 2:
Current expression: (-33*z)*(-13*z**2 + 2*z - 6) - 15*(-13*z**2 + 2*z - 6)</replace>
Simplifying the partial expression: -15*(-13*z**2 + 2*z - 6)
Expanding the part (-13*z**2 + 2*z - 6) using the distributive property, and we got: (2*z)*(-15) - 13*z**2*(-15) - 6*(-15)
Replacing -15*(-13*z**2 + 2*z - 6) with (2*z)*(-15) - 13*z**2*(-15) - 6*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-33*z)*(-13*z**2 + 2*z - 6) + (2*z)*(-15) - 13*z**2*(-15) + 90</replace>
Simplifying the partial expression: (-33*z)*(-13*z**2 + 2*z - 6)
Expanding the part (-13*z**2 + 2*z - 6) using the distributive property, and we got: (-33*z)*(2*z) + (-33*z)*(-13*z**2) - (-1)*198*z
Replacing (-33*z)*(-13*z**2 + 2*z - 6) with (-33*z)*(2*z) + (-33*z)*(-13*z**2) - (-1)*198*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*z)*(2*z) + (-33*z)*(-13*z**2) - 6*(-33)*z + (2*z)*(-15) - 13*z**2*(-15) + 90</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z**2)*-15 = 195*z**2
  (-13*z**2)*(-33*z) = 429*z**3
  (2*z)*-15 = -30*z
  (2*z)*(-33*z) = -66*z**2
  -6*-33*z = 198*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 429*z**3 - 66*z**2 + 195*z**2 - 30*z + 198*z + 90</replace>
Combining like terms, got 429*z**3 + 129*z**2 + 168*z + 90
<replace-#Step 5>#Step 6:
Current expression: 429*z**3 + 129*z**2 + 168*z + 90</replace>
No more calculations needed.
<answer>429*z**3 + 129*z**2 + 168*z + 90</answer>


Question:
Simplify this expression: -6*x**3*(4*x**2 + 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: -24*x**5 - 258*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: -6*x**3*(4*x**2 + 43)
Expanding the part (4*x**2 + 43) using the distributive property, and we got: 43*(-6*x**3) + (4*x**2)*(-6*x**3)
<replace-#Step 1>#Step 2:
Current expression: 43*(-6*x**3) + (4*x**2)*(-6*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  43*(-6*x**3) = -258*x**3
  (4*x**2)*(-6*x**3) = -24*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*x**5 - 258*x**3</replace>
No more calculations needed.
<answer>-24*x**5 - 258*x**3</answer>


Question:
Calculate the following: (28*y**2 + 64)*(47*y**2 + 49*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*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: (28*y**2 + 64)*(47*y**2 + 49*y)
Expanding the part (28*y**2 + 64) using the distributive property, and we got: (28*y**2)*(47*y**2 + 49*y) + 64*(47*y**2 + 49*y)
<replace-#Step 1>#Step 2:
Current expression: (28*y**2)*(47*y**2 + 49*y) + 64*(47*y**2 + 49*y)</replace>
Simplifying the partial expression: 64*(47*y**2 + 49*y)
Expanding the part (47*y**2 + 49*y) using the distributive property, and we got: (49*y)*64 + (47*y**2)*64
Replacing 64*(47*y**2 + 49*y) with (49*y)*64 + (47*y**2)*64 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (49*y)*64 + (28*y**2)*(47*y**2 + 49*y) + (47*y**2)*64</replace>
Simplifying the partial expression: (28*y**2)*(47*y**2 + 49*y)
Expanding the part (47*y**2 + 49*y) using the distributive property, and we got: (49*y)*(28*y**2) + (28*y**2)*(47*y**2)
Replacing (28*y**2)*(47*y**2 + 49*y) with (49*y)*(28*y**2) + (28*y**2)*(47*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (49*y)*(28*y**2) + (49*y)*64 + (28*y**2)*(47*y**2) + (47*y**2)*64</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (47*y**2)*64 = 3008*y**2
  (47*y**2)*(28*y**2) = 1316*y**4
  (49*y)*64 = 3136*y
  (49*y)*(28*y**2) = 1372*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y</replace>
No more calculations needed.
<answer>1316*y**4 + 1372*y**3 + 3008*y**2 + 3136*y</answer>


Question:
Simplify this expression: (-47*z**3 + 33*z**2 - 19*z)*(55*z**3 + 5*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: -2585*z**6 + 1580*z**5 - 880*z**4 + 187*z**3 - 198*z**2 + 114*z


Question:
Simplify this expression: (28 - 30*z**3)*(-15*z**3 + 11*z + 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: 450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728

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: (28 - 30*z**3)*(-15*z**3 + 11*z + 26)
Expanding the part (28 - 30*z**3) using the distributive property, and we got: (-30*z**3)*(-15*z**3 + 11*z + 26) + 28*(-15*z**3 + 11*z + 26)
<replace-#Step 1>#Step 2:
Current expression: (-30*z**3)*(-15*z**3 + 11*z + 26) + 28*(-15*z**3 + 11*z + 26)</replace>
Simplifying the partial expression: 28*(-15*z**3 + 11*z + 26)
Expanding the part (-15*z**3 + 11*z + 26) using the distributive property, and we got: (11*z)*28 - 15*z**3*28 + 26*28
Replacing 28*(-15*z**3 + 11*z + 26) with (11*z)*28 - 15*z**3*28 + 26*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*z)*28 + (-30*z**3)*(-15*z**3 + 11*z + 26) - 15*z**3*28 + 728</replace>
Simplifying the partial expression: (-30*z**3)*(-15*z**3 + 11*z + 26)
Expanding the part (-15*z**3 + 11*z + 26) using the distributive property, and we got: 26*(-30*z**3) + (11*z)*(-30*z**3) + (-30*z**3)*(-15*z**3)
Replacing (-30*z**3)*(-15*z**3 + 11*z + 26) with 26*(-30*z**3) + (11*z)*(-30*z**3) + (-30*z**3)*(-15*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 26*(-30)*z**3 + (11*z)*(-30*z**3) + (11*z)*28 + (-30*z**3)*(-15*z**3) - 15*z**3*28 + 728</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z**3)*28 = -420*z**3
  (-15*z**3)*(-30*z**3) = 450*z**6
  (11*z)*28 = 308*z
  (11*z)*(-30*z**3) = -330*z**4
  26*-30*z**3 = -780*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 450*z**6 - 330*z**4 - 780*z**3 - 420*z**3 + 308*z + 728</replace>
Combining like terms, got 450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728
<replace-#Step 5>#Step 6:
Current expression: 450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728</replace>
No more calculations needed.
<answer>450*z**6 - 330*z**4 - 1200*z**3 + 308*z + 728</answer>


Question:
Simplify this expression: (31*y**2 - 36)*(67*y**3 + 44*y**2 + 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2077*y**5 + 1364*y**4 - 2412*y**3 - 1212*y**2 - 432