Question:
Calculate the following: (36*z + 1)*(24*z**3 + 45*z**2 + 17*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: 864*z**4 + 1644*z**3 + 657*z**2 + 17*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: (36*z + 1)*(24*z**3 + 45*z**2 + 17*z)
Expanding the part (36*z + 1) using the distributive property, and we got: (36*z)*(24*z**3 + 45*z**2 + 17*z) + 1*(24*z**3 + 45*z**2 + 17*z)
<replace-#Step 1>#Step 2:
Current expression: (36*z)*(24*z**3 + 45*z**2 + 17*z) + 1*(24*z**3 + 45*z**2 + 17*z)</replace>
Simplifying the partial expression: 1*(24*z**3 + 45*z**2 + 17*z)
Expanding the part (24*z**3 + 45*z**2 + 17*z) using the distributive property, and we got: (17*z)*1 + (45*z**2)*1 + (24*z**3)*1
Replacing 1*(24*z**3 + 45*z**2 + 17*z) with (17*z)*1 + (45*z**2)*1 + (24*z**3)*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*z)*1 + (36*z)*(24*z**3 + 45*z**2 + 17*z) + (45*z**2)*1 + (24*z**3)*1</replace>
Simplifying the partial expression: (36*z)*(24*z**3 + 45*z**2 + 17*z)
Expanding the part (24*z**3 + 45*z**2 + 17*z) using the distributive property, and we got: (17*z)*(36*z) + (36*z)*(45*z**2) + (36*z)*(24*z**3)
Replacing (36*z)*(24*z**3 + 45*z**2 + 17*z) with (17*z)*(36*z) + (36*z)*(45*z**2) + (36*z)*(24*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (17*z)*(36*z) + (17*z)*1 + (36*z)*(45*z**2) + (36*z)*(24*z**3) + (45*z**2)*1 + (24*z**3)*1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*z)*1 = 17*z
  (17*z)*(36*z) = 612*z**2
  (24*z**3)*1 = 24*z**3
  (24*z**3)*(36*z) = 864*z**4
  (45*z**2)*1 = 45*z**2
  (45*z**2)*(36*z) = 1620*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 864*z**4 + 24*z**3 + 1620*z**3 + 45*z**2 + 612*z**2 + 17*z</replace>
Combining like terms, got 864*z**4 + 1644*z**3 + 657*z**2 + 17*z
<replace-#Step 5>#Step 6:
Current expression: 864*z**4 + 1644*z**3 + 657*z**2 + 17*z</replace>
No more calculations needed.
<answer>864*z**4 + 1644*z**3 + 657*z**2 + 17*z</answer>


Question:
Simplify this expression: (37*y - 34)*(-34*y**2 - 28*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: -1258*y**3 + 120*y**2 + 952*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: (37*y - 34)*(-34*y**2 - 28*y)
Expanding the part (37*y - 34) using the distributive property, and we got: (37*y)*(-34*y**2 - 28*y) - 34*(-34*y**2 - 28*y)
<replace-#Step 1>#Step 2:
Current expression: (37*y)*(-34*y**2 - 28*y) - 34*(-34*y**2 - 28*y)</replace>
Simplifying the partial expression: -34*(-34*y**2 - 28*y)
Expanding the part (-34*y**2 - 28*y) using the distributive property, and we got: -28*y*(-34) - 34*y**2*(-34)
Replacing -34*(-34*y**2 - 28*y) with -28*y*(-34) - 34*y**2*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*y*(-34) + (37*y)*(-34*y**2 - 28*y) - 34*y**2*(-34)</replace>
Simplifying the partial expression: (37*y)*(-34*y**2 - 28*y)
Expanding the part (-34*y**2 - 28*y) using the distributive property, and we got: (-28*y)*(37*y) + (37*y)*(-34*y**2)
Replacing (37*y)*(-34*y**2 - 28*y) with (-28*y)*(37*y) + (37*y)*(-34*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*y)*(37*y) - 28*y*(-34) + (37*y)*(-34*y**2) - 34*y**2*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*y**2)*-34 = 1156*y**2
  (-34*y**2)*(37*y) = -1258*y**3
  (-28*y)*-34 = 952*y
  (-28*y)*(37*y) = -1036*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1258*y**3 - 1036*y**2 + 1156*y**2 + 952*y</replace>
Combining like terms, got -1258*y**3 + 120*y**2 + 952*y
<replace-#Step 5>#Step 6:
Current expression: -1258*y**3 + 120*y**2 + 952*y</replace>
No more calculations needed.
<answer>-1258*y**3 + 120*y**2 + 952*y</answer>


Question:
Calculate the following: -282*y**2 + 66*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: -282*y**2 + 66*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: -282*y**2 + 66*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: -282*y**2 + 66*y</replace>
No more calculations needed.
<answer>-282*y**2 + 66*y</answer>


Question:
Calculate the following: (-31*x**3 - 22*x)*(23*x**3 - 30*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: -713*x**6 + 424*x**4 + 660*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: (-31*x**3 - 22*x)*(23*x**3 - 30*x)
Expanding the part (-31*x**3 - 22*x) using the distributive property, and we got: (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3 - 30*x)
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3 - 30*x)</replace>
Simplifying the partial expression: (-31*x**3)*(23*x**3 - 30*x)
Expanding the part (23*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-31*x**3) + (-31*x**3)*(23*x**3)
Replacing (-31*x**3)*(23*x**3 - 30*x) with (-30*x)*(-31*x**3) + (-31*x**3)*(23*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-30*x)*(-31*x**3) + (-22*x)*(23*x**3 - 30*x) + (-31*x**3)*(23*x**3)</replace>
Simplifying the partial expression: (-22*x)*(23*x**3 - 30*x)
Expanding the part (23*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-22*x) + (-22*x)*(23*x**3)
Replacing (-22*x)*(23*x**3 - 30*x) with (-30*x)*(-22*x) + (-22*x)*(23*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*x)*(-22*x) + (-30*x)*(-31*x**3) + (-22*x)*(23*x**3) + (-31*x**3)*(23*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*x)*(-31*x**3) = 930*x**4
  (-30*x)*(-22*x) = 660*x**2
  (23*x**3)*(-31*x**3) = -713*x**6
  (23*x**3)*(-22*x) = -506*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -713*x**6 - 506*x**4 + 930*x**4 + 660*x**2</replace>
Combining like terms, got -713*x**6 + 424*x**4 + 660*x**2
<replace-#Step 5>#Step 6:
Current expression: -713*x**6 + 424*x**4 + 660*x**2</replace>
No more calculations needed.
<answer>-713*x**6 + 424*x**4 + 660*x**2</answer>


Question:
Calculate the following: (48 - 26*z**3)*(37*z**3 + 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: -962*z**6 + 1022*z**3 + 1392

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (48 - 26*z**3)*(37*z**3 + 29)
Expanding the part (37*z**3 + 29) using the distributive property, and we got: (37*z**3)*(48 - 26*z**3) + 29*(48 - 26*z**3)
<replace-#Step 1>#Step 2:
Current expression: (37*z**3)*(48 - 26*z**3) + 29*(48 - 26*z**3)</replace>
Simplifying the partial expression: 29*(48 - 26*z**3)
Expanding the part (48 - 26*z**3) using the distributive property, and we got: -26*z**3*29 + 48*29
Replacing 29*(48 - 26*z**3) with -26*z**3*29 + 48*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -26*z**3*29 + (37*z**3)*(48 - 26*z**3) + 1392</replace>
Simplifying the partial expression: (37*z**3)*(48 - 26*z**3)
Expanding the part (48 - 26*z**3) using the distributive property, and we got: 48*(37*z**3) + (-26*z**3)*(37*z**3)
Replacing (37*z**3)*(48 - 26*z**3) with 48*(37*z**3) + (-26*z**3)*(37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 48*37*z**3 + (-26*z**3)*(37*z**3) - 26*z**3*29 + 1392</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-26*z**3)*29 = -754*z**3
  (-26*z**3)*(37*z**3) = -962*z**6
  48*37*z**3 = 1776*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -962*z**6 - 754*z**3 + 1776*z**3 + 1392</replace>
Combining like terms, got -962*z**6 + 1022*z**3 + 1392
<replace-#Step 5>#Step 6:
Current expression: -962*z**6 + 1022*z**3 + 1392</replace>
No more calculations needed.
<answer>-962*z**6 + 1022*z**3 + 1392</answer>


Question:
Calculate the following: (-5*x**3 + 7*x**2)*(27*x**3 - 7*x**2 + 35*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: -135*x**6 + 224*x**5 - 224*x**4 + 245*x**3


Question:
Simplify this expression: (-12*z**3 + 8*z**2)*(10*z**3 - 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: -120*z**6 + 80*z**5 + 180*z**3 - 120*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: (-12*z**3 + 8*z**2)*(10*z**3 - 15)
Expanding the part (10*z**3 - 15) using the distributive property, and we got: (10*z**3)*(-12*z**3 + 8*z**2) - 15*(-12*z**3 + 8*z**2)
<replace-#Step 1>#Step 2:
Current expression: (10*z**3)*(-12*z**3 + 8*z**2) - 15*(-12*z**3 + 8*z**2)</replace>
Simplifying the partial expression: -15*(-12*z**3 + 8*z**2)
Expanding the part (-12*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(-15) - 12*z**3*(-15)
Replacing -15*(-12*z**3 + 8*z**2) with (8*z**2)*(-15) - 12*z**3*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*z**2)*(-15) - 12*z**3*(-15) + (10*z**3)*(-12*z**3 + 8*z**2)</replace>
Simplifying the partial expression: (10*z**3)*(-12*z**3 + 8*z**2)
Expanding the part (-12*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(10*z**3) + (-12*z**3)*(10*z**3)
Replacing (10*z**3)*(-12*z**3 + 8*z**2) with (8*z**2)*(10*z**3) + (-12*z**3)*(10*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*z**2)*(10*z**3) + (8*z**2)*(-15) + (-12*z**3)*(10*z**3) - 12*z**3*(-15)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*z**3)*-15 = 180*z**3
  (-12*z**3)*(10*z**3) = -120*z**6
  (8*z**2)*-15 = -120*z**2
  (8*z**2)*(10*z**3) = 80*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -120*z**6 + 80*z**5 + 180*z**3 - 120*z**2</replace>
No more calculations needed.
<answer>-120*z**6 + 80*z**5 + 180*z**3 - 120*z**2</answer>


Question:
Calculate the following: -248*y**3 + 651*y**2 + 775*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: -248*y**3 + 651*y**2 + 775*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: -248*y**3 + 651*y**2 + 775*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: -248*y**3 + 651*y**2 + 775*y</replace>
No more calculations needed.
<answer>-248*y**3 + 651*y**2 + 775*y</answer>


Question:
Simplify this expression: 13*y*(42*y**3 + 22*y**2 - 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 546*y**4 + 286*y**3 - 299*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*(42*y**3 + 22*y**2 - 23)
Expanding the part (42*y**3 + 22*y**2 - 23) using the distributive property, and we got: -299*y + (13*y)*(22*y**2) + (13*y)*(42*y**3)
<replace-#Step 1>#Step 2:
Current expression: -299*y + (13*y)*(22*y**2) + (13*y)*(42*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -23*(13*y) = -299*y
  (22*y**2)*(13*y) = 286*y**3
  (42*y**3)*(13*y) = 546*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 546*y**4 + 286*y**3 - 299*y</replace>
No more calculations needed.
<answer>546*y**4 + 286*y**3 - 299*y</answer>


Question:
Simplify this expression: (48*x**2 + 6*x + 48)*(-36*x**3 + 17*x**2 - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1728*x**5 + 600*x**4 - 1626*x**3 + 336*x**2 - 60*x - 480


Question:
Simplify this expression: (33*y + 38)*(31*y**2 - y - 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1023*y**3 + 1145*y**2 - 335*y - 342

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*y + 38)*(31*y**2 - y - 9)
Expanding the part (33*y + 38) using the distributive property, and we got: (33*y)*(31*y**2 - y - 9) + 38*(31*y**2 - y - 9)
<replace-#Step 1>#Step 2:
Current expression: (33*y)*(31*y**2 - y - 9) + 38*(31*y**2 - y - 9)</replace>
Simplifying the partial expression: 38*(31*y**2 - y - 9)
Expanding the part (31*y**2 - y - 9) using the distributive property, and we got: -y*38 + (31*y**2)*38 - 9*38
Replacing 38*(31*y**2 - y - 9) with -y*38 + (31*y**2)*38 - 9*38 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -y*38 + (33*y)*(31*y**2 - y - 9) + (31*y**2)*38 - 342</replace>
Simplifying the partial expression: (33*y)*(31*y**2 - y - 9)
Expanding the part (31*y**2 - y - 9) using the distributive property, and we got: (-y)*(33*y) - 297*y + (33*y)*(31*y**2)
Replacing (33*y)*(31*y**2 - y - 9) with (-y)*(33*y) - 297*y + (33*y)*(31*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y)*(33*y) - y*38 - 9*33*y + (33*y)*(31*y**2) + (31*y**2)*38 - 342</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y)*38 = -38*y
  (-y)*(33*y) = -33*y**2
  (31*y**2)*38 = 1178*y**2
  (31*y**2)*(33*y) = 1023*y**3
  -9*33*y = -297*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1023*y**3 - 33*y**2 + 1178*y**2 - 297*y - 38*y - 342</replace>
Combining like terms, got 1023*y**3 + 1145*y**2 - 335*y - 342
<replace-#Step 5>#Step 6:
Current expression: 1023*y**3 + 1145*y**2 - 335*y - 342</replace>
No more calculations needed.
<answer>1023*y**3 + 1145*y**2 - 335*y - 342</answer>


Question:
Calculate the following: (13 - 29*y**3)*(4*y + 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: -116*y**4 - 174*y**3 + 52*y + 78

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 - 29*y**3)*(4*y + 6)
Expanding the part (4*y + 6) using the distributive property, and we got: (4*y)*(13 - 29*y**3) + 6*(13 - 29*y**3)
<replace-#Step 1>#Step 2:
Current expression: (4*y)*(13 - 29*y**3) + 6*(13 - 29*y**3)</replace>
Simplifying the partial expression: 6*(13 - 29*y**3)
Expanding the part (13 - 29*y**3) using the distributive property, and we got: -29*y**3*6 + 13*6
Replacing 6*(13 - 29*y**3) with -29*y**3*6 + 13*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*y)*(13 - 29*y**3) - 29*y**3*6 + 78</replace>
Simplifying the partial expression: (4*y)*(13 - 29*y**3)
Expanding the part (13 - 29*y**3) using the distributive property, and we got: 13*(4*y) + (4*y)*(-29*y**3)
Replacing (4*y)*(13 - 29*y**3) with 13*(4*y) + (4*y)*(-29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*4*y + (4*y)*(-29*y**3) - 29*y**3*6 + 78</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y**3)*6 = -174*y**3
  (-29*y**3)*(4*y) = -116*y**4
  13*4*y = 52*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -116*y**4 - 174*y**3 + 52*y + 78</replace>
No more calculations needed.
<answer>-116*y**4 - 174*y**3 + 52*y + 78</answer>


Question:
Simplify this expression: (30*x**3 - 47*x**2)*(50*x**3 + 3*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: 1500*x**6 - 2350*x**5 + 90*x**4 - 141*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: (30*x**3 - 47*x**2)*(50*x**3 + 3*x)
Expanding the part (30*x**3 - 47*x**2) using the distributive property, and we got: (-47*x**2)*(50*x**3 + 3*x) + (30*x**3)*(50*x**3 + 3*x)
<replace-#Step 1>#Step 2:
Current expression: (-47*x**2)*(50*x**3 + 3*x) + (30*x**3)*(50*x**3 + 3*x)</replace>
Simplifying the partial expression: (-47*x**2)*(50*x**3 + 3*x)
Expanding the part (50*x**3 + 3*x) using the distributive property, and we got: (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3)
Replacing (-47*x**2)*(50*x**3 + 3*x) with (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*x)*(-47*x**2) + (-47*x**2)*(50*x**3) + (30*x**3)*(50*x**3 + 3*x)</replace>
Simplifying the partial expression: (30*x**3)*(50*x**3 + 3*x)
Expanding the part (50*x**3 + 3*x) using the distributive property, and we got: (3*x)*(30*x**3) + (30*x**3)*(50*x**3)
Replacing (30*x**3)*(50*x**3 + 3*x) with (3*x)*(30*x**3) + (30*x**3)*(50*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*x)*(-47*x**2) + (3*x)*(30*x**3) + (-47*x**2)*(50*x**3) + (30*x**3)*(50*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*x)*(-47*x**2) = -141*x**3
  (3*x)*(30*x**3) = 90*x**4
  (50*x**3)*(-47*x**2) = -2350*x**5
  (50*x**3)*(30*x**3) = 1500*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3</replace>
No more calculations needed.
<answer>1500*x**6 - 2350*x**5 + 90*x**4 - 141*x**3</answer>


Question:
Calculate the following: (13 - 60*x)*(-33*x**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: 1980*x**3 - 429*x**2 + 1620*x - 351

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 - 60*x)*(-33*x**2 - 27)
Expanding the part (-33*x**2 - 27) using the distributive property, and we got: (-33*x**2)*(13 - 60*x) - 27*(13 - 60*x)
<replace-#Step 1>#Step 2:
Current expression: (-33*x**2)*(13 - 60*x) - 27*(13 - 60*x)</replace>
Simplifying the partial expression: -27*(13 - 60*x)
Expanding the part (13 - 60*x) using the distributive property, and we got: -60*x*(-27) + 13*(-27)
Replacing -27*(13 - 60*x) with -60*x*(-27) + 13*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -60*x*(-27) + (-33*x**2)*(13 - 60*x) - 351</replace>
Simplifying the partial expression: (-33*x**2)*(13 - 60*x)
Expanding the part (13 - 60*x) using the distributive property, and we got: (-60*x)*(-33*x**2) + 13*(-33*x**2)
Replacing (-33*x**2)*(13 - 60*x) with (-60*x)*(-33*x**2) + 13*(-33*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-60*x)*(-33*x**2) - 60*x*(-27) + 13*(-33)*x**2 - 351</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-60*x)*-27 = 1620*x
  (-60*x)*(-33*x**2) = 1980*x**3
  13*-33*x**2 = -429*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1980*x**3 - 429*x**2 + 1620*x - 351</replace>
No more calculations needed.
<answer>1980*x**3 - 429*x**2 + 1620*x - 351</answer>


Question:
Simplify this expression: (9 - y)*(12*y**3 - 59)
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: -12*y**4 + 108*y**3 + 59*y - 531

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9 - y)*(12*y**3 - 59)
Expanding the part (12*y**3 - 59) using the distributive property, and we got: (12*y**3)*(9 - y) - 59*(9 - y)
<replace-#Step 1>#Step 2:
Current expression: (12*y**3)*(9 - y) - 59*(9 - y)</replace>
Simplifying the partial expression: -59*(9 - y)
Expanding the part (9 - y) using the distributive property, and we got: -y*(-59) + 9*(-59)
Replacing -59*(9 - y) with -y*(-59) + 9*(-59) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -y*(-59) + (12*y**3)*(9 - y) - 531</replace>
Simplifying the partial expression: (12*y**3)*(9 - y)
Expanding the part (9 - y) using the distributive property, and we got: (-y)*(12*y**3) + 9*(12*y**3)
Replacing (12*y**3)*(9 - y) with (-y)*(12*y**3) + 9*(12*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y)*(12*y**3) - y*(-59) + 9*12*y**3 - 531</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y)*-59 = 59*y
  (-y)*(12*y**3) = -12*y**4
  9*12*y**3 = 108*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -12*y**4 + 108*y**3 + 59*y - 531</replace>
No more calculations needed.
<answer>-12*y**4 + 108*y**3 + 59*y - 531</answer>


Question:
Calculate the following: (16 - 56*y**3)*(37*y**3 - 21*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: -2072*y**6 + 1176*y**4 + 592*y**3 - 336*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16 - 56*y**3)*(37*y**3 - 21*y)
Expanding the part (16 - 56*y**3) using the distributive property, and we got: (-56*y**3)*(37*y**3 - 21*y) + 16*(37*y**3 - 21*y)
<replace-#Step 1>#Step 2:
Current expression: (-56*y**3)*(37*y**3 - 21*y) + 16*(37*y**3 - 21*y)</replace>
Simplifying the partial expression: 16*(37*y**3 - 21*y)
Expanding the part (37*y**3 - 21*y) using the distributive property, and we got: -21*y*16 + (37*y**3)*16
Replacing 16*(37*y**3 - 21*y) with -21*y*16 + (37*y**3)*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -21*y*16 + (-56*y**3)*(37*y**3 - 21*y) + (37*y**3)*16</replace>
Simplifying the partial expression: (-56*y**3)*(37*y**3 - 21*y)
Expanding the part (37*y**3 - 21*y) using the distributive property, and we got: (-21*y)*(-56*y**3) + (-56*y**3)*(37*y**3)
Replacing (-56*y**3)*(37*y**3 - 21*y) with (-21*y)*(-56*y**3) + (-56*y**3)*(37*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*y)*(-56*y**3) - 21*y*16 + (-56*y**3)*(37*y**3) + (37*y**3)*16</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*y)*16 = -336*y
  (-21*y)*(-56*y**3) = 1176*y**4
  (37*y**3)*16 = 592*y**3
  (37*y**3)*(-56*y**3) = -2072*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2072*y**6 + 1176*y**4 + 592*y**3 - 336*y</replace>
No more calculations needed.
<answer>-2072*y**6 + 1176*y**4 + 592*y**3 - 336*y</answer>


Question:
Calculate the following: 3*x*(3*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: 9*x**4 - 93*x**2 - 12*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 3*x*(3*x**3 - 31*x - 4)
Expanding the part (3*x**3 - 31*x - 4) using the distributive property, and we got: (-31*x)*(3*x) - 12*x + (3*x)*(3*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-31*x)*(3*x) - 12*x + (3*x)*(3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -4*(3*x) = -12*x
  (-31*x)*(3*x) = -93*x**2
  (3*x**3)*(3*x) = 9*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 9*x**4 - 93*x**2 - 12*x</replace>
No more calculations needed.
<answer>9*x**4 - 93*x**2 - 12*x</answer>


Question:
Calculate the following: (-42*x - 16)*(8*x**2 - 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: -336*x**3 - 128*x**2 + 1008*x + 384

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-42*x - 16)*(8*x**2 - 24)
Expanding the part (8*x**2 - 24) using the distributive property, and we got: (8*x**2)*(-42*x - 16) - 24*(-42*x - 16)
<replace-#Step 1>#Step 2:
Current expression: (8*x**2)*(-42*x - 16) - 24*(-42*x - 16)</replace>
Simplifying the partial expression: -24*(-42*x - 16)
Expanding the part (-42*x - 16) using the distributive property, and we got: -42*x*(-24) - 16*(-24)
Replacing -24*(-42*x - 16) with -42*x*(-24) - 16*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*x*(-24) + (8*x**2)*(-42*x - 16) + 384</replace>
Simplifying the partial expression: (8*x**2)*(-42*x - 16)
Expanding the part (-42*x - 16) using the distributive property, and we got: (-42*x)*(8*x**2) - 128*x**2
Replacing (8*x**2)*(-42*x - 16) with (-42*x)*(8*x**2) - 128*x**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*x)*(8*x**2) - 42*x*(-24) - 16*8*x**2 + 384</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x)*-24 = 1008*x
  (-42*x)*(8*x**2) = -336*x**3
  -16*8*x**2 = -128*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -336*x**3 - 128*x**2 + 1008*x + 384</replace>
No more calculations needed.
<answer>-336*x**3 - 128*x**2 + 1008*x + 384</answer>


Question:
Calculate the following: (-20*x - 39)*(-29*x**3 - 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: 580*x**4 + 1131*x**3 + 200*x + 390

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-20*x - 39)*(-29*x**3 - 10)
Expanding the part (-20*x - 39) using the distributive property, and we got: (-20*x)*(-29*x**3 - 10) - 39*(-29*x**3 - 10)
<replace-#Step 1>#Step 2:
Current expression: (-20*x)*(-29*x**3 - 10) - 39*(-29*x**3 - 10)</replace>
Simplifying the partial expression: -39*(-29*x**3 - 10)
Expanding the part (-29*x**3 - 10) using the distributive property, and we got: -29*x**3*(-39) - 10*(-39)
Replacing -39*(-29*x**3 - 10) with -29*x**3*(-39) - 10*(-39) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*x)*(-29*x**3 - 10) - 29*x**3*(-39) + 390</replace>
Simplifying the partial expression: (-20*x)*(-29*x**3 - 10)
Expanding the part (-29*x**3 - 10) using the distributive property, and we got: (-20*x)*(-29*x**3) - (-1)*200*x
Replacing (-20*x)*(-29*x**3 - 10) with (-20*x)*(-29*x**3) - (-1)*200*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*x)*(-29*x**3) - 10*(-20)*x - 29*x**3*(-39) + 390</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*x**3)*-39 = 1131*x**3
  (-29*x**3)*(-20*x) = 580*x**4
  -10*-20*x = 200*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 580*x**4 + 1131*x**3 + 200*x + 390</replace>
No more calculations needed.
<answer>580*x**4 + 1131*x**3 + 200*x + 390</answer>


Question:
Calculate the following: (28*x**3 + 2)*(26*x**3 + 14*x**2 + 4*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: 728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*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: (28*x**3 + 2)*(26*x**3 + 14*x**2 + 4*x)
Expanding the part (28*x**3 + 2) using the distributive property, and we got: (28*x**3)*(26*x**3 + 14*x**2 + 4*x) + 2*(26*x**3 + 14*x**2 + 4*x)
<replace-#Step 1>#Step 2:
Current expression: (28*x**3)*(26*x**3 + 14*x**2 + 4*x) + 2*(26*x**3 + 14*x**2 + 4*x)</replace>
Simplifying the partial expression: 2*(26*x**3 + 14*x**2 + 4*x)
Expanding the part (26*x**3 + 14*x**2 + 4*x) using the distributive property, and we got: (4*x)*2 + (14*x**2)*2 + (26*x**3)*2
Replacing 2*(26*x**3 + 14*x**2 + 4*x) with (4*x)*2 + (14*x**2)*2 + (26*x**3)*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*x)*2 + (14*x**2)*2 + (26*x**3)*2 + (28*x**3)*(26*x**3 + 14*x**2 + 4*x)</replace>
Simplifying the partial expression: (28*x**3)*(26*x**3 + 14*x**2 + 4*x)
Expanding the part (26*x**3 + 14*x**2 + 4*x) using the distributive property, and we got: (4*x)*(28*x**3) + (14*x**2)*(28*x**3) + (26*x**3)*(28*x**3)
Replacing (28*x**3)*(26*x**3 + 14*x**2 + 4*x) with (4*x)*(28*x**3) + (14*x**2)*(28*x**3) + (26*x**3)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (4*x)*(28*x**3) + (4*x)*2 + (14*x**2)*(28*x**3) + (14*x**2)*2 + (26*x**3)*(28*x**3) + (26*x**3)*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*x)*2 = 8*x
  (4*x)*(28*x**3) = 112*x**4
  (14*x**2)*2 = 28*x**2
  (14*x**2)*(28*x**3) = 392*x**5
  (26*x**3)*2 = 52*x**3
  (26*x**3)*(28*x**3) = 728*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x</replace>
No more calculations needed.
<answer>728*x**6 + 392*x**5 + 112*x**4 + 52*x**3 + 28*x**2 + 8*x</answer>


Question:
Calculate the following: (28*x**2 - 4)*(-34*x**3 + 13*x**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: -952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 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: (28*x**2 - 4)*(-34*x**3 + 13*x**2 + 2)
Expanding the part (28*x**2 - 4) using the distributive property, and we got: (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 4*(-34*x**3 + 13*x**2 + 2)
<replace-#Step 1>#Step 2:
Current expression: (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 4*(-34*x**3 + 13*x**2 + 2)</replace>
Simplifying the partial expression: -4*(-34*x**3 + 13*x**2 + 2)
Expanding the part (-34*x**3 + 13*x**2 + 2) using the distributive property, and we got: (13*x**2)*(-4) - 34*x**3*(-4) + 2*(-4)
Replacing -4*(-34*x**3 + 13*x**2 + 2) with (13*x**2)*(-4) - 34*x**3*(-4) + 2*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (13*x**2)*(-4) + (28*x**2)*(-34*x**3 + 13*x**2 + 2) - 34*x**3*(-4) - 8</replace>
Simplifying the partial expression: (28*x**2)*(-34*x**3 + 13*x**2 + 2)
Expanding the part (-34*x**3 + 13*x**2 + 2) using the distributive property, and we got: 2*(28*x**2) + (13*x**2)*(28*x**2) + (28*x**2)*(-34*x**3)
Replacing (28*x**2)*(-34*x**3 + 13*x**2 + 2) with 2*(28*x**2) + (13*x**2)*(28*x**2) + (28*x**2)*(-34*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 2*28*x**2 + (13*x**2)*(28*x**2) + (13*x**2)*(-4) + (28*x**2)*(-34*x**3) - 34*x**3*(-4) - 8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**3)*-4 = 136*x**3
  (-34*x**3)*(28*x**2) = -952*x**5
  (13*x**2)*-4 = -52*x**2
  (13*x**2)*(28*x**2) = 364*x**4
  2*28*x**2 = 56*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -952*x**5 + 364*x**4 + 136*x**3 - 52*x**2 + 56*x**2 - 8</replace>
Combining like terms, got -952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8
<replace-#Step 5>#Step 6:
Current expression: -952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8</replace>
No more calculations needed.
<answer>-952*x**5 + 364*x**4 + 136*x**3 + 4*x**2 - 8</answer>


Question:
Simplify this expression: -20*x**3*(42*x**3 + 46*x**2 + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -840*x**6 - 920*x**5 - 140*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: -20*x**3*(42*x**3 + 46*x**2 + 7)
Expanding the part (42*x**3 + 46*x**2 + 7) using the distributive property, and we got: 7*(-20*x**3) + (46*x**2)*(-20*x**3) + (-20*x**3)*(42*x**3)
<replace-#Step 1>#Step 2:
Current expression: 7*(-20*x**3) + (46*x**2)*(-20*x**3) + (-20*x**3)*(42*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  7*(-20*x**3) = -140*x**3
  (42*x**3)*(-20*x**3) = -840*x**6
  (46*x**2)*(-20*x**3) = -920*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -840*x**6 - 920*x**5 - 140*x**3</replace>
No more calculations needed.
<answer>-840*x**6 - 920*x**5 - 140*x**3</answer>


Question:
Simplify this expression: (-41*z**2 + 3*z)*(50*z**3 + 11*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: -2050*z**5 - 301*z**4 + 33*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: (-41*z**2 + 3*z)*(50*z**3 + 11*z**2)
Expanding the part (-41*z**2 + 3*z) using the distributive property, and we got: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(50*z**3 + 11*z**2)
<replace-#Step 1>#Step 2:
Current expression: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(50*z**3 + 11*z**2)</replace>
Simplifying the partial expression: (-41*z**2)*(50*z**3 + 11*z**2)
Expanding the part (50*z**3 + 11*z**2) using the distributive property, and we got: (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)
Replacing (-41*z**2)*(50*z**3 + 11*z**2) with (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*(50*z**3 + 11*z**2) + (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)</replace>
Simplifying the partial expression: (3*z)*(50*z**3 + 11*z**2)
Expanding the part (50*z**3 + 11*z**2) using the distributive property, and we got: (3*z)*(11*z**2) + (3*z)*(50*z**3)
Replacing (3*z)*(50*z**3 + 11*z**2) with (3*z)*(11*z**2) + (3*z)*(50*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*z)*(11*z**2) + (3*z)*(50*z**3) + (-41*z**2)*(11*z**2) + (-41*z**2)*(50*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*z**2)*(-41*z**2) = -451*z**4
  (11*z**2)*(3*z) = 33*z**3
  (50*z**3)*(-41*z**2) = -2050*z**5
  (50*z**3)*(3*z) = 150*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2050*z**5 - 451*z**4 + 150*z**4 + 33*z**3</replace>
Combining like terms, got -2050*z**5 - 301*z**4 + 33*z**3
<replace-#Step 5>#Step 6:
Current expression: -2050*z**5 - 301*z**4 + 33*z**3</replace>
No more calculations needed.
<answer>-2050*z**5 - 301*z**4 + 33*z**3</answer>


Question:
Simplify this expression: (-39*z**3 - 42*z)*(13*z**3 + 2*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: -507*z**6 - 78*z**5 - 546*z**4 - 84*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: (-39*z**3 - 42*z)*(13*z**3 + 2*z**2)
Expanding the part (-39*z**3 - 42*z) using the distributive property, and we got: (-42*z)*(13*z**3 + 2*z**2) + (-39*z**3)*(13*z**3 + 2*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-42*z)*(13*z**3 + 2*z**2) + (-39*z**3)*(13*z**3 + 2*z**2)</replace>
Simplifying the partial expression: (-42*z)*(13*z**3 + 2*z**2)
Expanding the part (13*z**3 + 2*z**2) using the distributive property, and we got: (-42*z)*(2*z**2) + (-42*z)*(13*z**3)
Replacing (-42*z)*(13*z**3 + 2*z**2) with (-42*z)*(2*z**2) + (-42*z)*(13*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-42*z)*(2*z**2) + (-42*z)*(13*z**3) + (-39*z**3)*(13*z**3 + 2*z**2)</replace>
Simplifying the partial expression: (-39*z**3)*(13*z**3 + 2*z**2)
Expanding the part (13*z**3 + 2*z**2) using the distributive property, and we got: (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3)
Replacing (-39*z**3)*(13*z**3 + 2*z**2) with (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*z)*(2*z**2) + (-42*z)*(13*z**3) + (2*z**2)*(-39*z**3) + (-39*z**3)*(13*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*z**2)*(-42*z) = -84*z**3
  (2*z**2)*(-39*z**3) = -78*z**5
  (13*z**3)*(-42*z) = -546*z**4
  (13*z**3)*(-39*z**3) = -507*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -507*z**6 - 78*z**5 - 546*z**4 - 84*z**3</replace>
No more calculations needed.
<answer>-507*z**6 - 78*z**5 - 546*z**4 - 84*z**3</answer>


Question:
Calculate the following: (-15*z**3 + 13*z**2 + 26)*(-2*z**3 - 39*z**2 + 7*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: 30*z**6 + 559*z**5 - 612*z**4 + 39*z**3 - 1014*z**2 + 182*z


Question:
Simplify this expression: -42*x*(-4*x**3 - 29*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: 168*x**4 + 1218*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: -42*x*(-4*x**3 - 29*x)
Expanding the part (-4*x**3 - 29*x) using the distributive property, and we got: (-42*x)*(-29*x) + (-42*x)*(-4*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-42*x)*(-29*x) + (-42*x)*(-4*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*x)*(-42*x) = 1218*x**2
  (-4*x**3)*(-42*x) = 168*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 168*x**4 + 1218*x**2</replace>
No more calculations needed.
<answer>168*x**4 + 1218*x**2</answer>


Question:
Calculate the following: (-8*z**2 - 15*z - 28)*(-48*z**3 + 3*z**2 - 24*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: 384*z**5 + 696*z**4 + 1491*z**3 + 228*z**2 + 582*z - 168


Question:
Simplify this expression: -1296*y**3 + 243*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: -1296*y**3 + 243*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: -1296*y**3 + 243*y**2
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: -1296*y**3 + 243*y**2</replace>
No more calculations needed.
<answer>-1296*y**3 + 243*y**2</answer>


Question:
Simplify this expression: (5 - 31*y**3)*(-2*y**2 + 7*y - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (5 - 31*y**3)*(-2*y**2 + 7*y - 10)
Expanding the part (5 - 31*y**3) using the distributive property, and we got: (-31*y**3)*(-2*y**2 + 7*y - 10) + 5*(-2*y**2 + 7*y - 10)
<replace-#Step 1>#Step 2:
Current expression: (-31*y**3)*(-2*y**2 + 7*y - 10) + 5*(-2*y**2 + 7*y - 10)</replace>
Simplifying the partial expression: 5*(-2*y**2 + 7*y - 10)
Expanding the part (-2*y**2 + 7*y - 10) using the distributive property, and we got: (7*y)*5 - 2*y**2*5 - 10*5
Replacing 5*(-2*y**2 + 7*y - 10) with (7*y)*5 - 2*y**2*5 - 10*5 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*y)*5 - 2*y**2*5 + (-31*y**3)*(-2*y**2 + 7*y - 10) - 50</replace>
Simplifying the partial expression: (-31*y**3)*(-2*y**2 + 7*y - 10)
Expanding the part (-2*y**2 + 7*y - 10) using the distributive property, and we got: -(-1)*310*y**3 + (7*y)*(-31*y**3) + (-2*y**2)*(-31*y**3)
Replacing (-31*y**3)*(-2*y**2 + 7*y - 10) with -(-1)*310*y**3 + (7*y)*(-31*y**3) + (-2*y**2)*(-31*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -10*(-31)*y**3 + (7*y)*(-31*y**3) + (7*y)*5 + (-2*y**2)*(-31*y**3) - 2*y**2*5 - 50</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*y**2)*5 = -10*y**2
  (-2*y**2)*(-31*y**3) = 62*y**5
  (7*y)*5 = 35*y
  (7*y)*(-31*y**3) = -217*y**4
  -10*-31*y**3 = 310*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50</replace>
No more calculations needed.
<answer>62*y**5 - 217*y**4 + 310*y**3 - 10*y**2 + 35*y - 50</answer>


Question:
Simplify this expression: (50*y - 8)*(16*y**3 + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 800*y**4 - 128*y**3 + 300*y - 48

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*y - 8)*(16*y**3 + 6)
Expanding the part (50*y - 8) using the distributive property, and we got: (50*y)*(16*y**3 + 6) - 8*(16*y**3 + 6)
<replace-#Step 1>#Step 2:
Current expression: (50*y)*(16*y**3 + 6) - 8*(16*y**3 + 6)</replace>
Simplifying the partial expression: -8*(16*y**3 + 6)
Expanding the part (16*y**3 + 6) using the distributive property, and we got: (16*y**3)*(-8) + 6*(-8)
Replacing -8*(16*y**3 + 6) with (16*y**3)*(-8) + 6*(-8) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*y)*(16*y**3 + 6) + (16*y**3)*(-8) - 48</replace>
Simplifying the partial expression: (50*y)*(16*y**3 + 6)
Expanding the part (16*y**3 + 6) using the distributive property, and we got: 6*(50*y) + (50*y)*(16*y**3)
Replacing (50*y)*(16*y**3 + 6) with 6*(50*y) + (50*y)*(16*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 6*50*y + (50*y)*(16*y**3) + (16*y**3)*(-8) - 48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*y**3)*-8 = -128*y**3
  (16*y**3)*(50*y) = 800*y**4
  6*50*y = 300*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 800*y**4 - 128*y**3 + 300*y - 48</replace>
No more calculations needed.
<answer>800*y**4 - 128*y**3 + 300*y - 48</answer>


Question:
Calculate the following: (-45*x**3 - 3*x)*(-49*x**3 + 13*x**2 - 49*x + 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: 2205*x**6 - 585*x**5 + 2352*x**4 - 1884*x**3 + 147*x**2 - 123*x


Question:
Calculate the following: (-61*x**2 + 38*x)*(81*x**3 + 26*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: -4941*x**5 + 1492*x**4 + 988*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: (-61*x**2 + 38*x)*(81*x**3 + 26*x**2)
Expanding the part (-61*x**2 + 38*x) using the distributive property, and we got: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(81*x**3 + 26*x**2)
<replace-#Step 1>#Step 2:
Current expression: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(81*x**3 + 26*x**2)</replace>
Simplifying the partial expression: (-61*x**2)*(81*x**3 + 26*x**2)
Expanding the part (81*x**3 + 26*x**2) using the distributive property, and we got: (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)
Replacing (-61*x**2)*(81*x**3 + 26*x**2) with (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (38*x)*(81*x**3 + 26*x**2) + (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)</replace>
Simplifying the partial expression: (38*x)*(81*x**3 + 26*x**2)
Expanding the part (81*x**3 + 26*x**2) using the distributive property, and we got: (38*x)*(26*x**2) + (38*x)*(81*x**3)
Replacing (38*x)*(81*x**3 + 26*x**2) with (38*x)*(26*x**2) + (38*x)*(81*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (38*x)*(26*x**2) + (38*x)*(81*x**3) + (-61*x**2)*(26*x**2) + (-61*x**2)*(81*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (26*x**2)*(-61*x**2) = -1586*x**4
  (26*x**2)*(38*x) = 988*x**3
  (81*x**3)*(-61*x**2) = -4941*x**5
  (81*x**3)*(38*x) = 3078*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -4941*x**5 - 1586*x**4 + 3078*x**4 + 988*x**3</replace>
Combining like terms, got -4941*x**5 + 1492*x**4 + 988*x**3
<replace-#Step 5>#Step 6:
Current expression: -4941*x**5 + 1492*x**4 + 988*x**3</replace>
No more calculations needed.
<answer>-4941*x**5 + 1492*x**4 + 988*x**3</answer>


Question:
Calculate the following: -26*z**3*(24*z**2 - 49*z - 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -624*z**5 + 1274*z**4 + 598*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: -26*z**3*(24*z**2 - 49*z - 23)
Expanding the part (24*z**2 - 49*z - 23) using the distributive property, and we got: (-49*z)*(-26*z**3) - (-1)*598*z**3 + (24*z**2)*(-26*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-49*z)*(-26*z**3) - (-1)*598*z**3 + (24*z**2)*(-26*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -23*(-26*z**3) = 598*z**3
  (-49*z)*(-26*z**3) = 1274*z**4
  (24*z**2)*(-26*z**3) = -624*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -624*z**5 + 1274*z**4 + 598*z**3</replace>
No more calculations needed.
<answer>-624*z**5 + 1274*z**4 + 598*z**3</answer>


Question:
Calculate the following: -28*z**3 - 1344*z**2 + 56
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: -28*z**3 - 1344*z**2 + 56

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*z**3 - 1344*z**2 + 56
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: -28*z**3 - 1344*z**2 + 56</replace>
No more calculations needed.
<answer>-28*z**3 - 1344*z**2 + 56</answer>


Question:
Simplify this expression: (-20*x**3 - 51*x**2 - 32*x)*(-42*x**3 + 44*x**2 + 32*x - 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: 840*x**6 + 1262*x**5 - 1540*x**4 - 2520*x**3 + 302*x**2 + 832*x


Question:
Simplify this expression: (14*y**3 - 21)*(-39*y**3 + 13*y**2 - 15*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: -546*y**6 + 182*y**5 - 210*y**4 + 819*y**3 - 273*y**2 + 315*y


Question:
Simplify this expression: (25*z**2 - 24*z)*(23*z**3 + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 575*z**5 - 552*z**4 + 1050*z**2 - 1008*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: (25*z**2 - 24*z)*(23*z**3 + 42)
Expanding the part (23*z**3 + 42) using the distributive property, and we got: (23*z**3)*(25*z**2 - 24*z) + 42*(25*z**2 - 24*z)
<replace-#Step 1>#Step 2:
Current expression: (23*z**3)*(25*z**2 - 24*z) + 42*(25*z**2 - 24*z)</replace>
Simplifying the partial expression: 42*(25*z**2 - 24*z)
Expanding the part (25*z**2 - 24*z) using the distributive property, and we got: -24*z*42 + (25*z**2)*42
Replacing 42*(25*z**2 - 24*z) with -24*z*42 + (25*z**2)*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*z*42 + (25*z**2)*42 + (23*z**3)*(25*z**2 - 24*z)</replace>
Simplifying the partial expression: (23*z**3)*(25*z**2 - 24*z)
Expanding the part (25*z**2 - 24*z) using the distributive property, and we got: (-24*z)*(23*z**3) + (25*z**2)*(23*z**3)
Replacing (23*z**3)*(25*z**2 - 24*z) with (-24*z)*(23*z**3) + (25*z**2)*(23*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*z)*(23*z**3) - 24*z*42 + (25*z**2)*(23*z**3) + (25*z**2)*42</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*z)*42 = -1008*z
  (-24*z)*(23*z**3) = -552*z**4
  (25*z**2)*42 = 1050*z**2
  (25*z**2)*(23*z**3) = 575*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 575*z**5 - 552*z**4 + 1050*z**2 - 1008*z</replace>
No more calculations needed.
<answer>575*z**5 - 552*z**4 + 1050*z**2 - 1008*z</answer>


Question:
Calculate the following: (9*x**3 - 25*x**2 + 25*x)*(37*x**3 - 26*x**2 - 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 333*x**6 - 1159*x**5 + 1575*x**4 - 731*x**3 + 225*x**2 - 225*x


Question:
Calculate the following: (-41*z**3 - 33)*(-30*z**3 - 36*z**2 - 47*z + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1230*z**6 + 1476*z**5 + 1927*z**4 - 855*z**3 + 1188*z**2 + 1551*z - 1485


Question:
Calculate the following: (25 - 18*x**2)*(-16*x**3 + 5*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: 288*x**5 - 490*x**3 + 125*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: (25 - 18*x**2)*(-16*x**3 + 5*x)
Expanding the part (25 - 18*x**2) using the distributive property, and we got: (-18*x**2)*(-16*x**3 + 5*x) + 25*(-16*x**3 + 5*x)
<replace-#Step 1>#Step 2:
Current expression: (-18*x**2)*(-16*x**3 + 5*x) + 25*(-16*x**3 + 5*x)</replace>
Simplifying the partial expression: 25*(-16*x**3 + 5*x)
Expanding the part (-16*x**3 + 5*x) using the distributive property, and we got: (5*x)*25 - 16*x**3*25
Replacing 25*(-16*x**3 + 5*x) with (5*x)*25 - 16*x**3*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*x)*25 + (-18*x**2)*(-16*x**3 + 5*x) - 16*x**3*25</replace>
Simplifying the partial expression: (-18*x**2)*(-16*x**3 + 5*x)
Expanding the part (-16*x**3 + 5*x) using the distributive property, and we got: (5*x)*(-18*x**2) + (-18*x**2)*(-16*x**3)
Replacing (-18*x**2)*(-16*x**3 + 5*x) with (5*x)*(-18*x**2) + (-18*x**2)*(-16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (5*x)*(-18*x**2) + (5*x)*25 + (-18*x**2)*(-16*x**3) - 16*x**3*25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*x**3)*25 = -400*x**3
  (-16*x**3)*(-18*x**2) = 288*x**5
  (5*x)*25 = 125*x
  (5*x)*(-18*x**2) = -90*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 288*x**5 - 400*x**3 - 90*x**3 + 125*x</replace>
Combining like terms, got 288*x**5 - 490*x**3 + 125*x
<replace-#Step 5>#Step 6:
Current expression: 288*x**5 - 490*x**3 + 125*x</replace>
No more calculations needed.
<answer>288*x**5 - 490*x**3 + 125*x</answer>


Question:
Calculate the following: -12*z**3*(7*z**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: -84*z**5 + 696*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: -12*z**3*(7*z**2 - 58)
Expanding the part (7*z**2 - 58) using the distributive property, and we got: -(-1)*696*z**3 + (7*z**2)*(-12*z**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*696*z**3 + (7*z**2)*(-12*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -58*(-12*z**3) = 696*z**3
  (7*z**2)*(-12*z**3) = -84*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -84*z**5 + 696*z**3</replace>
No more calculations needed.
<answer>-84*z**5 + 696*z**3</answer>


Question:
Calculate the following: 24*y**3*(-77*y**3 + 37*y**2 + 31*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1848*y**6 + 888*y**5 + 744*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: 24*y**3*(-77*y**3 + 37*y**2 + 31*y)
Expanding the part (-77*y**3 + 37*y**2 + 31*y) using the distributive property, and we got: (31*y)*(24*y**3) + (37*y**2)*(24*y**3) + (-77*y**3)*(24*y**3)
<replace-#Step 1>#Step 2:
Current expression: (31*y)*(24*y**3) + (37*y**2)*(24*y**3) + (-77*y**3)*(24*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-77*y**3)*(24*y**3) = -1848*y**6
  (31*y)*(24*y**3) = 744*y**4
  (37*y**2)*(24*y**3) = 888*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1848*y**6 + 888*y**5 + 744*y**4</replace>
No more calculations needed.
<answer>-1848*y**6 + 888*y**5 + 744*y**4</answer>


Question:
Simplify this expression: (21*z**2 + 20*z + 27)*(-19*z**3 - 13*z + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -399*z**5 - 380*z**4 - 786*z**3 + 622*z**2 + 489*z + 1134


Question:
Calculate the following: (10*x - 43)*(20*x**3 + 12*x**2 + 43*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 200*x**4 - 740*x**3 - 86*x**2 - 1849*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: (10*x - 43)*(20*x**3 + 12*x**2 + 43*x)
Expanding the part (10*x - 43) using the distributive property, and we got: (10*x)*(20*x**3 + 12*x**2 + 43*x) - 43*(20*x**3 + 12*x**2 + 43*x)
<replace-#Step 1>#Step 2:
Current expression: (10*x)*(20*x**3 + 12*x**2 + 43*x) - 43*(20*x**3 + 12*x**2 + 43*x)</replace>
Simplifying the partial expression: -43*(20*x**3 + 12*x**2 + 43*x)
Expanding the part (20*x**3 + 12*x**2 + 43*x) using the distributive property, and we got: (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)
Replacing -43*(20*x**3 + 12*x**2 + 43*x) with (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*x)*(20*x**3 + 12*x**2 + 43*x) + (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)</replace>
Simplifying the partial expression: (10*x)*(20*x**3 + 12*x**2 + 43*x)
Expanding the part (20*x**3 + 12*x**2 + 43*x) using the distributive property, and we got: (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3)
Replacing (10*x)*(20*x**3 + 12*x**2 + 43*x) with (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*x)*(43*x) + (10*x)*(12*x**2) + (10*x)*(20*x**3) + (43*x)*(-43) + (12*x**2)*(-43) + (20*x**3)*(-43)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*x**2)*-43 = -516*x**2
  (12*x**2)*(10*x) = 120*x**3
  (20*x**3)*-43 = -860*x**3
  (20*x**3)*(10*x) = 200*x**4
  (43*x)*-43 = -1849*x
  (43*x)*(10*x) = 430*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 200*x**4 - 860*x**3 + 120*x**3 - 516*x**2 + 430*x**2 - 1849*x</replace>
Combining like terms, got 200*x**4 - 740*x**3 - 86*x**2 - 1849*x
<replace-#Step 5>#Step 6:
Current expression: 200*x**4 - 740*x**3 - 86*x**2 - 1849*x</replace>
No more calculations needed.
<answer>200*x**4 - 740*x**3 - 86*x**2 - 1849*x</answer>


Question:
Simplify this expression: 34*x**3*(-27*x**2 + 18*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: -918*x**5 + 612*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: 34*x**3*(-27*x**2 + 18*x)
Expanding the part (-27*x**2 + 18*x) using the distributive property, and we got: (18*x)*(34*x**3) + (-27*x**2)*(34*x**3)
<replace-#Step 1>#Step 2:
Current expression: (18*x)*(34*x**3) + (-27*x**2)*(34*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*x**2)*(34*x**3) = -918*x**5
  (18*x)*(34*x**3) = 612*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -918*x**5 + 612*x**4</replace>
No more calculations needed.
<answer>-918*x**5 + 612*x**4</answer>


Question:
Calculate the following: (-34*z**3 - 44)*(-13*z**3 - 48*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: 442*z**6 + 1632*z**5 + 572*z**3 + 2112*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: (-34*z**3 - 44)*(-13*z**3 - 48*z**2)
Expanding the part (-34*z**3 - 44) using the distributive property, and we got: (-34*z**3)*(-13*z**3 - 48*z**2) - 44*(-13*z**3 - 48*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-34*z**3)*(-13*z**3 - 48*z**2) - 44*(-13*z**3 - 48*z**2)</replace>
Simplifying the partial expression: -44*(-13*z**3 - 48*z**2)
Expanding the part (-13*z**3 - 48*z**2) using the distributive property, and we got: -48*z**2*(-44) - 13*z**3*(-44)
Replacing -44*(-13*z**3 - 48*z**2) with -48*z**2*(-44) - 13*z**3*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*z**2*(-44) + (-34*z**3)*(-13*z**3 - 48*z**2) - 13*z**3*(-44)</replace>
Simplifying the partial expression: (-34*z**3)*(-13*z**3 - 48*z**2)
Expanding the part (-13*z**3 - 48*z**2) using the distributive property, and we got: (-48*z**2)*(-34*z**3) + (-34*z**3)*(-13*z**3)
Replacing (-34*z**3)*(-13*z**3 - 48*z**2) with (-48*z**2)*(-34*z**3) + (-34*z**3)*(-13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*z**2)*(-34*z**3) - 48*z**2*(-44) + (-34*z**3)*(-13*z**3) - 13*z**3*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*z**2)*-44 = 2112*z**2
  (-48*z**2)*(-34*z**3) = 1632*z**5
  (-13*z**3)*-44 = 572*z**3
  (-13*z**3)*(-34*z**3) = 442*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2</replace>
No more calculations needed.
<answer>442*z**6 + 1632*z**5 + 572*z**3 + 2112*z**2</answer>


Question:
Simplify this expression: -53*z**3*(-14*z**2 + z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 742*z**5 - 53*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -53*z**3*(-14*z**2 + z)
Expanding the part (-14*z**2 + z) using the distributive property, and we got: z*(-53*z**3) + (-14*z**2)*(-53*z**3)
<replace-#Step 1>#Step 2:
Current expression: z*(-53*z**3) + (-14*z**2)*(-53*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  z*(-53*z**3) = -53*z**4
  (-14*z**2)*(-53*z**3) = 742*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 742*z**5 - 53*z**4</replace>
No more calculations needed.
<answer>742*z**5 - 53*z**4</answer>


Question:
Calculate the following: 58*y**2*(13*y**3 + 22*y + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 754*y**5 + 1276*y**3 + 1798*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: 58*y**2*(13*y**3 + 22*y + 31)
Expanding the part (13*y**3 + 22*y + 31) using the distributive property, and we got: 31*(58*y**2) + (22*y)*(58*y**2) + (58*y**2)*(13*y**3)
<replace-#Step 1>#Step 2:
Current expression: 31*(58*y**2) + (22*y)*(58*y**2) + (58*y**2)*(13*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  31*(58*y**2) = 1798*y**2
  (13*y**3)*(58*y**2) = 754*y**5
  (22*y)*(58*y**2) = 1276*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 754*y**5 + 1276*y**3 + 1798*y**2</replace>
No more calculations needed.
<answer>754*y**5 + 1276*y**3 + 1798*y**2</answer>


Question:
Calculate the following: (-41*x**2 - 30)*(-29*x**3 - 56*x**2 + 21*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1189*x**5 + 2296*x**4 + 9*x**3 + 1680*x**2 - 630*x


Question:
Simplify this expression: -540*z**3 + 1260*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: -540*z**3 + 1260*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: -540*z**3 + 1260*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -540*z**3 + 1260*z</replace>
No more calculations needed.
<answer>-540*z**3 + 1260*z</answer>


Question:
Calculate the following: (9*y**3 + 9*y**2)*(-39*y**3 - 47*y**2 - 23*y - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -351*y**6 - 774*y**5 - 630*y**4 - 405*y**3 - 198*y**2


Question:
Calculate the following: (-44*y**3 + 51*y + 28)*(20*y**3 - 31*y**2 + 28*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: -880*y**6 + 1364*y**5 - 212*y**4 - 1021*y**3 + 560*y**2 + 784*y


Question:
Calculate the following: (-62*x**3 - 6)*(-21*x**2 - 28*x - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-62*x**3 - 6)*(-21*x**2 - 28*x - 14)
Expanding the part (-62*x**3 - 6) using the distributive property, and we got: (-62*x**3)*(-21*x**2 - 28*x - 14) - 6*(-21*x**2 - 28*x - 14)
<replace-#Step 1>#Step 2:
Current expression: (-62*x**3)*(-21*x**2 - 28*x - 14) - 6*(-21*x**2 - 28*x - 14)</replace>
Simplifying the partial expression: -6*(-21*x**2 - 28*x - 14)
Expanding the part (-21*x**2 - 28*x - 14) using the distributive property, and we got: -28*x*(-6) - 21*x**2*(-6) - 14*(-6)
Replacing -6*(-21*x**2 - 28*x - 14) with -28*x*(-6) - 21*x**2*(-6) - 14*(-6) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*x*(-6) - 21*x**2*(-6) + (-62*x**3)*(-21*x**2 - 28*x - 14) + 84</replace>
Simplifying the partial expression: (-62*x**3)*(-21*x**2 - 28*x - 14)
Expanding the part (-21*x**2 - 28*x - 14) using the distributive property, and we got: (-28*x)*(-62*x**3) - (-1)*868*x**3 + (-21*x**2)*(-62*x**3)
Replacing (-62*x**3)*(-21*x**2 - 28*x - 14) with (-28*x)*(-62*x**3) - (-1)*868*x**3 + (-21*x**2)*(-62*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*x)*(-62*x**3) - 28*x*(-6) - 14*(-62)*x**3 + (-21*x**2)*(-62*x**3) - 21*x**2*(-6) + 84</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*x)*-6 = 168*x
  (-28*x)*(-62*x**3) = 1736*x**4
  (-21*x**2)*-6 = 126*x**2
  (-21*x**2)*(-62*x**3) = 1302*x**5
  -14*-62*x**3 = 868*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84</replace>
No more calculations needed.
<answer>1302*x**5 + 1736*x**4 + 868*x**3 + 126*x**2 + 168*x + 84</answer>


Question:
Calculate the following: (29 - 4*x)*(28*x**3 + 7*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: -112*x**4 + 784*x**3 + 203*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29 - 4*x)*(28*x**3 + 7*x**2)
Expanding the part (29 - 4*x) using the distributive property, and we got: (-4*x)*(28*x**3 + 7*x**2) + 29*(28*x**3 + 7*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-4*x)*(28*x**3 + 7*x**2) + 29*(28*x**3 + 7*x**2)</replace>
Simplifying the partial expression: 29*(28*x**3 + 7*x**2)
Expanding the part (28*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*29 + (28*x**3)*29
Replacing 29*(28*x**3 + 7*x**2) with (7*x**2)*29 + (28*x**3)*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-4*x)*(28*x**3 + 7*x**2) + (7*x**2)*29 + (28*x**3)*29</replace>
Simplifying the partial expression: (-4*x)*(28*x**3 + 7*x**2)
Expanding the part (28*x**3 + 7*x**2) using the distributive property, and we got: (-4*x)*(7*x**2) + (-4*x)*(28*x**3)
Replacing (-4*x)*(28*x**3 + 7*x**2) with (-4*x)*(7*x**2) + (-4*x)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*x)*(7*x**2) + (-4*x)*(28*x**3) + (7*x**2)*29 + (28*x**3)*29</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*x**2)*29 = 203*x**2
  (7*x**2)*(-4*x) = -28*x**3
  (28*x**3)*29 = 812*x**3
  (28*x**3)*(-4*x) = -112*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -112*x**4 - 28*x**3 + 812*x**3 + 203*x**2</replace>
Combining like terms, got -112*x**4 + 784*x**3 + 203*x**2
<replace-#Step 5>#Step 6:
Current expression: -112*x**4 + 784*x**3 + 203*x**2</replace>
No more calculations needed.
<answer>-112*x**4 + 784*x**3 + 203*x**2</answer>


Question:
Calculate the following: 32*z*(-91*z**3 + 32*z**2 + 4*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: -2912*z**4 + 1024*z**3 + 128*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: 32*z*(-91*z**3 + 32*z**2 + 4*z)
Expanding the part (-91*z**3 + 32*z**2 + 4*z) using the distributive property, and we got: (4*z)*(32*z) + (32*z)*(32*z**2) + (32*z)*(-91*z**3)
<replace-#Step 1>#Step 2:
Current expression: (4*z)*(32*z) + (32*z)*(32*z**2) + (32*z)*(-91*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-91*z**3)*(32*z) = -2912*z**4
  (4*z)*(32*z) = 128*z**2
  (32*z**2)*(32*z) = 1024*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2912*z**4 + 1024*z**3 + 128*z**2</replace>
No more calculations needed.
<answer>-2912*z**4 + 1024*z**3 + 128*z**2</answer>


Question:
Simplify this expression: (-31*x**3 + 41*x**2)*(8*x**3 - 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -248*x**6 + 328*x**5 + 93*x**3 - 123*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: (-31*x**3 + 41*x**2)*(8*x**3 - 3)
Expanding the part (8*x**3 - 3) using the distributive property, and we got: (8*x**3)*(-31*x**3 + 41*x**2) - 3*(-31*x**3 + 41*x**2)
<replace-#Step 1>#Step 2:
Current expression: (8*x**3)*(-31*x**3 + 41*x**2) - 3*(-31*x**3 + 41*x**2)</replace>
Simplifying the partial expression: -3*(-31*x**3 + 41*x**2)
Expanding the part (-31*x**3 + 41*x**2) using the distributive property, and we got: (41*x**2)*(-3) - 31*x**3*(-3)
Replacing -3*(-31*x**3 + 41*x**2) with (41*x**2)*(-3) - 31*x**3*(-3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (41*x**2)*(-3) - 31*x**3*(-3) + (8*x**3)*(-31*x**3 + 41*x**2)</replace>
Simplifying the partial expression: (8*x**3)*(-31*x**3 + 41*x**2)
Expanding the part (-31*x**3 + 41*x**2) using the distributive property, and we got: (41*x**2)*(8*x**3) + (-31*x**3)*(8*x**3)
Replacing (8*x**3)*(-31*x**3 + 41*x**2) with (41*x**2)*(8*x**3) + (-31*x**3)*(8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (41*x**2)*(8*x**3) + (41*x**2)*(-3) + (-31*x**3)*(8*x**3) - 31*x**3*(-3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*x**3)*-3 = 93*x**3
  (-31*x**3)*(8*x**3) = -248*x**6
  (41*x**2)*-3 = -123*x**2
  (41*x**2)*(8*x**3) = 328*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -248*x**6 + 328*x**5 + 93*x**3 - 123*x**2</replace>
No more calculations needed.
<answer>-248*x**6 + 328*x**5 + 93*x**3 - 123*x**2</answer>


Question:
Simplify this expression: (32 - 3*y**2)*(35*y**3 + 35*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: -105*y**5 - 105*y**4 + 1120*y**3 + 1120*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: (32 - 3*y**2)*(35*y**3 + 35*y**2)
Expanding the part (32 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(35*y**3 + 35*y**2) + 32*(35*y**3 + 35*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-3*y**2)*(35*y**3 + 35*y**2) + 32*(35*y**3 + 35*y**2)</replace>
Simplifying the partial expression: 32*(35*y**3 + 35*y**2)
Expanding the part (35*y**3 + 35*y**2) using the distributive property, and we got: (35*y**2)*32 + (35*y**3)*32
Replacing 32*(35*y**3 + 35*y**2) with (35*y**2)*32 + (35*y**3)*32 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-3*y**2)*(35*y**3 + 35*y**2) + (35*y**2)*32 + (35*y**3)*32</replace>
Simplifying the partial expression: (-3*y**2)*(35*y**3 + 35*y**2)
Expanding the part (35*y**3 + 35*y**2) using the distributive property, and we got: (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3)
Replacing (-3*y**2)*(35*y**3 + 35*y**2) with (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*y**2)*(35*y**2) + (-3*y**2)*(35*y**3) + (35*y**2)*32 + (35*y**3)*32</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*y**2)*32 = 1120*y**2
  (35*y**2)*(-3*y**2) = -105*y**4
  (35*y**3)*32 = 1120*y**3
  (35*y**3)*(-3*y**2) = -105*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2</replace>
No more calculations needed.
<answer>-105*y**5 - 105*y**4 + 1120*y**3 + 1120*y**2</answer>


Question:
Calculate the following: -8*y*(43*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: -344*y**2 - 128*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: -8*y*(43*y + 16)
Expanding the part (43*y + 16) using the distributive property, and we got: (-8*y)*(43*y) + 16*(-8*y)
<replace-#Step 1>#Step 2:
Current expression: (-8*y)*(43*y) + 16*(-8*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  16*(-8*y) = -128*y
  (43*y)*(-8*y) = -344*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -344*y**2 - 128*y</replace>
No more calculations needed.
<answer>-344*y**2 - 128*y</answer>


Question:
Calculate the following: (-43*z**2 - 44*z - 45)*(33*z**3 + 2*z**2 + 12*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: -1419*z**5 - 1538*z**4 - 2089*z**3 - 618*z**2 - 540*z


Question:
Simplify this expression: 12*y**3*(-15*y**3 - 23*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: -180*y**6 - 276*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: 12*y**3*(-15*y**3 - 23*y**2)
Expanding the part (-15*y**3 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(12*y**3) + (-15*y**3)*(12*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-23*y**2)*(12*y**3) + (-15*y**3)*(12*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*y**2)*(12*y**3) = -276*y**5
  (-15*y**3)*(12*y**3) = -180*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -180*y**6 - 276*y**5</replace>
No more calculations needed.
<answer>-180*y**6 - 276*y**5</answer>


Question:
Simplify this expression: (4 - 5*x**3)*(-35*x**3 + 35*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: 175*x**6 - 175*x**5 - 140*x**3 + 140*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 - 5*x**3)*(-35*x**3 + 35*x**2)
Expanding the part (4 - 5*x**3) using the distributive property, and we got: (-5*x**3)*(-35*x**3 + 35*x**2) + 4*(-35*x**3 + 35*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-5*x**3)*(-35*x**3 + 35*x**2) + 4*(-35*x**3 + 35*x**2)</replace>
Simplifying the partial expression: 4*(-35*x**3 + 35*x**2)
Expanding the part (-35*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*4 - 35*x**3*4
Replacing 4*(-35*x**3 + 35*x**2) with (35*x**2)*4 - 35*x**3*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*x**2)*4 - 35*x**3*4 + (-5*x**3)*(-35*x**3 + 35*x**2)</replace>
Simplifying the partial expression: (-5*x**3)*(-35*x**3 + 35*x**2)
Expanding the part (-35*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-5*x**3) + (-35*x**3)*(-5*x**3)
Replacing (-5*x**3)*(-35*x**3 + 35*x**2) with (35*x**2)*(-5*x**3) + (-35*x**3)*(-5*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (35*x**2)*(-5*x**3) + (35*x**2)*4 + (-35*x**3)*(-5*x**3) - 35*x**3*4</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x**3)*4 = -140*x**3
  (-35*x**3)*(-5*x**3) = 175*x**6
  (35*x**2)*4 = 140*x**2
  (35*x**2)*(-5*x**3) = -175*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 175*x**6 - 175*x**5 - 140*x**3 + 140*x**2</replace>
No more calculations needed.
<answer>175*x**6 - 175*x**5 - 140*x**3 + 140*x**2</answer>


Question:
Simplify this expression: -512*z**3 - 64
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: -512*z**3 - 64

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: -512*z**3 - 64
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: -512*z**3 - 64</replace>
No more calculations needed.
<answer>-512*z**3 - 64</answer>


Question:
Simplify this expression: 49*x**3*(47*x**2 - 35*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: 2303*x**5 - 1715*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: 49*x**3*(47*x**2 - 35*x)
Expanding the part (47*x**2 - 35*x) using the distributive property, and we got: (-35*x)*(49*x**3) + (47*x**2)*(49*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-35*x)*(49*x**3) + (47*x**2)*(49*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x)*(49*x**3) = -1715*x**4
  (47*x**2)*(49*x**3) = 2303*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2303*x**5 - 1715*x**4</replace>
No more calculations needed.
<answer>2303*x**5 - 1715*x**4</answer>