Question:
Simplify this expression: (27*x**2 - 36)*(13*x**3 + 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: 351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*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: (27*x**2 - 36)*(13*x**3 + x**2 + 4*x)
Expanding the part (27*x**2 - 36) using the distributive property, and we got: (27*x**2)*(13*x**3 + x**2 + 4*x) - 36*(13*x**3 + x**2 + 4*x)
<replace-#Step 1>#Step 2:
Current expression: (27*x**2)*(13*x**3 + x**2 + 4*x) - 36*(13*x**3 + x**2 + 4*x)</replace>
Simplifying the partial expression: -36*(13*x**3 + x**2 + 4*x)
Expanding the part (13*x**3 + x**2 + 4*x) using the distributive property, and we got: x**2*(-36) + (4*x)*(-36) + (13*x**3)*(-36)
Replacing -36*(13*x**3 + x**2 + 4*x) with x**2*(-36) + (4*x)*(-36) + (13*x**3)*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: x**2*(-36) + (4*x)*(-36) + (27*x**2)*(13*x**3 + x**2 + 4*x) + (13*x**3)*(-36)</replace>
Simplifying the partial expression: (27*x**2)*(13*x**3 + x**2 + 4*x)
Expanding the part (13*x**3 + x**2 + 4*x) using the distributive property, and we got: x**2*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(13*x**3)
Replacing (27*x**2)*(13*x**3 + x**2 + 4*x) with x**2*(27*x**2) + (4*x)*(27*x**2) + (27*x**2)*(13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: x**2*(27*x**2) + x**2*(-36) + (4*x)*(27*x**2) + (4*x)*(-36) + (27*x**2)*(13*x**3) + (13*x**3)*(-36)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x**2*-36 = -36*x**2
  x**2*(27*x**2) = 27*x**4
  (4*x)*-36 = -144*x
  (4*x)*(27*x**2) = 108*x**3
  (13*x**3)*-36 = -468*x**3
  (13*x**3)*(27*x**2) = 351*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 351*x**5 + 27*x**4 - 468*x**3 + 108*x**3 - 36*x**2 - 144*x</replace>
Combining like terms, got 351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x
<replace-#Step 5>#Step 6:
Current expression: 351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x</replace>
No more calculations needed.
<answer>351*x**5 + 27*x**4 - 360*x**3 - 36*x**2 - 144*x</answer>


Question:
Simplify this expression: (25 - 24*x)*(39 - 39*x**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 936*x**4 - 975*x**3 - 936*x + 975

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 - 24*x)*(39 - 39*x**3)
Expanding the part (25 - 24*x) using the distributive property, and we got: (-24*x)*(39 - 39*x**3) + 25*(39 - 39*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-24*x)*(39 - 39*x**3) + 25*(39 - 39*x**3)</replace>
Simplifying the partial expression: 25*(39 - 39*x**3)
Expanding the part (39 - 39*x**3) using the distributive property, and we got: -39*x**3*25 + 39*25
Replacing 25*(39 - 39*x**3) with -39*x**3*25 + 39*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-24*x)*(39 - 39*x**3) - 39*x**3*25 + 975</replace>
Simplifying the partial expression: (-24*x)*(39 - 39*x**3)
Expanding the part (39 - 39*x**3) using the distributive property, and we got: (-24*x)*(-39*x**3) + 39*(-24*x)
Replacing (-24*x)*(39 - 39*x**3) with (-24*x)*(-39*x**3) + 39*(-24*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*x)*(-39*x**3) + 39*(-24)*x - 39*x**3*25 + 975</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*25 = -975*x**3
  (-39*x**3)*(-24*x) = 936*x**4
  39*-24*x = -936*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 936*x**4 - 975*x**3 - 936*x + 975</replace>
No more calculations needed.
<answer>936*x**4 - 975*x**3 - 936*x + 975</answer>


Question:
Calculate the following: (-54*z**3 + 20*z)*(-54*z**2 + 42*z - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2916*z**5 - 2268*z**4 - 216*z**3 + 840*z**2 - 320*z


Question:
Simplify this expression: (-10*z**2 - 8*z)*(32*z**3 + 2*z - 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*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: (-10*z**2 - 8*z)*(32*z**3 + 2*z - 34)
Expanding the part (-10*z**2 - 8*z) using the distributive property, and we got: (-8*z)*(32*z**3 + 2*z - 34) + (-10*z**2)*(32*z**3 + 2*z - 34)
<replace-#Step 1>#Step 2:
Current expression: (-8*z)*(32*z**3 + 2*z - 34) + (-10*z**2)*(32*z**3 + 2*z - 34)</replace>
Simplifying the partial expression: (-10*z**2)*(32*z**3 + 2*z - 34)
Expanding the part (32*z**3 + 2*z - 34) using the distributive property, and we got: -(-1)*340*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3)
Replacing (-10*z**2)*(32*z**3 + 2*z - 34) with -(-1)*340*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-8*z)*(32*z**3 + 2*z - 34) - 34*(-10)*z**2 + (2*z)*(-10*z**2) + (-10*z**2)*(32*z**3)</replace>
Simplifying the partial expression: (-8*z)*(32*z**3 + 2*z - 34)
Expanding the part (32*z**3 + 2*z - 34) using the distributive property, and we got: (-8*z)*(2*z) + (-8*z)*(32*z**3) - (-1)*272*z
Replacing (-8*z)*(32*z**3 + 2*z - 34) with (-8*z)*(2*z) + (-8*z)*(32*z**3) - (-1)*272*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*z)*(2*z) + (-8*z)*(32*z**3) - 34*(-10)*z**2 - 34*(-8)*z + (2*z)*(-10*z**2) + (-10*z**2)*(32*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)*(-10*z**2) = -20*z**3
  (2*z)*(-8*z) = -16*z**2
  (32*z**3)*(-10*z**2) = -320*z**5
  (32*z**3)*(-8*z) = -256*z**4
  -34*-10*z**2 = 340*z**2
  -34*-8*z = 272*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -320*z**5 - 256*z**4 - 20*z**3 - 16*z**2 + 340*z**2 + 272*z</replace>
Combining like terms, got -320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z
<replace-#Step 5>#Step 6:
Current expression: -320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z</replace>
No more calculations needed.
<answer>-320*z**5 - 256*z**4 - 20*z**3 + 324*z**2 + 272*z</answer>


Question:
Calculate the following: -37*y**3*(-3*y**3 + 30*y - 1)
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: 111*y**6 - 1110*y**4 + 37*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -37*y**3*(-3*y**3 + 30*y - 1)
Expanding the part (-3*y**3 + 30*y - 1) using the distributive property, and we got: -(-1)*37*y**3 + (30*y)*(-37*y**3) + (-37*y**3)*(-3*y**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*37*y**3 + (30*y)*(-37*y**3) + (-37*y**3)*(-3*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -1*(-37*y**3) = 37*y**3
  (-3*y**3)*(-37*y**3) = 111*y**6
  (30*y)*(-37*y**3) = -1110*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 111*y**6 - 1110*y**4 + 37*y**3</replace>
No more calculations needed.
<answer>111*y**6 - 1110*y**4 + 37*y**3</answer>


Question:
Simplify this expression: (10 - 23*x**3)*(-38*x**3 + 28*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 874*x**6 - 644*x**4 - 380*x**3 + 280*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 - 23*x**3)*(-38*x**3 + 28*x)
Expanding the part (10 - 23*x**3) using the distributive property, and we got: (-23*x**3)*(-38*x**3 + 28*x) + 10*(-38*x**3 + 28*x)
<replace-#Step 1>#Step 2:
Current expression: (-23*x**3)*(-38*x**3 + 28*x) + 10*(-38*x**3 + 28*x)</replace>
Simplifying the partial expression: 10*(-38*x**3 + 28*x)
Expanding the part (-38*x**3 + 28*x) using the distributive property, and we got: (28*x)*10 - 38*x**3*10
Replacing 10*(-38*x**3 + 28*x) with (28*x)*10 - 38*x**3*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*x)*10 - 38*x**3*10 + (-23*x**3)*(-38*x**3 + 28*x)</replace>
Simplifying the partial expression: (-23*x**3)*(-38*x**3 + 28*x)
Expanding the part (-38*x**3 + 28*x) using the distributive property, and we got: (28*x)*(-23*x**3) + (-38*x**3)*(-23*x**3)
Replacing (-23*x**3)*(-38*x**3 + 28*x) with (28*x)*(-23*x**3) + (-38*x**3)*(-23*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*x)*(-23*x**3) + (28*x)*10 + (-38*x**3)*(-23*x**3) - 38*x**3*10</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**3)*10 = -380*x**3
  (-38*x**3)*(-23*x**3) = 874*x**6
  (28*x)*10 = 280*x
  (28*x)*(-23*x**3) = -644*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 874*x**6 - 644*x**4 - 380*x**3 + 280*x</replace>
No more calculations needed.
<answer>874*x**6 - 644*x**4 - 380*x**3 + 280*x</answer>


Question:
Calculate the following: (18 - 2*z**3)*(-22*z**3 - 78*z**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: 44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (18 - 2*z**3)*(-22*z**3 - 78*z**2 + 9)
Expanding the part (18 - 2*z**3) using the distributive property, and we got: (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 18*(-22*z**3 - 78*z**2 + 9)
<replace-#Step 1>#Step 2:
Current expression: (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 18*(-22*z**3 - 78*z**2 + 9)</replace>
Simplifying the partial expression: 18*(-22*z**3 - 78*z**2 + 9)
Expanding the part (-22*z**3 - 78*z**2 + 9) using the distributive property, and we got: -78*z**2*18 - 22*z**3*18 + 9*18
Replacing 18*(-22*z**3 - 78*z**2 + 9) with -78*z**2*18 - 22*z**3*18 + 9*18 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -78*z**2*18 - 22*z**3*18 + (-2*z**3)*(-22*z**3 - 78*z**2 + 9) + 162</replace>
Simplifying the partial expression: (-2*z**3)*(-22*z**3 - 78*z**2 + 9)
Expanding the part (-22*z**3 - 78*z**2 + 9) using the distributive property, and we got: 9*(-2*z**3) + (-78*z**2)*(-2*z**3) + (-22*z**3)*(-2*z**3)
Replacing (-2*z**3)*(-22*z**3 - 78*z**2 + 9) with 9*(-2*z**3) + (-78*z**2)*(-2*z**3) + (-22*z**3)*(-2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 9*(-2)*z**3 + (-78*z**2)*(-2*z**3) - 78*z**2*18 + (-22*z**3)*(-2*z**3) - 22*z**3*18 + 162</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-78*z**2)*18 = -1404*z**2
  (-78*z**2)*(-2*z**3) = 156*z**5
  (-22*z**3)*18 = -396*z**3
  (-22*z**3)*(-2*z**3) = 44*z**6
  9*-2*z**3 = -18*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 44*z**6 + 156*z**5 - 396*z**3 - 18*z**3 - 1404*z**2 + 162</replace>
Combining like terms, got 44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162
<replace-#Step 5>#Step 6:
Current expression: 44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162</replace>
No more calculations needed.
<answer>44*z**6 + 156*z**5 - 414*z**3 - 1404*z**2 + 162</answer>


Question:
Calculate the following: (12*x**2 + 42)*(3*x**3 + 35*x - 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: 36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (12*x**2 + 42)*(3*x**3 + 35*x - 27)
Expanding the part (12*x**2 + 42) using the distributive property, and we got: (12*x**2)*(3*x**3 + 35*x - 27) + 42*(3*x**3 + 35*x - 27)
<replace-#Step 1>#Step 2:
Current expression: (12*x**2)*(3*x**3 + 35*x - 27) + 42*(3*x**3 + 35*x - 27)</replace>
Simplifying the partial expression: 42*(3*x**3 + 35*x - 27)
Expanding the part (3*x**3 + 35*x - 27) using the distributive property, and we got: (35*x)*42 + (3*x**3)*42 - 27*42
Replacing 42*(3*x**3 + 35*x - 27) with (35*x)*42 + (3*x**3)*42 - 27*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*x)*42 + (12*x**2)*(3*x**3 + 35*x - 27) + (3*x**3)*42 - 1134</replace>
Simplifying the partial expression: (12*x**2)*(3*x**3 + 35*x - 27)
Expanding the part (3*x**3 + 35*x - 27) using the distributive property, and we got: -324*x**2 + (35*x)*(12*x**2) + (12*x**2)*(3*x**3)
Replacing (12*x**2)*(3*x**3 + 35*x - 27) with -324*x**2 + (35*x)*(12*x**2) + (12*x**2)*(3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -27*12*x**2 + (35*x)*(12*x**2) + (35*x)*42 + (12*x**2)*(3*x**3) + (3*x**3)*42 - 1134</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*x**3)*42 = 126*x**3
  (3*x**3)*(12*x**2) = 36*x**5
  (35*x)*42 = 1470*x
  (35*x)*(12*x**2) = 420*x**3
  -27*12*x**2 = -324*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 36*x**5 + 126*x**3 + 420*x**3 - 324*x**2 + 1470*x - 1134</replace>
Combining like terms, got 36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134
<replace-#Step 5>#Step 6:
Current expression: 36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134</replace>
No more calculations needed.
<answer>36*x**5 + 546*x**3 - 324*x**2 + 1470*x - 1134</answer>


Question:
Simplify this expression: (-28*z - 42)*(-27*z**3 + 34*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 756*z**4 + 1134*z**3 - 952*z**2 - 1428*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: (-28*z - 42)*(-27*z**3 + 34*z)
Expanding the part (-28*z - 42) using the distributive property, and we got: (-28*z)*(-27*z**3 + 34*z) - 42*(-27*z**3 + 34*z)
<replace-#Step 1>#Step 2:
Current expression: (-28*z)*(-27*z**3 + 34*z) - 42*(-27*z**3 + 34*z)</replace>
Simplifying the partial expression: -42*(-27*z**3 + 34*z)
Expanding the part (-27*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-42) - 27*z**3*(-42)
Replacing -42*(-27*z**3 + 34*z) with (34*z)*(-42) - 27*z**3*(-42) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-28*z)*(-27*z**3 + 34*z) + (34*z)*(-42) - 27*z**3*(-42)</replace>
Simplifying the partial expression: (-28*z)*(-27*z**3 + 34*z)
Expanding the part (-27*z**3 + 34*z) using the distributive property, and we got: (-28*z)*(34*z) + (-28*z)*(-27*z**3)
Replacing (-28*z)*(-27*z**3 + 34*z) with (-28*z)*(34*z) + (-28*z)*(-27*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*z)*(34*z) + (-28*z)*(-27*z**3) + (34*z)*(-42) - 27*z**3*(-42)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*z**3)*-42 = 1134*z**3
  (-27*z**3)*(-28*z) = 756*z**4
  (34*z)*-42 = -1428*z
  (34*z)*(-28*z) = -952*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 756*z**4 + 1134*z**3 - 952*z**2 - 1428*z</replace>
No more calculations needed.
<answer>756*z**4 + 1134*z**3 - 952*z**2 - 1428*z</answer>


Question:
Calculate the following: (16*x**2 + 38)*(-5*x**3 + 41*x**2 - 39*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: -80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*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: (16*x**2 + 38)*(-5*x**3 + 41*x**2 - 39*x)
Expanding the part (16*x**2 + 38) using the distributive property, and we got: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + 38*(-5*x**3 + 41*x**2 - 39*x)
<replace-#Step 1>#Step 2:
Current expression: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + 38*(-5*x**3 + 41*x**2 - 39*x)</replace>
Simplifying the partial expression: 38*(-5*x**3 + 41*x**2 - 39*x)
Expanding the part (-5*x**3 + 41*x**2 - 39*x) using the distributive property, and we got: -39*x*38 + (41*x**2)*38 - 5*x**3*38
Replacing 38*(-5*x**3 + 41*x**2 - 39*x) with -39*x*38 + (41*x**2)*38 - 5*x**3*38 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*x*38 + (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) + (41*x**2)*38 - 5*x**3*38</replace>
Simplifying the partial expression: (16*x**2)*(-5*x**3 + 41*x**2 - 39*x)
Expanding the part (-5*x**3 + 41*x**2 - 39*x) using the distributive property, and we got: (-39*x)*(16*x**2) + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3)
Replacing (16*x**2)*(-5*x**3 + 41*x**2 - 39*x) with (-39*x)*(16*x**2) + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*x)*(16*x**2) - 39*x*38 + (16*x**2)*(41*x**2) + (16*x**2)*(-5*x**3) + (41*x**2)*38 - 5*x**3*38</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x)*38 = -1482*x
  (-39*x)*(16*x**2) = -624*x**3
  (-5*x**3)*38 = -190*x**3
  (-5*x**3)*(16*x**2) = -80*x**5
  (41*x**2)*38 = 1558*x**2
  (41*x**2)*(16*x**2) = 656*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -80*x**5 + 656*x**4 - 624*x**3 - 190*x**3 + 1558*x**2 - 1482*x</replace>
Combining like terms, got -80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x
<replace-#Step 5>#Step 6:
Current expression: -80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x</replace>
No more calculations needed.
<answer>-80*x**5 + 656*x**4 - 814*x**3 + 1558*x**2 - 1482*x</answer>


Question:
Simplify this expression: (x**2 + 44*x)*(32*x**3 - 13*x**2 - 20*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: 32*x**5 + 1395*x**4 - 592*x**3 - 880*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: (x**2 + 44*x)*(32*x**3 - 13*x**2 - 20*x)
Expanding the part (x**2 + 44*x) using the distributive property, and we got: x**2*(32*x**3 - 13*x**2 - 20*x) + (44*x)*(32*x**3 - 13*x**2 - 20*x)
<replace-#Step 1>#Step 2:
Current expression: x**2*(32*x**3 - 13*x**2 - 20*x) + (44*x)*(32*x**3 - 13*x**2 - 20*x)</replace>
Simplifying the partial expression: x**2*(32*x**3 - 13*x**2 - 20*x)
Expanding the part (32*x**3 - 13*x**2 - 20*x) using the distributive property, and we got: (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3)
Replacing x**2*(32*x**3 - 13*x**2 - 20*x) with (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*x)*x**2 + (-13*x**2)*x**2 + x**2*(32*x**3) + (44*x)*(32*x**3 - 13*x**2 - 20*x)</replace>
Simplifying the partial expression: (44*x)*(32*x**3 - 13*x**2 - 20*x)
Expanding the part (32*x**3 - 13*x**2 - 20*x) using the distributive property, and we got: (-20*x)*(44*x) + (44*x)*(-13*x**2) + (44*x)*(32*x**3)
Replacing (44*x)*(32*x**3 - 13*x**2 - 20*x) with (-20*x)*(44*x) + (44*x)*(-13*x**2) + (44*x)*(32*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*x)*x**2 + (-20*x)*(44*x) + (-13*x**2)*x**2 + x**2*(32*x**3) + (44*x)*(-13*x**2) + (44*x)*(32*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x)*x**2 = -20*x**3
  (-20*x)*(44*x) = -880*x**2
  (-13*x**2)*x**2 = -13*x**4
  (-13*x**2)*(44*x) = -572*x**3
  (32*x**3)*x**2 = 32*x**5
  (32*x**3)*(44*x) = 1408*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 32*x**5 - 13*x**4 + 1408*x**4 - 572*x**3 - 20*x**3 - 880*x**2</replace>
Combining like terms, got 32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2
<replace-#Step 5>#Step 6:
Current expression: 32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2</replace>
No more calculations needed.
<answer>32*x**5 + 1395*x**4 - 592*x**3 - 880*x**2</answer>


Question:
Simplify this expression: (36*x**3 + 37*x)*(-43*x**3 + 23*x**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: -1548*x**6 + 828*x**5 - 1591*x**4 + 23*x**3 - 851*x


Question:
Simplify this expression: -9*z**2*(43*z**3 + 2*z - 33)
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: -387*z**5 - 18*z**3 + 297*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: -9*z**2*(43*z**3 + 2*z - 33)
Expanding the part (43*z**3 + 2*z - 33) using the distributive property, and we got: -(-1)*297*z**2 + (2*z)*(-9*z**2) + (-9*z**2)*(43*z**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*297*z**2 + (2*z)*(-9*z**2) + (-9*z**2)*(43*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -33*(-9*z**2) = 297*z**2
  (2*z)*(-9*z**2) = -18*z**3
  (43*z**3)*(-9*z**2) = -387*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -387*z**5 - 18*z**3 + 297*z**2</replace>
No more calculations needed.
<answer>-387*z**5 - 18*z**3 + 297*z**2</answer>


Question:
Calculate the following: (-59*z**3 - 37*z)*(-49*z**3 - 39*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: 2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*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: (-59*z**3 - 37*z)*(-49*z**3 - 39*z**2)
Expanding the part (-59*z**3 - 37*z) using the distributive property, and we got: (-37*z)*(-49*z**3 - 39*z**2) + (-59*z**3)*(-49*z**3 - 39*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-37*z)*(-49*z**3 - 39*z**2) + (-59*z**3)*(-49*z**3 - 39*z**2)</replace>
Simplifying the partial expression: (-59*z**3)*(-49*z**3 - 39*z**2)
Expanding the part (-49*z**3 - 39*z**2) using the distributive property, and we got: (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)
Replacing (-59*z**3)*(-49*z**3 - 39*z**2) with (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*z)*(-49*z**3 - 39*z**2) + (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)</replace>
Simplifying the partial expression: (-37*z)*(-49*z**3 - 39*z**2)
Expanding the part (-49*z**3 - 39*z**2) using the distributive property, and we got: (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3)
Replacing (-37*z)*(-49*z**3 - 39*z**2) with (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*z)*(-39*z**2) + (-37*z)*(-49*z**3) + (-39*z**2)*(-59*z**3) + (-59*z**3)*(-49*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*z**3)*(-59*z**3) = 2891*z**6
  (-49*z**3)*(-37*z) = 1813*z**4
  (-39*z**2)*(-59*z**3) = 2301*z**5
  (-39*z**2)*(-37*z) = 1443*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3</replace>
No more calculations needed.
<answer>2891*z**6 + 2301*z**5 + 1813*z**4 + 1443*z**3</answer>


Question:
Simplify this expression: -6*x**2*(20*x**2 + 22*x - 54)
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*x**4 - 132*x**3 + 324*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: -6*x**2*(20*x**2 + 22*x - 54)
Expanding the part (20*x**2 + 22*x - 54) using the distributive property, and we got: -(-1)*324*x**2 + (22*x)*(-6*x**2) + (-6*x**2)*(20*x**2)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*324*x**2 + (22*x)*(-6*x**2) + (-6*x**2)*(20*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -54*(-6*x**2) = 324*x**2
  (20*x**2)*(-6*x**2) = -120*x**4
  (22*x)*(-6*x**2) = -132*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -120*x**4 - 132*x**3 + 324*x**2</replace>
No more calculations needed.
<answer>-120*x**4 - 132*x**3 + 324*x**2</answer>


Question:
Simplify this expression: (-32*x**3 + 24*x)*(-14*x**3 - x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 448*x**6 + 32*x**5 - 336*x**4 - 24*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: (-32*x**3 + 24*x)*(-14*x**3 - x**2)
Expanding the part (-14*x**3 - x**2) using the distributive property, and we got: (-x**2)*(-32*x**3 + 24*x) + (-14*x**3)*(-32*x**3 + 24*x)
<replace-#Step 1>#Step 2:
Current expression: (-x**2)*(-32*x**3 + 24*x) + (-14*x**3)*(-32*x**3 + 24*x)</replace>
Simplifying the partial expression: (-x**2)*(-32*x**3 + 24*x)
Expanding the part (-32*x**3 + 24*x) using the distributive property, and we got: (24*x)*(-x**2) + (-x**2)*(-32*x**3)
Replacing (-x**2)*(-32*x**3 + 24*x) with (24*x)*(-x**2) + (-x**2)*(-32*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (24*x)*(-x**2) + (-x**2)*(-32*x**3) + (-14*x**3)*(-32*x**3 + 24*x)</replace>
Simplifying the partial expression: (-14*x**3)*(-32*x**3 + 24*x)
Expanding the part (-32*x**3 + 24*x) using the distributive property, and we got: (24*x)*(-14*x**3) + (-32*x**3)*(-14*x**3)
Replacing (-14*x**3)*(-32*x**3 + 24*x) with (24*x)*(-14*x**3) + (-32*x**3)*(-14*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (24*x)*(-x**2) + (24*x)*(-14*x**3) + (-x**2)*(-32*x**3) + (-32*x**3)*(-14*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*x**3)*(-x**2) = 32*x**5
  (-32*x**3)*(-14*x**3) = 448*x**6
  (24*x)*(-x**2) = -24*x**3
  (24*x)*(-14*x**3) = -336*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 448*x**6 + 32*x**5 - 336*x**4 - 24*x**3</replace>
No more calculations needed.
<answer>448*x**6 + 32*x**5 - 336*x**4 - 24*x**3</answer>


Question:
Calculate the following: (8*y**3 + 34*y**2 - 48)*(22*y**3 - 27*y**2 - 20)
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: 176*y**6 + 532*y**5 - 918*y**4 - 1216*y**3 + 616*y**2 + 960


Question:
Simplify this expression: -7*y**3*(-26*y**3 - 6*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: 182*y**6 + 42*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: -7*y**3*(-26*y**3 - 6*y)
Expanding the part (-26*y**3 - 6*y) using the distributive property, and we got: (-6*y)*(-7*y**3) + (-26*y**3)*(-7*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-6*y)*(-7*y**3) + (-26*y**3)*(-7*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-26*y**3)*(-7*y**3) = 182*y**6
  (-6*y)*(-7*y**3) = 42*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 182*y**6 + 42*y**4</replace>
No more calculations needed.
<answer>182*y**6 + 42*y**4</answer>


Question:
Simplify this expression: 160*y - 60
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: 160*y - 60

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: 160*y - 60
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: 160*y - 60</replace>
No more calculations needed.
<answer>160*y - 60</answer>


Question:
Calculate the following: (35 - 18*y**2)*(20*y**2 + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -360*y**4 - 38*y**2 + 1435

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (35 - 18*y**2)*(20*y**2 + 41)
Expanding the part (35 - 18*y**2) using the distributive property, and we got: (-18*y**2)*(20*y**2 + 41) + 35*(20*y**2 + 41)
<replace-#Step 1>#Step 2:
Current expression: (-18*y**2)*(20*y**2 + 41) + 35*(20*y**2 + 41)</replace>
Simplifying the partial expression: 35*(20*y**2 + 41)
Expanding the part (20*y**2 + 41) using the distributive property, and we got: (20*y**2)*35 + 41*35
Replacing 35*(20*y**2 + 41) with (20*y**2)*35 + 41*35 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*y**2)*(20*y**2 + 41) + (20*y**2)*35 + 1435</replace>
Simplifying the partial expression: (-18*y**2)*(20*y**2 + 41)
Expanding the part (20*y**2 + 41) using the distributive property, and we got: 41*(-18*y**2) + (-18*y**2)*(20*y**2)
Replacing (-18*y**2)*(20*y**2 + 41) with 41*(-18*y**2) + (-18*y**2)*(20*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 41*(-18)*y**2 + (-18*y**2)*(20*y**2) + (20*y**2)*35 + 1435</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*y**2)*35 = 700*y**2
  (20*y**2)*(-18*y**2) = -360*y**4
  41*-18*y**2 = -738*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -360*y**4 - 738*y**2 + 700*y**2 + 1435</replace>
Combining like terms, got -360*y**4 - 38*y**2 + 1435
<replace-#Step 5>#Step 6:
Current expression: -360*y**4 - 38*y**2 + 1435</replace>
No more calculations needed.
<answer>-360*y**4 - 38*y**2 + 1435</answer>


Question:
Simplify this expression: -92*y**2 - 1702
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: -92*y**2 - 1702

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: -92*y**2 - 1702
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: -92*y**2 - 1702</replace>
No more calculations needed.
<answer>-92*y**2 - 1702</answer>


Question:
Simplify this expression: (z**2 - 3*z)*(-8*z**3 + 49*z**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: -8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (z**2 - 3*z)*(-8*z**3 + 49*z**2 - 24)
Expanding the part (z**2 - 3*z) using the distributive property, and we got: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(-8*z**3 + 49*z**2 - 24)
<replace-#Step 1>#Step 2:
Current expression: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(-8*z**3 + 49*z**2 - 24)</replace>
Simplifying the partial expression: z**2*(-8*z**3 + 49*z**2 - 24)
Expanding the part (-8*z**3 + 49*z**2 - 24) using the distributive property, and we got: z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2
Replacing z**2*(-8*z**3 + 49*z**2 - 24) with z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-3*z)*(-8*z**3 + 49*z**2 - 24) + z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2</replace>
Simplifying the partial expression: (-3*z)*(-8*z**3 + 49*z**2 - 24)
Expanding the part (-8*z**3 + 49*z**2 - 24) using the distributive property, and we got: (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) - (-1)*72*z
Replacing (-3*z)*(-8*z**3 + 49*z**2 - 24) with (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) - (-1)*72*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*z)*(49*z**2) + (-3*z)*(-8*z**3) + z**2*(49*z**2) + z**2*(-8*z**3) - 24*z**2 - 24*(-3)*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*z**3)*z**2 = -8*z**5
  (-8*z**3)*(-3*z) = 24*z**4
  (49*z**2)*z**2 = 49*z**4
  (49*z**2)*(-3*z) = -147*z**3
  -24*-3*z = 72*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -8*z**5 + 24*z**4 + 49*z**4 - 147*z**3 - 24*z**2 + 72*z</replace>
Combining like terms, got -8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z
<replace-#Step 5>#Step 6:
Current expression: -8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z</replace>
No more calculations needed.
<answer>-8*z**5 + 73*z**4 - 147*z**3 - 24*z**2 + 72*z</answer>


Question:
Simplify this expression: 33*z**2*(9*z**2 - 45*z + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 297*z**4 - 1485*z**3 + 1122*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: 33*z**2*(9*z**2 - 45*z + 34)
Expanding the part (9*z**2 - 45*z + 34) using the distributive property, and we got: (-45*z)*(33*z**2) + 34*(33*z**2) + (9*z**2)*(33*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-45*z)*(33*z**2) + 34*(33*z**2) + (9*z**2)*(33*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  34*(33*z**2) = 1122*z**2
  (-45*z)*(33*z**2) = -1485*z**3
  (9*z**2)*(33*z**2) = 297*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 297*z**4 - 1485*z**3 + 1122*z**2</replace>
No more calculations needed.
<answer>297*z**4 - 1485*z**3 + 1122*z**2</answer>


Question:
Simplify this expression: 924*y - 957
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 924*y - 957

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: 924*y - 957
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: 924*y - 957</replace>
No more calculations needed.
<answer>924*y - 957</answer>


Question:
Calculate the following: 1440*z**3 + 1440*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: 1440*z**3 + 1440*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: 1440*z**3 + 1440*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: 1440*z**3 + 1440*z</replace>
No more calculations needed.
<answer>1440*z**3 + 1440*z</answer>


Question:
Simplify this expression: (-29*y**3 + 27*y**2 + 20)*(35*y**3 + 33*y**2 - 20*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: -1015*y**6 - 12*y**5 + 1471*y**4 + 102*y**3 + 714*y**2 - 400*y + 40


Question:
Simplify this expression: (-87*y**3 - 36*y**2)*(-33*y**3 - 49*y**2 + 38*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: 2871*y**6 + 5451*y**5 - 1542*y**4 - 1368*y**3


Question:
Simplify this expression: (-15*y**3 - 46)*(13*y**3 - 3*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: -195*y**6 + 45*y**5 - 598*y**3 + 138*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: (-15*y**3 - 46)*(13*y**3 - 3*y**2)
Expanding the part (-15*y**3 - 46) using the distributive property, and we got: (-15*y**3)*(13*y**3 - 3*y**2) - 46*(13*y**3 - 3*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**3)*(13*y**3 - 3*y**2) - 46*(13*y**3 - 3*y**2)</replace>
Simplifying the partial expression: -46*(13*y**3 - 3*y**2)
Expanding the part (13*y**3 - 3*y**2) using the distributive property, and we got: -3*y**2*(-46) + (13*y**3)*(-46)
Replacing -46*(13*y**3 - 3*y**2) with -3*y**2*(-46) + (13*y**3)*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3*y**2*(-46) + (-15*y**3)*(13*y**3 - 3*y**2) + (13*y**3)*(-46)</replace>
Simplifying the partial expression: (-15*y**3)*(13*y**3 - 3*y**2)
Expanding the part (13*y**3 - 3*y**2) using the distributive property, and we got: (-3*y**2)*(-15*y**3) + (-15*y**3)*(13*y**3)
Replacing (-15*y**3)*(13*y**3 - 3*y**2) with (-3*y**2)*(-15*y**3) + (-15*y**3)*(13*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*y**2)*(-15*y**3) - 3*y**2*(-46) + (-15*y**3)*(13*y**3) + (13*y**3)*(-46)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*y**2)*-46 = 138*y**2
  (-3*y**2)*(-15*y**3) = 45*y**5
  (13*y**3)*-46 = -598*y**3
  (13*y**3)*(-15*y**3) = -195*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -195*y**6 + 45*y**5 - 598*y**3 + 138*y**2</replace>
No more calculations needed.
<answer>-195*y**6 + 45*y**5 - 598*y**3 + 138*y**2</answer>


Question:
Calculate the following: (-29*x**3 - 24*x**2)*(28*x**3 + 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -812*x**6 - 672*x**5 - 725*x**3 - 600*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-29*x**3 - 24*x**2)*(28*x**3 + 25)
Expanding the part (28*x**3 + 25) using the distributive property, and we got: (28*x**3)*(-29*x**3 - 24*x**2) + 25*(-29*x**3 - 24*x**2)
<replace-#Step 1>#Step 2:
Current expression: (28*x**3)*(-29*x**3 - 24*x**2) + 25*(-29*x**3 - 24*x**2)</replace>
Simplifying the partial expression: 25*(-29*x**3 - 24*x**2)
Expanding the part (-29*x**3 - 24*x**2) using the distributive property, and we got: -24*x**2*25 - 29*x**3*25
Replacing 25*(-29*x**3 - 24*x**2) with -24*x**2*25 - 29*x**3*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*x**2*25 - 29*x**3*25 + (28*x**3)*(-29*x**3 - 24*x**2)</replace>
Simplifying the partial expression: (28*x**3)*(-29*x**3 - 24*x**2)
Expanding the part (-29*x**3 - 24*x**2) using the distributive property, and we got: (-24*x**2)*(28*x**3) + (-29*x**3)*(28*x**3)
Replacing (28*x**3)*(-29*x**3 - 24*x**2) with (-24*x**2)*(28*x**3) + (-29*x**3)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*x**2)*(28*x**3) - 24*x**2*25 + (-29*x**3)*(28*x**3) - 29*x**3*25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*x**3)*25 = -725*x**3
  (-29*x**3)*(28*x**3) = -812*x**6
  (-24*x**2)*25 = -600*x**2
  (-24*x**2)*(28*x**3) = -672*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -812*x**6 - 672*x**5 - 725*x**3 - 600*x**2</replace>
No more calculations needed.
<answer>-812*x**6 - 672*x**5 - 725*x**3 - 600*x**2</answer>


Question:
Simplify this expression: (-24*y**3 - 50)*(50*y**3 + 3*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: -1200*y**6 - 72*y**5 - 2500*y**3 - 150*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: (-24*y**3 - 50)*(50*y**3 + 3*y**2)
Expanding the part (-24*y**3 - 50) using the distributive property, and we got: (-24*y**3)*(50*y**3 + 3*y**2) - 50*(50*y**3 + 3*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-24*y**3)*(50*y**3 + 3*y**2) - 50*(50*y**3 + 3*y**2)</replace>
Simplifying the partial expression: -50*(50*y**3 + 3*y**2)
Expanding the part (50*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(-50) + (50*y**3)*(-50)
Replacing -50*(50*y**3 + 3*y**2) with (3*y**2)*(-50) + (50*y**3)*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*y**2)*(-50) + (-24*y**3)*(50*y**3 + 3*y**2) + (50*y**3)*(-50)</replace>
Simplifying the partial expression: (-24*y**3)*(50*y**3 + 3*y**2)
Expanding the part (50*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*(-24*y**3) + (-24*y**3)*(50*y**3)
Replacing (-24*y**3)*(50*y**3 + 3*y**2) with (3*y**2)*(-24*y**3) + (-24*y**3)*(50*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*y**2)*(-24*y**3) + (3*y**2)*(-50) + (-24*y**3)*(50*y**3) + (50*y**3)*(-50)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**2)*-50 = -150*y**2
  (3*y**2)*(-24*y**3) = -72*y**5
  (50*y**3)*-50 = -2500*y**3
  (50*y**3)*(-24*y**3) = -1200*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2</replace>
No more calculations needed.
<answer>-1200*y**6 - 72*y**5 - 2500*y**3 - 150*y**2</answer>


Question:
Simplify this expression: (20*y**2 + 53)*(30*y**3 + 25*y**2 + 42*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: 600*y**5 + 500*y**4 + 2430*y**3 + 1325*y**2 + 2226*y


Question:
Calculate the following: (-11*x - 1)*(23*x**3 + 15*x**2 + 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: -253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-11*x - 1)*(23*x**3 + 15*x**2 + 4)
Expanding the part (-11*x - 1) using the distributive property, and we got: (-11*x)*(23*x**3 + 15*x**2 + 4) - (23*x**3 + 15*x**2 + 4)
<replace-#Step 1>#Step 2:
Current expression: (-11*x)*(23*x**3 + 15*x**2 + 4) - (23*x**3 + 15*x**2 + 4)</replace>
Simplifying the partial expression: -(23*x**3 + 15*x**2 + 4)
Expanding the part (23*x**3 + 15*x**2 + 4) using the distributive property, and we got: (15*x**2)*(-1) + (23*x**3)*(-1) + 4*(-1)
Replacing -(23*x**3 + 15*x**2 + 4) with (15*x**2)*(-1) + (23*x**3)*(-1) + 4*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*x)*(23*x**3 + 15*x**2 + 4) + (15*x**2)*(-1) + (23*x**3)*(-1) - 4</replace>
Simplifying the partial expression: (-11*x)*(23*x**3 + 15*x**2 + 4)
Expanding the part (23*x**3 + 15*x**2 + 4) using the distributive property, and we got: (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11*x)
Replacing (-11*x)*(23*x**3 + 15*x**2 + 4) with (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*x)*(15*x**2) + (-11*x)*(23*x**3) + 4*(-11)*x + (15*x**2)*(-1) + (23*x**3)*(-1) - 4</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*x**2)*-1 = -15*x**2
  (15*x**2)*(-11*x) = -165*x**3
  (23*x**3)*-1 = -23*x**3
  (23*x**3)*(-11*x) = -253*x**4
  4*-11*x = -44*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -253*x**4 - 165*x**3 - 23*x**3 - 15*x**2 - 44*x - 4</replace>
Combining like terms, got -253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4
<replace-#Step 5>#Step 6:
Current expression: -253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4</replace>
No more calculations needed.
<answer>-253*x**4 - 188*x**3 - 15*x**2 - 44*x - 4</answer>


Question:
Simplify this expression: (-9*y - 9)*(43*y**3 + 44*y**2 - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-9*y - 9)*(43*y**3 + 44*y**2 - 32)
Expanding the part (-9*y - 9) using the distributive property, and we got: (-9*y)*(43*y**3 + 44*y**2 - 32) - 9*(43*y**3 + 44*y**2 - 32)
<replace-#Step 1>#Step 2:
Current expression: (-9*y)*(43*y**3 + 44*y**2 - 32) - 9*(43*y**3 + 44*y**2 - 32)</replace>
Simplifying the partial expression: -9*(43*y**3 + 44*y**2 - 32)
Expanding the part (43*y**3 + 44*y**2 - 32) using the distributive property, and we got: (44*y**2)*(-9) + (43*y**3)*(-9) - 32*(-9)
Replacing -9*(43*y**3 + 44*y**2 - 32) with (44*y**2)*(-9) + (43*y**3)*(-9) - 32*(-9) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*y)*(43*y**3 + 44*y**2 - 32) + (44*y**2)*(-9) + (43*y**3)*(-9) + 288</replace>
Simplifying the partial expression: (-9*y)*(43*y**3 + 44*y**2 - 32)
Expanding the part (43*y**3 + 44*y**2 - 32) using the distributive property, and we got: (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - (-1)*288*y
Replacing (-9*y)*(43*y**3 + 44*y**2 - 32) with (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - (-1)*288*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*y)*(44*y**2) + (-9*y)*(43*y**3) - 32*(-9)*y + (44*y**2)*(-9) + (43*y**3)*(-9) + 288</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*y**3)*-9 = -387*y**3
  (43*y**3)*(-9*y) = -387*y**4
  (44*y**2)*-9 = -396*y**2
  (44*y**2)*(-9*y) = -396*y**3
  -32*-9*y = 288*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -387*y**4 - 396*y**3 - 387*y**3 - 396*y**2 + 288*y + 288</replace>
Combining like terms, got -387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288
<replace-#Step 5>#Step 6:
Current expression: -387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288</replace>
No more calculations needed.
<answer>-387*y**4 - 783*y**3 - 396*y**2 + 288*y + 288</answer>


Question:
Simplify this expression: (25*y**2 + 5*y)*(27*y**3 - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 675*y**5 + 135*y**4 - 600*y**2 - 120*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: (25*y**2 + 5*y)*(27*y**3 - 24)
Expanding the part (27*y**3 - 24) using the distributive property, and we got: (27*y**3)*(25*y**2 + 5*y) - 24*(25*y**2 + 5*y)
<replace-#Step 1>#Step 2:
Current expression: (27*y**3)*(25*y**2 + 5*y) - 24*(25*y**2 + 5*y)</replace>
Simplifying the partial expression: -24*(25*y**2 + 5*y)
Expanding the part (25*y**2 + 5*y) using the distributive property, and we got: (5*y)*(-24) + (25*y**2)*(-24)
Replacing -24*(25*y**2 + 5*y) with (5*y)*(-24) + (25*y**2)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*y)*(-24) + (25*y**2)*(-24) + (27*y**3)*(25*y**2 + 5*y)</replace>
Simplifying the partial expression: (27*y**3)*(25*y**2 + 5*y)
Expanding the part (25*y**2 + 5*y) using the distributive property, and we got: (5*y)*(27*y**3) + (25*y**2)*(27*y**3)
Replacing (27*y**3)*(25*y**2 + 5*y) with (5*y)*(27*y**3) + (25*y**2)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (5*y)*(27*y**3) + (5*y)*(-24) + (25*y**2)*(27*y**3) + (25*y**2)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y)*-24 = -120*y
  (5*y)*(27*y**3) = 135*y**4
  (25*y**2)*-24 = -600*y**2
  (25*y**2)*(27*y**3) = 675*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 675*y**5 + 135*y**4 - 600*y**2 - 120*y</replace>
No more calculations needed.
<answer>675*y**5 + 135*y**4 - 600*y**2 - 120*y</answer>


Question:
Simplify this expression: (-29*y**2 - 36)*(48*y**3 - 8*y**2 + 2*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: -1392*y**5 + 232*y**4 - 1786*y**3 + 288*y**2 - 72*y


Question:
Simplify this expression: (26 - 48*y)*(80*y**3 - 33*y**2 + 35)
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: -3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910

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 - 48*y)*(80*y**3 - 33*y**2 + 35)
Expanding the part (26 - 48*y) using the distributive property, and we got: (-48*y)*(80*y**3 - 33*y**2 + 35) + 26*(80*y**3 - 33*y**2 + 35)
<replace-#Step 1>#Step 2:
Current expression: (-48*y)*(80*y**3 - 33*y**2 + 35) + 26*(80*y**3 - 33*y**2 + 35)</replace>
Simplifying the partial expression: 26*(80*y**3 - 33*y**2 + 35)
Expanding the part (80*y**3 - 33*y**2 + 35) using the distributive property, and we got: -33*y**2*26 + (80*y**3)*26 + 35*26
Replacing 26*(80*y**3 - 33*y**2 + 35) with -33*y**2*26 + (80*y**3)*26 + 35*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-48*y)*(80*y**3 - 33*y**2 + 35) - 33*y**2*26 + (80*y**3)*26 + 910</replace>
Simplifying the partial expression: (-48*y)*(80*y**3 - 33*y**2 + 35)
Expanding the part (80*y**3 - 33*y**2 + 35) using the distributive property, and we got: (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48*y)
Replacing (-48*y)*(80*y**3 - 33*y**2 + 35) with (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*y)*(-33*y**2) + (-48*y)*(80*y**3) + 35*(-48)*y - 33*y**2*26 + (80*y**3)*26 + 910</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y**2)*26 = -858*y**2
  (-33*y**2)*(-48*y) = 1584*y**3
  (80*y**3)*26 = 2080*y**3
  (80*y**3)*(-48*y) = -3840*y**4
  35*-48*y = -1680*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3840*y**4 + 1584*y**3 + 2080*y**3 - 858*y**2 - 1680*y + 910</replace>
Combining like terms, got -3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910
<replace-#Step 5>#Step 6:
Current expression: -3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910</replace>
No more calculations needed.
<answer>-3840*y**4 + 3664*y**3 - 858*y**2 - 1680*y + 910</answer>


Question:
Calculate the following: 48*y*(2*y**3 + 39*y + 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: 96*y**4 + 1872*y**2 + 2160*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: 48*y*(2*y**3 + 39*y + 45)
Expanding the part (2*y**3 + 39*y + 45) using the distributive property, and we got: 45*(48*y) + (39*y)*(48*y) + (48*y)*(2*y**3)
<replace-#Step 1>#Step 2:
Current expression: 45*(48*y) + (39*y)*(48*y) + (48*y)*(2*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  45*(48*y) = 2160*y
  (2*y**3)*(48*y) = 96*y**4
  (39*y)*(48*y) = 1872*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 96*y**4 + 1872*y**2 + 2160*y</replace>
No more calculations needed.
<answer>96*y**4 + 1872*y**2 + 2160*y</answer>


Question:
Calculate the following: (47*y**2 - 26*y)*(-49*y**3 + 50*y**2 - 35)
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*y**5 + 3624*y**4 - 1300*y**3 - 1645*y**2 + 910*y


Question:
Calculate the following: (29*x**2 + 9*x)*(-66*x**3 - 7*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: -1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29*x**2 + 9*x)*(-66*x**3 - 7*x)
Expanding the part (-66*x**3 - 7*x) using the distributive property, and we got: (-7*x)*(29*x**2 + 9*x) + (-66*x**3)*(29*x**2 + 9*x)
<replace-#Step 1>#Step 2:
Current expression: (-7*x)*(29*x**2 + 9*x) + (-66*x**3)*(29*x**2 + 9*x)</replace>
Simplifying the partial expression: (-66*x**3)*(29*x**2 + 9*x)
Expanding the part (29*x**2 + 9*x) using the distributive property, and we got: (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)
Replacing (-66*x**3)*(29*x**2 + 9*x) with (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-7*x)*(29*x**2 + 9*x) + (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)</replace>
Simplifying the partial expression: (-7*x)*(29*x**2 + 9*x)
Expanding the part (29*x**2 + 9*x) using the distributive property, and we got: (-7*x)*(9*x) + (-7*x)*(29*x**2)
Replacing (-7*x)*(29*x**2 + 9*x) with (-7*x)*(9*x) + (-7*x)*(29*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*x)*(9*x) + (-7*x)*(29*x**2) + (9*x)*(-66*x**3) + (29*x**2)*(-66*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*x)*(-66*x**3) = -594*x**4
  (9*x)*(-7*x) = -63*x**2
  (29*x**2)*(-66*x**3) = -1914*x**5
  (29*x**2)*(-7*x) = -203*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2</replace>
No more calculations needed.
<answer>-1914*x**5 - 594*x**4 - 203*x**3 - 63*x**2</answer>


Question:
Simplify this expression: (20*y**2 - 21*y)*(-22*y**3 - 20*y**2 - 16*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -440*y**5 + 62*y**4 + 100*y**3 + 336*y**2


Question:
Simplify this expression: (-53*z**2 + 4*z)*(-3*z**3 - 73*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: 159*z**5 - 12*z**4 + 3869*z**3 - 292*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: (-53*z**2 + 4*z)*(-3*z**3 - 73*z)
Expanding the part (-3*z**3 - 73*z) using the distributive property, and we got: (-73*z)*(-53*z**2 + 4*z) + (-3*z**3)*(-53*z**2 + 4*z)
<replace-#Step 1>#Step 2:
Current expression: (-73*z)*(-53*z**2 + 4*z) + (-3*z**3)*(-53*z**2 + 4*z)</replace>
Simplifying the partial expression: (-73*z)*(-53*z**2 + 4*z)
Expanding the part (-53*z**2 + 4*z) using the distributive property, and we got: (-73*z)*(4*z) + (-73*z)*(-53*z**2)
Replacing (-73*z)*(-53*z**2 + 4*z) with (-73*z)*(4*z) + (-73*z)*(-53*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-73*z)*(4*z) + (-73*z)*(-53*z**2) + (-3*z**3)*(-53*z**2 + 4*z)</replace>
Simplifying the partial expression: (-3*z**3)*(-53*z**2 + 4*z)
Expanding the part (-53*z**2 + 4*z) using the distributive property, and we got: (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3)
Replacing (-3*z**3)*(-53*z**2 + 4*z) with (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-73*z)*(4*z) + (-73*z)*(-53*z**2) + (4*z)*(-3*z**3) + (-53*z**2)*(-3*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-53*z**2)*(-73*z) = 3869*z**3
  (-53*z**2)*(-3*z**3) = 159*z**5
  (4*z)*(-73*z) = -292*z**2
  (4*z)*(-3*z**3) = -12*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2</replace>
No more calculations needed.
<answer>159*z**5 - 12*z**4 + 3869*z**3 - 292*z**2</answer>


Question:
Calculate the following: (9 - 11*y**2)*(13 - 44*y**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 484*y**5 - 396*y**3 - 143*y**2 + 117

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 - 11*y**2)*(13 - 44*y**3)
Expanding the part (9 - 11*y**2) using the distributive property, and we got: (-11*y**2)*(13 - 44*y**3) + 9*(13 - 44*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*y**2)*(13 - 44*y**3) + 9*(13 - 44*y**3)</replace>
Simplifying the partial expression: 9*(13 - 44*y**3)
Expanding the part (13 - 44*y**3) using the distributive property, and we got: -44*y**3*9 + 13*9
Replacing 9*(13 - 44*y**3) with -44*y**3*9 + 13*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*y**2)*(13 - 44*y**3) - 44*y**3*9 + 117</replace>
Simplifying the partial expression: (-11*y**2)*(13 - 44*y**3)
Expanding the part (13 - 44*y**3) using the distributive property, and we got: 13*(-11*y**2) + (-11*y**2)*(-44*y**3)
Replacing (-11*y**2)*(13 - 44*y**3) with 13*(-11*y**2) + (-11*y**2)*(-44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*(-11)*y**2 + (-11*y**2)*(-44*y**3) - 44*y**3*9 + 117</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*y**3)*9 = -396*y**3
  (-44*y**3)*(-11*y**2) = 484*y**5
  13*-11*y**2 = -143*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 484*y**5 - 396*y**3 - 143*y**2 + 117</replace>
No more calculations needed.
<answer>484*y**5 - 396*y**3 - 143*y**2 + 117</answer>


Question:
Calculate the following: (-19*y**2 + 37*y + 22)*(50*y**2 + 46*y + 21)
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: -950*y**4 + 976*y**3 + 2403*y**2 + 1789*y + 462


Question:
Simplify this expression: -38*x**2*(-35*x**3 - 33)
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: 1330*x**5 + 1254*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: -38*x**2*(-35*x**3 - 33)
Expanding the part (-35*x**3 - 33) using the distributive property, and we got: -(-1)*1254*x**2 + (-38*x**2)*(-35*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*1254*x**2 + (-38*x**2)*(-35*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -33*(-38*x**2) = 1254*x**2
  (-35*x**3)*(-38*x**2) = 1330*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1330*x**5 + 1254*x**2</replace>
No more calculations needed.
<answer>1330*x**5 + 1254*x**2</answer>


Question:
Calculate the following: 84*x**3*(6*x**3 + 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 504*x**6 + 3612*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: 84*x**3*(6*x**3 + 43)
Expanding the part (6*x**3 + 43) using the distributive property, and we got: 43*(84*x**3) + (6*x**3)*(84*x**3)
<replace-#Step 1>#Step 2:
Current expression: 43*(84*x**3) + (6*x**3)*(84*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  43*(84*x**3) = 3612*x**3
  (6*x**3)*(84*x**3) = 504*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 504*x**6 + 3612*x**3</replace>
No more calculations needed.
<answer>504*x**6 + 3612*x**3</answer>


Question:
Calculate the following: (2 - 12*z**3)*(42*z**2 + 33)
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: -504*z**5 - 396*z**3 + 84*z**2 + 66

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2 - 12*z**3)*(42*z**2 + 33)
Expanding the part (2 - 12*z**3) using the distributive property, and we got: (-12*z**3)*(42*z**2 + 33) + 2*(42*z**2 + 33)
<replace-#Step 1>#Step 2:
Current expression: (-12*z**3)*(42*z**2 + 33) + 2*(42*z**2 + 33)</replace>
Simplifying the partial expression: 2*(42*z**2 + 33)
Expanding the part (42*z**2 + 33) using the distributive property, and we got: (42*z**2)*2 + 33*2
Replacing 2*(42*z**2 + 33) with (42*z**2)*2 + 33*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z**2)*2 + (-12*z**3)*(42*z**2 + 33) + 66</replace>
Simplifying the partial expression: (-12*z**3)*(42*z**2 + 33)
Expanding the part (42*z**2 + 33) using the distributive property, and we got: 33*(-12*z**3) + (42*z**2)*(-12*z**3)
Replacing (-12*z**3)*(42*z**2 + 33) with 33*(-12*z**3) + (42*z**2)*(-12*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*(-12)*z**3 + (42*z**2)*(-12*z**3) + (42*z**2)*2 + 66</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (42*z**2)*2 = 84*z**2
  (42*z**2)*(-12*z**3) = -504*z**5
  33*-12*z**3 = -396*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -504*z**5 - 396*z**3 + 84*z**2 + 66</replace>
No more calculations needed.
<answer>-504*z**5 - 396*z**3 + 84*z**2 + 66</answer>


Question:
Calculate the following: -24*z*(-11*z**2 - 6*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: 264*z**3 + 144*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: -24*z*(-11*z**2 - 6*z)
Expanding the part (-11*z**2 - 6*z) using the distributive property, and we got: (-24*z)*(-6*z) + (-24*z)*(-11*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-24*z)*(-6*z) + (-24*z)*(-11*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z**2)*(-24*z) = 264*z**3
  (-6*z)*(-24*z) = 144*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 264*z**3 + 144*z**2</replace>
No more calculations needed.
<answer>264*z**3 + 144*z**2</answer>


Question:
Calculate the following: (6 - 31*y**2)*(55*y**3 - 13*y**2 - 2*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: -1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (6 - 31*y**2)*(55*y**3 - 13*y**2 - 2*y)
Expanding the part (6 - 31*y**2) using the distributive property, and we got: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) + 6*(55*y**3 - 13*y**2 - 2*y)
<replace-#Step 1>#Step 2:
Current expression: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) + 6*(55*y**3 - 13*y**2 - 2*y)</replace>
Simplifying the partial expression: 6*(55*y**3 - 13*y**2 - 2*y)
Expanding the part (55*y**3 - 13*y**2 - 2*y) using the distributive property, and we got: -2*y*6 - 13*y**2*6 + (55*y**3)*6
Replacing 6*(55*y**3 - 13*y**2 - 2*y) with -2*y*6 - 13*y**2*6 + (55*y**3)*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*y*6 + (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) - 13*y**2*6 + (55*y**3)*6</replace>
Simplifying the partial expression: (-31*y**2)*(55*y**3 - 13*y**2 - 2*y)
Expanding the part (55*y**3 - 13*y**2 - 2*y) using the distributive property, and we got: (-2*y)*(-31*y**2) + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3)
Replacing (-31*y**2)*(55*y**3 - 13*y**2 - 2*y) with (-2*y)*(-31*y**2) + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(-31*y**2) - 2*y*6 + (-31*y**2)*(-13*y**2) + (-31*y**2)*(55*y**3) - 13*y**2*6 + (55*y**3)*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*y**2)*6 = -78*y**2
  (-13*y**2)*(-31*y**2) = 403*y**4
  (-2*y)*6 = -12*y
  (-2*y)*(-31*y**2) = 62*y**3
  (55*y**3)*6 = 330*y**3
  (55*y**3)*(-31*y**2) = -1705*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1705*y**5 + 403*y**4 + 62*y**3 + 330*y**3 - 78*y**2 - 12*y</replace>
Combining like terms, got -1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y
<replace-#Step 5>#Step 6:
Current expression: -1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y</replace>
No more calculations needed.
<answer>-1705*y**5 + 403*y**4 + 392*y**3 - 78*y**2 - 12*y</answer>


Question:
Calculate the following: (21*y**3 - 41*y**2)*(60*y**3 - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*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: (21*y**3 - 41*y**2)*(60*y**3 - 48)
Expanding the part (60*y**3 - 48) using the distributive property, and we got: (60*y**3)*(21*y**3 - 41*y**2) - 48*(21*y**3 - 41*y**2)
<replace-#Step 1>#Step 2:
Current expression: (60*y**3)*(21*y**3 - 41*y**2) - 48*(21*y**3 - 41*y**2)</replace>
Simplifying the partial expression: -48*(21*y**3 - 41*y**2)
Expanding the part (21*y**3 - 41*y**2) using the distributive property, and we got: -41*y**2*(-48) + (21*y**3)*(-48)
Replacing -48*(21*y**3 - 41*y**2) with -41*y**2*(-48) + (21*y**3)*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*y**2*(-48) + (21*y**3)*(-48) + (60*y**3)*(21*y**3 - 41*y**2)</replace>
Simplifying the partial expression: (60*y**3)*(21*y**3 - 41*y**2)
Expanding the part (21*y**3 - 41*y**2) using the distributive property, and we got: (-41*y**2)*(60*y**3) + (21*y**3)*(60*y**3)
Replacing (60*y**3)*(21*y**3 - 41*y**2) with (-41*y**2)*(60*y**3) + (21*y**3)*(60*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*y**2)*(60*y**3) - 41*y**2*(-48) + (21*y**3)*(60*y**3) + (21*y**3)*(-48)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**2)*-48 = 1968*y**2
  (-41*y**2)*(60*y**3) = -2460*y**5
  (21*y**3)*-48 = -1008*y**3
  (21*y**3)*(60*y**3) = 1260*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2</replace>
No more calculations needed.
<answer>1260*y**6 - 2460*y**5 - 1008*y**3 + 1968*y**2</answer>


Question:
Calculate the following: (15*x**2 + 24)*(-x**2 + 29*x + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (15*x**2 + 24)*(-x**2 + 29*x + 49)
Expanding the part (15*x**2 + 24) using the distributive property, and we got: (15*x**2)*(-x**2 + 29*x + 49) + 24*(-x**2 + 29*x + 49)
<replace-#Step 1>#Step 2:
Current expression: (15*x**2)*(-x**2 + 29*x + 49) + 24*(-x**2 + 29*x + 49)</replace>
Simplifying the partial expression: 24*(-x**2 + 29*x + 49)
Expanding the part (-x**2 + 29*x + 49) using the distributive property, and we got: (29*x)*24 - x**2*24 + 49*24
Replacing 24*(-x**2 + 29*x + 49) with (29*x)*24 - x**2*24 + 49*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*x)*24 - x**2*24 + (15*x**2)*(-x**2 + 29*x + 49) + 1176</replace>
Simplifying the partial expression: (15*x**2)*(-x**2 + 29*x + 49)
Expanding the part (-x**2 + 29*x + 49) using the distributive property, and we got: 49*(15*x**2) + (29*x)*(15*x**2) + (-x**2)*(15*x**2)
Replacing (15*x**2)*(-x**2 + 29*x + 49) with 49*(15*x**2) + (29*x)*(15*x**2) + (-x**2)*(15*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 49*15*x**2 + (29*x)*(15*x**2) + (29*x)*24 + (-x**2)*(15*x**2) - x**2*24 + 1176</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**2)*24 = -24*x**2
  (-x**2)*(15*x**2) = -15*x**4
  (29*x)*24 = 696*x
  (29*x)*(15*x**2) = 435*x**3
  49*15*x**2 = 735*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -15*x**4 + 435*x**3 - 24*x**2 + 735*x**2 + 696*x + 1176</replace>
Combining like terms, got -15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176
<replace-#Step 5>#Step 6:
Current expression: -15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176</replace>
No more calculations needed.
<answer>-15*x**4 + 435*x**3 + 711*x**2 + 696*x + 1176</answer>


Question:
Simplify this expression: (-21*z**3 - 40)*(32*z**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: -672*z**6 - 1217*z**3 + 120

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-21*z**3 - 40)*(32*z**3 - 3)
Expanding the part (-21*z**3 - 40) using the distributive property, and we got: (-21*z**3)*(32*z**3 - 3) - 40*(32*z**3 - 3)
<replace-#Step 1>#Step 2:
Current expression: (-21*z**3)*(32*z**3 - 3) - 40*(32*z**3 - 3)</replace>
Simplifying the partial expression: -40*(32*z**3 - 3)
Expanding the part (32*z**3 - 3) using the distributive property, and we got: (32*z**3)*(-40) - 3*(-40)
Replacing -40*(32*z**3 - 3) with (32*z**3)*(-40) - 3*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*z**3)*(32*z**3 - 3) + (32*z**3)*(-40) + 120</replace>
Simplifying the partial expression: (-21*z**3)*(32*z**3 - 3)
Expanding the part (32*z**3 - 3) using the distributive property, and we got: -(-1)*63*z**3 + (-21*z**3)*(32*z**3)
Replacing (-21*z**3)*(32*z**3 - 3) with -(-1)*63*z**3 + (-21*z**3)*(32*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -3*(-21)*z**3 + (-21*z**3)*(32*z**3) + (32*z**3)*(-40) + 120</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*z**3)*-40 = -1280*z**3
  (32*z**3)*(-21*z**3) = -672*z**6
  -3*-21*z**3 = 63*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -672*z**6 - 1280*z**3 + 63*z**3 + 120</replace>
Combining like terms, got -672*z**6 - 1217*z**3 + 120
<replace-#Step 5>#Step 6:
Current expression: -672*z**6 - 1217*z**3 + 120</replace>
No more calculations needed.
<answer>-672*z**6 - 1217*z**3 + 120</answer>


Question:
Simplify this expression: (6 - 14*z)*(88*z + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1232*z**2 - 158*z + 294

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (6 - 14*z)*(88*z + 49)
Expanding the part (6 - 14*z) using the distributive property, and we got: (-14*z)*(88*z + 49) + 6*(88*z + 49)
<replace-#Step 1>#Step 2:
Current expression: (-14*z)*(88*z + 49) + 6*(88*z + 49)</replace>
Simplifying the partial expression: 6*(88*z + 49)
Expanding the part (88*z + 49) using the distributive property, and we got: (88*z)*6 + 49*6
Replacing 6*(88*z + 49) with (88*z)*6 + 49*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-14*z)*(88*z + 49) + (88*z)*6 + 294</replace>
Simplifying the partial expression: (-14*z)*(88*z + 49)
Expanding the part (88*z + 49) using the distributive property, and we got: (-14*z)*(88*z) + 49*(-14*z)
Replacing (-14*z)*(88*z + 49) with (-14*z)*(88*z) + 49*(-14*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*z)*(88*z) + 49*(-14)*z + (88*z)*6 + 294</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (88*z)*6 = 528*z
  (88*z)*(-14*z) = -1232*z**2
  49*-14*z = -686*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1232*z**2 - 686*z + 528*z + 294</replace>
Combining like terms, got -1232*z**2 - 158*z + 294
<replace-#Step 5>#Step 6:
Current expression: -1232*z**2 - 158*z + 294</replace>
No more calculations needed.
<answer>-1232*z**2 - 158*z + 294</answer>


Question:
Simplify this expression: (-5*y**2 - 17*y + 26)*(6*y**3 - 23*y**2 + 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*y**5 + 13*y**4 + 547*y**3 - 788*y**2 - 646*y + 988


Question:
Calculate the following: (42*x**3 + 13*x)*(48*x**3 - 12*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: 2016*x**6 + 120*x**4 - 156*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**3 + 13*x)*(48*x**3 - 12*x)
Expanding the part (48*x**3 - 12*x) using the distributive property, and we got: (-12*x)*(42*x**3 + 13*x) + (48*x**3)*(42*x**3 + 13*x)
<replace-#Step 1>#Step 2:
Current expression: (-12*x)*(42*x**3 + 13*x) + (48*x**3)*(42*x**3 + 13*x)</replace>
Simplifying the partial expression: (-12*x)*(42*x**3 + 13*x)
Expanding the part (42*x**3 + 13*x) using the distributive property, and we got: (-12*x)*(13*x) + (-12*x)*(42*x**3)
Replacing (-12*x)*(42*x**3 + 13*x) with (-12*x)*(13*x) + (-12*x)*(42*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-12*x)*(13*x) + (-12*x)*(42*x**3) + (48*x**3)*(42*x**3 + 13*x)</replace>
Simplifying the partial expression: (48*x**3)*(42*x**3 + 13*x)
Expanding the part (42*x**3 + 13*x) using the distributive property, and we got: (13*x)*(48*x**3) + (42*x**3)*(48*x**3)
Replacing (48*x**3)*(42*x**3 + 13*x) with (13*x)*(48*x**3) + (42*x**3)*(48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-12*x)*(13*x) + (-12*x)*(42*x**3) + (13*x)*(48*x**3) + (42*x**3)*(48*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (13*x)*(-12*x) = -156*x**2
  (13*x)*(48*x**3) = 624*x**4
  (42*x**3)*(-12*x) = -504*x**4
  (42*x**3)*(48*x**3) = 2016*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2016*x**6 - 504*x**4 + 624*x**4 - 156*x**2</replace>
Combining like terms, got 2016*x**6 + 120*x**4 - 156*x**2
<replace-#Step 5>#Step 6:
Current expression: 2016*x**6 + 120*x**4 - 156*x**2</replace>
No more calculations needed.
<answer>2016*x**6 + 120*x**4 - 156*x**2</answer>


Question:
Calculate the following: (-15*z - 28)*(-35*z**3 - 77*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: 525*z**4 + 980*z**3 + 1155*z**2 + 2156*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*z - 28)*(-35*z**3 - 77*z)
Expanding the part (-15*z - 28) using the distributive property, and we got: (-15*z)*(-35*z**3 - 77*z) - 28*(-35*z**3 - 77*z)
<replace-#Step 1>#Step 2:
Current expression: (-15*z)*(-35*z**3 - 77*z) - 28*(-35*z**3 - 77*z)</replace>
Simplifying the partial expression: -28*(-35*z**3 - 77*z)
Expanding the part (-35*z**3 - 77*z) using the distributive property, and we got: -77*z*(-28) - 35*z**3*(-28)
Replacing -28*(-35*z**3 - 77*z) with -77*z*(-28) - 35*z**3*(-28) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -77*z*(-28) + (-15*z)*(-35*z**3 - 77*z) - 35*z**3*(-28)</replace>
Simplifying the partial expression: (-15*z)*(-35*z**3 - 77*z)
Expanding the part (-35*z**3 - 77*z) using the distributive property, and we got: (-77*z)*(-15*z) + (-15*z)*(-35*z**3)
Replacing (-15*z)*(-35*z**3 - 77*z) with (-77*z)*(-15*z) + (-15*z)*(-35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-77*z)*(-15*z) - 77*z*(-28) + (-15*z)*(-35*z**3) - 35*z**3*(-28)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-77*z)*-28 = 2156*z
  (-77*z)*(-15*z) = 1155*z**2
  (-35*z**3)*-28 = 980*z**3
  (-35*z**3)*(-15*z) = 525*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 525*z**4 + 980*z**3 + 1155*z**2 + 2156*z</replace>
No more calculations needed.
<answer>525*z**4 + 980*z**3 + 1155*z**2 + 2156*z</answer>


Question:
Simplify this expression: -39*y**3*(-28*y**3 + 10*y + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1092*y**6 - 390*y**4 - 1404*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -39*y**3*(-28*y**3 + 10*y + 36)
Expanding the part (-28*y**3 + 10*y + 36) using the distributive property, and we got: 36*(-39*y**3) + (10*y)*(-39*y**3) + (-39*y**3)*(-28*y**3)
<replace-#Step 1>#Step 2:
Current expression: 36*(-39*y**3) + (10*y)*(-39*y**3) + (-39*y**3)*(-28*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  36*(-39*y**3) = -1404*y**3
  (-28*y**3)*(-39*y**3) = 1092*y**6
  (10*y)*(-39*y**3) = -390*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1092*y**6 - 390*y**4 - 1404*y**3</replace>
No more calculations needed.
<answer>1092*y**6 - 390*y**4 - 1404*y**3</answer>