Question:
Simplify this expression: (-9*z**3 - 6*z)*(29*z**3 - 17*z**2 + 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: -261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-9*z**3 - 6*z)*(29*z**3 - 17*z**2 + 1)
Expanding the part (-9*z**3 - 6*z) using the distributive property, and we got: (-6*z)*(29*z**3 - 17*z**2 + 1) + (-9*z**3)*(29*z**3 - 17*z**2 + 1)
<replace-#Step 1>#Step 2:
Current expression: (-6*z)*(29*z**3 - 17*z**2 + 1) + (-9*z**3)*(29*z**3 - 17*z**2 + 1)</replace>
Simplifying the partial expression: (-9*z**3)*(29*z**3 - 17*z**2 + 1)
Expanding the part (29*z**3 - 17*z**2 + 1) using the distributive property, and we got: 1*(-9*z**3) + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)
Replacing (-9*z**3)*(29*z**3 - 17*z**2 + 1) with 1*(-9*z**3) + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-6*z)*(29*z**3 - 17*z**2 + 1) - 9*z**3 + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)</replace>
Simplifying the partial expression: (-6*z)*(29*z**3 - 17*z**2 + 1)
Expanding the part (29*z**3 - 17*z**2 + 1) using the distributive property, and we got: (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) + 1*(-6*z)
Replacing (-6*z)*(29*z**3 - 17*z**2 + 1) with (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) + 1*(-6*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*z)*(-17*z**2) + (-6*z)*(29*z**3) - 9*z**3 - 6*z + (-17*z**2)*(-9*z**3) + (-9*z**3)*(29*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*z**2)*(-9*z**3) = 153*z**5
  (-17*z**2)*(-6*z) = 102*z**3
  (29*z**3)*(-9*z**3) = -261*z**6
  (29*z**3)*(-6*z) = -174*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -261*z**6 + 153*z**5 - 174*z**4 - 9*z**3 + 102*z**3 - 6*z</replace>
Combining like terms, got -261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z
<replace-#Step 5>#Step 6:
Current expression: -261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z</replace>
No more calculations needed.
<answer>-261*z**6 + 153*z**5 - 174*z**4 + 93*z**3 - 6*z</answer>


Question:
Calculate the following: (17 - 14*z**3)*(40*z**2 + 12*z + 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17 - 14*z**3)*(40*z**2 + 12*z + 13)
Expanding the part (17 - 14*z**3) using the distributive property, and we got: (-14*z**3)*(40*z**2 + 12*z + 13) + 17*(40*z**2 + 12*z + 13)
<replace-#Step 1>#Step 2:
Current expression: (-14*z**3)*(40*z**2 + 12*z + 13) + 17*(40*z**2 + 12*z + 13)</replace>
Simplifying the partial expression: 17*(40*z**2 + 12*z + 13)
Expanding the part (40*z**2 + 12*z + 13) using the distributive property, and we got: (12*z)*17 + (40*z**2)*17 + 13*17
Replacing 17*(40*z**2 + 12*z + 13) with (12*z)*17 + (40*z**2)*17 + 13*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*z)*17 + (40*z**2)*17 + (-14*z**3)*(40*z**2 + 12*z + 13) + 221</replace>
Simplifying the partial expression: (-14*z**3)*(40*z**2 + 12*z + 13)
Expanding the part (40*z**2 + 12*z + 13) using the distributive property, and we got: 13*(-14*z**3) + (12*z)*(-14*z**3) + (40*z**2)*(-14*z**3)
Replacing (-14*z**3)*(40*z**2 + 12*z + 13) with 13*(-14*z**3) + (12*z)*(-14*z**3) + (40*z**2)*(-14*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 13*(-14)*z**3 + (12*z)*(-14*z**3) + (12*z)*17 + (40*z**2)*(-14*z**3) + (40*z**2)*17 + 221</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*z)*17 = 204*z
  (12*z)*(-14*z**3) = -168*z**4
  (40*z**2)*17 = 680*z**2
  (40*z**2)*(-14*z**3) = -560*z**5
  13*-14*z**3 = -182*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221</replace>
No more calculations needed.
<answer>-560*z**5 - 168*z**4 - 182*z**3 + 680*z**2 + 204*z + 221</answer>


Question:
Calculate the following: (-54*y**3 - 22*y**2 - 28)*(-29*y**3 + 18*y**2 + 10*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: 1566*y**6 - 334*y**5 - 936*y**4 + 592*y**3 - 504*y**2 - 280*y


Question:
Simplify this expression: (11*z**3 + 17*z**2)*(-23*z**3 + 35*z**2 - 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -253*z**6 - 6*z**5 + 595*z**4 - 286*z**3 - 442*z**2


Question:
Calculate the following: (30*x**3 + 14*x**2)*(-47*x**3 + 8*x + 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: -1410*x**6 - 658*x**5 + 240*x**4 + 742*x**3 + 294*x**2


Question:
Calculate the following: (8*x + 39)*(54*x**3 - 42*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: 432*x**4 + 1770*x**3 - 1638*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: (8*x + 39)*(54*x**3 - 42*x**2)
Expanding the part (8*x + 39) using the distributive property, and we got: (8*x)*(54*x**3 - 42*x**2) + 39*(54*x**3 - 42*x**2)
<replace-#Step 1>#Step 2:
Current expression: (8*x)*(54*x**3 - 42*x**2) + 39*(54*x**3 - 42*x**2)</replace>
Simplifying the partial expression: 39*(54*x**3 - 42*x**2)
Expanding the part (54*x**3 - 42*x**2) using the distributive property, and we got: -42*x**2*39 + (54*x**3)*39
Replacing 39*(54*x**3 - 42*x**2) with -42*x**2*39 + (54*x**3)*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*x)*(54*x**3 - 42*x**2) - 42*x**2*39 + (54*x**3)*39</replace>
Simplifying the partial expression: (8*x)*(54*x**3 - 42*x**2)
Expanding the part (54*x**3 - 42*x**2) using the distributive property, and we got: (8*x)*(-42*x**2) + (8*x)*(54*x**3)
Replacing (8*x)*(54*x**3 - 42*x**2) with (8*x)*(-42*x**2) + (8*x)*(54*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*x)*(-42*x**2) + (8*x)*(54*x**3) - 42*x**2*39 + (54*x**3)*39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x**2)*39 = -1638*x**2
  (-42*x**2)*(8*x) = -336*x**3
  (54*x**3)*39 = 2106*x**3
  (54*x**3)*(8*x) = 432*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 432*x**4 - 336*x**3 + 2106*x**3 - 1638*x**2</replace>
Combining like terms, got 432*x**4 + 1770*x**3 - 1638*x**2
<replace-#Step 5>#Step 6:
Current expression: 432*x**4 + 1770*x**3 - 1638*x**2</replace>
No more calculations needed.
<answer>432*x**4 + 1770*x**3 - 1638*x**2</answer>


Question:
Calculate the following: 54*y*(44*y - 53)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2376*y**2 - 2862*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: 54*y*(44*y - 53)
Expanding the part (44*y - 53) using the distributive property, and we got: -2862*y + (44*y)*(54*y)
<replace-#Step 1>#Step 2:
Current expression: -2862*y + (44*y)*(54*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -53*(54*y) = -2862*y
  (44*y)*(54*y) = 2376*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2376*y**2 - 2862*y</replace>
No more calculations needed.
<answer>2376*y**2 - 2862*y</answer>


Question:
Calculate the following: (33*z + 37)*(35*z**3 + 2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1155*z**4 + 1295*z**3 + 66*z + 74

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 + 37)*(35*z**3 + 2)
Expanding the part (35*z**3 + 2) using the distributive property, and we got: (35*z**3)*(33*z + 37) + 2*(33*z + 37)
<replace-#Step 1>#Step 2:
Current expression: (35*z**3)*(33*z + 37) + 2*(33*z + 37)</replace>
Simplifying the partial expression: 2*(33*z + 37)
Expanding the part (33*z + 37) using the distributive property, and we got: (33*z)*2 + 37*2
Replacing 2*(33*z + 37) with (33*z)*2 + 37*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*z)*2 + (35*z**3)*(33*z + 37) + 74</replace>
Simplifying the partial expression: (35*z**3)*(33*z + 37)
Expanding the part (33*z + 37) using the distributive property, and we got: 37*(35*z**3) + (33*z)*(35*z**3)
Replacing (35*z**3)*(33*z + 37) with 37*(35*z**3) + (33*z)*(35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 37*35*z**3 + (33*z)*(35*z**3) + (33*z)*2 + 74</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*z)*2 = 66*z
  (33*z)*(35*z**3) = 1155*z**4
  37*35*z**3 = 1295*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1155*z**4 + 1295*z**3 + 66*z + 74</replace>
No more calculations needed.
<answer>1155*z**4 + 1295*z**3 + 66*z + 74</answer>


Question:
Calculate the following: (8 - 15*y)*(2*y**3 - 36*y**2 + 40*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*y**4 + 556*y**3 - 888*y**2 + 320*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (8 - 15*y)*(2*y**3 - 36*y**2 + 40*y)
Expanding the part (8 - 15*y) using the distributive property, and we got: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + 8*(2*y**3 - 36*y**2 + 40*y)
<replace-#Step 1>#Step 2:
Current expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + 8*(2*y**3 - 36*y**2 + 40*y)</replace>
Simplifying the partial expression: 8*(2*y**3 - 36*y**2 + 40*y)
Expanding the part (2*y**3 - 36*y**2 + 40*y) using the distributive property, and we got: (40*y)*8 - 36*y**2*8 + (2*y**3)*8
Replacing 8*(2*y**3 - 36*y**2 + 40*y) with (40*y)*8 - 36*y**2*8 + (2*y**3)*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y) + (40*y)*8 - 36*y**2*8 + (2*y**3)*8</replace>
Simplifying the partial expression: (-15*y)*(2*y**3 - 36*y**2 + 40*y)
Expanding the part (2*y**3 - 36*y**2 + 40*y) using the distributive property, and we got: (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3)
Replacing (-15*y)*(2*y**3 - 36*y**2 + 40*y) with (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-15*y)*(40*y) + (-15*y)*(-36*y**2) + (-15*y)*(2*y**3) + (40*y)*8 - 36*y**2*8 + (2*y**3)*8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*y**2)*8 = -288*y**2
  (-36*y**2)*(-15*y) = 540*y**3
  (2*y**3)*8 = 16*y**3
  (2*y**3)*(-15*y) = -30*y**4
  (40*y)*8 = 320*y
  (40*y)*(-15*y) = -600*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -30*y**4 + 16*y**3 + 540*y**3 - 600*y**2 - 288*y**2 + 320*y</replace>
Combining like terms, got -30*y**4 + 556*y**3 - 888*y**2 + 320*y
<replace-#Step 5>#Step 6:
Current expression: -30*y**4 + 556*y**3 - 888*y**2 + 320*y</replace>
No more calculations needed.
<answer>-30*y**4 + 556*y**3 - 888*y**2 + 320*y</answer>


Question:
Calculate the following: (39*x**3 + 31*x**2)*(86*x**3 - x - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*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: (39*x**3 + 31*x**2)*(86*x**3 - x - 10)
Expanding the part (39*x**3 + 31*x**2) using the distributive property, and we got: (31*x**2)*(86*x**3 - x - 10) + (39*x**3)*(86*x**3 - x - 10)
<replace-#Step 1>#Step 2:
Current expression: (31*x**2)*(86*x**3 - x - 10) + (39*x**3)*(86*x**3 - x - 10)</replace>
Simplifying the partial expression: (31*x**2)*(86*x**3 - x - 10)
Expanding the part (86*x**3 - x - 10) using the distributive property, and we got: (-x)*(31*x**2) - 310*x**2 + (31*x**2)*(86*x**3)
Replacing (31*x**2)*(86*x**3 - x - 10) with (-x)*(31*x**2) - 310*x**2 + (31*x**2)*(86*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-x)*(31*x**2) - 10*31*x**2 + (31*x**2)*(86*x**3) + (39*x**3)*(86*x**3 - x - 10)</replace>
Simplifying the partial expression: (39*x**3)*(86*x**3 - x - 10)
Expanding the part (86*x**3 - x - 10) using the distributive property, and we got: (-x)*(39*x**3) - 390*x**3 + (39*x**3)*(86*x**3)
Replacing (39*x**3)*(86*x**3 - x - 10) with (-x)*(39*x**3) - 390*x**3 + (39*x**3)*(86*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-x)*(31*x**2) + (-x)*(39*x**3) - 10*39*x**3 - 10*31*x**2 + (31*x**2)*(86*x**3) + (39*x**3)*(86*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x)*(31*x**2) = -31*x**3
  (-x)*(39*x**3) = -39*x**4
  (86*x**3)*(31*x**2) = 2666*x**5
  (86*x**3)*(39*x**3) = 3354*x**6
  -10*31*x**2 = -310*x**2
  -10*39*x**3 = -390*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3354*x**6 + 2666*x**5 - 39*x**4 - 390*x**3 - 31*x**3 - 310*x**2</replace>
Combining like terms, got 3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2
<replace-#Step 5>#Step 6:
Current expression: 3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2</replace>
No more calculations needed.
<answer>3354*x**6 + 2666*x**5 - 39*x**4 - 421*x**3 - 310*x**2</answer>


Question:
Simplify this expression: (-14*y**2 + 17*y)*(20*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: -280*y**5 + 340*y**4 + 336*y**2 - 408*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-14*y**2 + 17*y)*(20*y**3 - 24)
Expanding the part (20*y**3 - 24) using the distributive property, and we got: (20*y**3)*(-14*y**2 + 17*y) - 24*(-14*y**2 + 17*y)
<replace-#Step 1>#Step 2:
Current expression: (20*y**3)*(-14*y**2 + 17*y) - 24*(-14*y**2 + 17*y)</replace>
Simplifying the partial expression: -24*(-14*y**2 + 17*y)
Expanding the part (-14*y**2 + 17*y) using the distributive property, and we got: (17*y)*(-24) - 14*y**2*(-24)
Replacing -24*(-14*y**2 + 17*y) with (17*y)*(-24) - 14*y**2*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*y)*(-24) - 14*y**2*(-24) + (20*y**3)*(-14*y**2 + 17*y)</replace>
Simplifying the partial expression: (20*y**3)*(-14*y**2 + 17*y)
Expanding the part (-14*y**2 + 17*y) using the distributive property, and we got: (17*y)*(20*y**3) + (-14*y**2)*(20*y**3)
Replacing (20*y**3)*(-14*y**2 + 17*y) with (17*y)*(20*y**3) + (-14*y**2)*(20*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (17*y)*(20*y**3) + (17*y)*(-24) + (-14*y**2)*(20*y**3) - 14*y**2*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*y**2)*-24 = 336*y**2
  (-14*y**2)*(20*y**3) = -280*y**5
  (17*y)*-24 = -408*y
  (17*y)*(20*y**3) = 340*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -280*y**5 + 340*y**4 + 336*y**2 - 408*y</replace>
No more calculations needed.
<answer>-280*y**5 + 340*y**4 + 336*y**2 - 408*y</answer>


Question:
Simplify this expression: (15*y**2 - 43*y)*(43*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: 645*y**5 - 1849*y**4 - 90*y**3 + 258*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**2 - 43*y)*(43*y**3 - 6*y)
Expanding the part (15*y**2 - 43*y) using the distributive property, and we got: (-43*y)*(43*y**3 - 6*y) + (15*y**2)*(43*y**3 - 6*y)
<replace-#Step 1>#Step 2:
Current expression: (-43*y)*(43*y**3 - 6*y) + (15*y**2)*(43*y**3 - 6*y)</replace>
Simplifying the partial expression: (-43*y)*(43*y**3 - 6*y)
Expanding the part (43*y**3 - 6*y) using the distributive property, and we got: (-43*y)*(-6*y) + (-43*y)*(43*y**3)
Replacing (-43*y)*(43*y**3 - 6*y) with (-43*y)*(-6*y) + (-43*y)*(43*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*y)*(-6*y) + (-43*y)*(43*y**3) + (15*y**2)*(43*y**3 - 6*y)</replace>
Simplifying the partial expression: (15*y**2)*(43*y**3 - 6*y)
Expanding the part (43*y**3 - 6*y) using the distributive property, and we got: (-6*y)*(15*y**2) + (15*y**2)*(43*y**3)
Replacing (15*y**2)*(43*y**3 - 6*y) with (-6*y)*(15*y**2) + (15*y**2)*(43*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*y)*(-6*y) + (-43*y)*(43*y**3) + (-6*y)*(15*y**2) + (15*y**2)*(43*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-6*y)*(-43*y) = 258*y**2
  (-6*y)*(15*y**2) = -90*y**3
  (43*y**3)*(-43*y) = -1849*y**4
  (43*y**3)*(15*y**2) = 645*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2</replace>
No more calculations needed.
<answer>645*y**5 - 1849*y**4 - 90*y**3 + 258*y**2</answer>


Question:
Simplify this expression: (8 - 36*x)*(2*x**2 + 42*x + 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -72*x**3 - 1496*x**2 - 240*x + 128

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (8 - 36*x)*(2*x**2 + 42*x + 16)
Expanding the part (8 - 36*x) using the distributive property, and we got: (-36*x)*(2*x**2 + 42*x + 16) + 8*(2*x**2 + 42*x + 16)
<replace-#Step 1>#Step 2:
Current expression: (-36*x)*(2*x**2 + 42*x + 16) + 8*(2*x**2 + 42*x + 16)</replace>
Simplifying the partial expression: 8*(2*x**2 + 42*x + 16)
Expanding the part (2*x**2 + 42*x + 16) using the distributive property, and we got: (42*x)*8 + (2*x**2)*8 + 16*8
Replacing 8*(2*x**2 + 42*x + 16) with (42*x)*8 + (2*x**2)*8 + 16*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*x)*(2*x**2 + 42*x + 16) + (42*x)*8 + (2*x**2)*8 + 128</replace>
Simplifying the partial expression: (-36*x)*(2*x**2 + 42*x + 16)
Expanding the part (2*x**2 + 42*x + 16) using the distributive property, and we got: (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36*x)
Replacing (-36*x)*(2*x**2 + 42*x + 16) with (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*x)*(42*x) + (-36*x)*(2*x**2) + 16*(-36)*x + (42*x)*8 + (2*x**2)*8 + 128</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*x**2)*8 = 16*x**2
  (2*x**2)*(-36*x) = -72*x**3
  (42*x)*8 = 336*x
  (42*x)*(-36*x) = -1512*x**2
  16*-36*x = -576*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -72*x**3 - 1512*x**2 + 16*x**2 - 576*x + 336*x + 128</replace>
Combining like terms, got -72*x**3 - 1496*x**2 - 240*x + 128
<replace-#Step 5>#Step 6:
Current expression: -72*x**3 - 1496*x**2 - 240*x + 128</replace>
No more calculations needed.
<answer>-72*x**3 - 1496*x**2 - 240*x + 128</answer>


Question:
Calculate the following: (-46*y**3 - 6)*(15*y**3 - 23*y**2 - 14*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: -690*y**6 + 1058*y**5 + 644*y**4 - 90*y**3 + 138*y**2 + 84*y


Question:
Calculate the following: (-32*x**3 + 39*x**2)*(40*x**3 - 37*x**2 + 22*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: -1280*x**6 + 2744*x**5 - 2147*x**4 + 858*x**3


Question:
Calculate the following: (-4*z**3 - 34*z**2 - 40)*(62*z**3 - 40*z**2 + 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: -248*z**6 - 1948*z**5 + 1360*z**4 - 2624*z**3 + 376*z**2 - 1440


Question:
Simplify this expression: (-65*y**3 + 35*y)*(31*y**3 - 35*y**2 + 22*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: -2015*y**6 + 2275*y**5 - 345*y**4 - 1225*y**3 + 770*y**2


Question:
Calculate the following: (-36*z**2 - 30*z + 14)*(-33*z**2 + 34*z + 4)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1188*z**4 - 234*z**3 - 1626*z**2 + 356*z + 56


Question:
Simplify this expression: (33*x**3 + 5)*(-20*x**3 - 8*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: -660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (33*x**3 + 5)*(-20*x**3 - 8*x - 49)
Expanding the part (33*x**3 + 5) using the distributive property, and we got: (33*x**3)*(-20*x**3 - 8*x - 49) + 5*(-20*x**3 - 8*x - 49)
<replace-#Step 1>#Step 2:
Current expression: (33*x**3)*(-20*x**3 - 8*x - 49) + 5*(-20*x**3 - 8*x - 49)</replace>
Simplifying the partial expression: 5*(-20*x**3 - 8*x - 49)
Expanding the part (-20*x**3 - 8*x - 49) using the distributive property, and we got: -8*x*5 - 20*x**3*5 - 49*5
Replacing 5*(-20*x**3 - 8*x - 49) with -8*x*5 - 20*x**3*5 - 49*5 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*x*5 - 20*x**3*5 + (33*x**3)*(-20*x**3 - 8*x - 49) - 245</replace>
Simplifying the partial expression: (33*x**3)*(-20*x**3 - 8*x - 49)
Expanding the part (-20*x**3 - 8*x - 49) using the distributive property, and we got: (-8*x)*(33*x**3) - 1617*x**3 + (-20*x**3)*(33*x**3)
Replacing (33*x**3)*(-20*x**3 - 8*x - 49) with (-8*x)*(33*x**3) - 1617*x**3 + (-20*x**3)*(33*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*x)*(33*x**3) - 8*x*5 - 49*33*x**3 + (-20*x**3)*(33*x**3) - 20*x**3*5 - 245</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x**3)*5 = -100*x**3
  (-20*x**3)*(33*x**3) = -660*x**6
  (-8*x)*5 = -40*x
  (-8*x)*(33*x**3) = -264*x**4
  -49*33*x**3 = -1617*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -660*x**6 - 264*x**4 - 1617*x**3 - 100*x**3 - 40*x - 245</replace>
Combining like terms, got -660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245
<replace-#Step 5>#Step 6:
Current expression: -660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245</replace>
No more calculations needed.
<answer>-660*x**6 - 264*x**4 - 1717*x**3 - 40*x - 245</answer>


Question:
Calculate the following: (11*y**2 - 34)*(4*y**3 + 52*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: 44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11*y**2 - 34)*(4*y**3 + 52*y**2)
Expanding the part (11*y**2 - 34) using the distributive property, and we got: (11*y**2)*(4*y**3 + 52*y**2) - 34*(4*y**3 + 52*y**2)
<replace-#Step 1>#Step 2:
Current expression: (11*y**2)*(4*y**3 + 52*y**2) - 34*(4*y**3 + 52*y**2)</replace>
Simplifying the partial expression: -34*(4*y**3 + 52*y**2)
Expanding the part (4*y**3 + 52*y**2) using the distributive property, and we got: (52*y**2)*(-34) + (4*y**3)*(-34)
Replacing -34*(4*y**3 + 52*y**2) with (52*y**2)*(-34) + (4*y**3)*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*y**2)*(4*y**3 + 52*y**2) + (52*y**2)*(-34) + (4*y**3)*(-34)</replace>
Simplifying the partial expression: (11*y**2)*(4*y**3 + 52*y**2)
Expanding the part (4*y**3 + 52*y**2) using the distributive property, and we got: (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3)
Replacing (11*y**2)*(4*y**3 + 52*y**2) with (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*y**2)*(52*y**2) + (11*y**2)*(4*y**3) + (52*y**2)*(-34) + (4*y**3)*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*y**3)*-34 = -136*y**3
  (4*y**3)*(11*y**2) = 44*y**5
  (52*y**2)*-34 = -1768*y**2
  (52*y**2)*(11*y**2) = 572*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2</replace>
No more calculations needed.
<answer>44*y**5 + 572*y**4 - 136*y**3 - 1768*y**2</answer>


Question:
Calculate the following: -2548*x**3 + 539*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: -2548*x**3 + 539*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: -2548*x**3 + 539*x**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -2548*x**3 + 539*x**2</replace>
No more calculations needed.
<answer>-2548*x**3 + 539*x**2</answer>


Question:
Simplify this expression: (9*x + 3)*(25*x**2 + 50*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: 225*x**3 + 525*x**2 + 150*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: (9*x + 3)*(25*x**2 + 50*x)
Expanding the part (9*x + 3) using the distributive property, and we got: (9*x)*(25*x**2 + 50*x) + 3*(25*x**2 + 50*x)
<replace-#Step 1>#Step 2:
Current expression: (9*x)*(25*x**2 + 50*x) + 3*(25*x**2 + 50*x)</replace>
Simplifying the partial expression: 3*(25*x**2 + 50*x)
Expanding the part (25*x**2 + 50*x) using the distributive property, and we got: (50*x)*3 + (25*x**2)*3
Replacing 3*(25*x**2 + 50*x) with (50*x)*3 + (25*x**2)*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*x)*(25*x**2 + 50*x) + (50*x)*3 + (25*x**2)*3</replace>
Simplifying the partial expression: (9*x)*(25*x**2 + 50*x)
Expanding the part (25*x**2 + 50*x) using the distributive property, and we got: (9*x)*(50*x) + (9*x)*(25*x**2)
Replacing (9*x)*(25*x**2 + 50*x) with (9*x)*(50*x) + (9*x)*(25*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*x)*(50*x) + (9*x)*(25*x**2) + (50*x)*3 + (25*x**2)*3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*x**2)*3 = 75*x**2
  (25*x**2)*(9*x) = 225*x**3
  (50*x)*3 = 150*x
  (50*x)*(9*x) = 450*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 225*x**3 + 75*x**2 + 450*x**2 + 150*x</replace>
Combining like terms, got 225*x**3 + 525*x**2 + 150*x
<replace-#Step 5>#Step 6:
Current expression: 225*x**3 + 525*x**2 + 150*x</replace>
No more calculations needed.
<answer>225*x**3 + 525*x**2 + 150*x</answer>


Question:
Calculate the following: (25 - 4*x**3)*(-4*x**3 + 43*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: 16*x**6 - 172*x**5 - 100*x**3 + 1075*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: (25 - 4*x**3)*(-4*x**3 + 43*x**2)
Expanding the part (25 - 4*x**3) using the distributive property, and we got: (-4*x**3)*(-4*x**3 + 43*x**2) + 25*(-4*x**3 + 43*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-4*x**3)*(-4*x**3 + 43*x**2) + 25*(-4*x**3 + 43*x**2)</replace>
Simplifying the partial expression: 25*(-4*x**3 + 43*x**2)
Expanding the part (-4*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*25 - 4*x**3*25
Replacing 25*(-4*x**3 + 43*x**2) with (43*x**2)*25 - 4*x**3*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x**2)*25 + (-4*x**3)*(-4*x**3 + 43*x**2) - 4*x**3*25</replace>
Simplifying the partial expression: (-4*x**3)*(-4*x**3 + 43*x**2)
Expanding the part (-4*x**3 + 43*x**2) using the distributive property, and we got: (43*x**2)*(-4*x**3) + (-4*x**3)*(-4*x**3)
Replacing (-4*x**3)*(-4*x**3 + 43*x**2) with (43*x**2)*(-4*x**3) + (-4*x**3)*(-4*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (43*x**2)*(-4*x**3) + (43*x**2)*25 + (-4*x**3)*(-4*x**3) - 4*x**3*25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x**3)*25 = -100*x**3
  (-4*x**3)*(-4*x**3) = 16*x**6
  (43*x**2)*25 = 1075*x**2
  (43*x**2)*(-4*x**3) = -172*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2</replace>
No more calculations needed.
<answer>16*x**6 - 172*x**5 - 100*x**3 + 1075*x**2</answer>


Question:
Calculate the following: (-8*y**3 - 71*y**2)*(-6*y**3 - 37*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: 48*y**6 + 426*y**5 + 296*y**4 + 2627*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: (-8*y**3 - 71*y**2)*(-6*y**3 - 37*y)
Expanding the part (-8*y**3 - 71*y**2) using the distributive property, and we got: (-71*y**2)*(-6*y**3 - 37*y) + (-8*y**3)*(-6*y**3 - 37*y)
<replace-#Step 1>#Step 2:
Current expression: (-71*y**2)*(-6*y**3 - 37*y) + (-8*y**3)*(-6*y**3 - 37*y)</replace>
Simplifying the partial expression: (-71*y**2)*(-6*y**3 - 37*y)
Expanding the part (-6*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3)
Replacing (-71*y**2)*(-6*y**3 - 37*y) with (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*y)*(-71*y**2) + (-71*y**2)*(-6*y**3) + (-8*y**3)*(-6*y**3 - 37*y)</replace>
Simplifying the partial expression: (-8*y**3)*(-6*y**3 - 37*y)
Expanding the part (-6*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(-8*y**3) + (-8*y**3)*(-6*y**3)
Replacing (-8*y**3)*(-6*y**3 - 37*y) with (-37*y)*(-8*y**3) + (-8*y**3)*(-6*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*y)*(-71*y**2) + (-37*y)*(-8*y**3) + (-71*y**2)*(-6*y**3) + (-8*y**3)*(-6*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*y)*(-71*y**2) = 2627*y**3
  (-37*y)*(-8*y**3) = 296*y**4
  (-6*y**3)*(-71*y**2) = 426*y**5
  (-6*y**3)*(-8*y**3) = 48*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3</replace>
No more calculations needed.
<answer>48*y**6 + 426*y**5 + 296*y**4 + 2627*y**3</answer>


Question:
Simplify this expression: (7*x**3 - 36)*(38*x**3 - 79*x**2 + 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: 266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756

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*x**3 - 36)*(38*x**3 - 79*x**2 + 21)
Expanding the part (7*x**3 - 36) using the distributive property, and we got: (7*x**3)*(38*x**3 - 79*x**2 + 21) - 36*(38*x**3 - 79*x**2 + 21)
<replace-#Step 1>#Step 2:
Current expression: (7*x**3)*(38*x**3 - 79*x**2 + 21) - 36*(38*x**3 - 79*x**2 + 21)</replace>
Simplifying the partial expression: -36*(38*x**3 - 79*x**2 + 21)
Expanding the part (38*x**3 - 79*x**2 + 21) using the distributive property, and we got: -79*x**2*(-36) + (38*x**3)*(-36) + 21*(-36)
Replacing -36*(38*x**3 - 79*x**2 + 21) with -79*x**2*(-36) + (38*x**3)*(-36) + 21*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -79*x**2*(-36) + (7*x**3)*(38*x**3 - 79*x**2 + 21) + (38*x**3)*(-36) - 756</replace>
Simplifying the partial expression: (7*x**3)*(38*x**3 - 79*x**2 + 21)
Expanding the part (38*x**3 - 79*x**2 + 21) using the distributive property, and we got: 21*(7*x**3) + (-79*x**2)*(7*x**3) + (7*x**3)*(38*x**3)
Replacing (7*x**3)*(38*x**3 - 79*x**2 + 21) with 21*(7*x**3) + (-79*x**2)*(7*x**3) + (7*x**3)*(38*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 21*7*x**3 + (-79*x**2)*(7*x**3) - 79*x**2*(-36) + (7*x**3)*(38*x**3) + (38*x**3)*(-36) - 756</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-79*x**2)*-36 = 2844*x**2
  (-79*x**2)*(7*x**3) = -553*x**5
  (38*x**3)*-36 = -1368*x**3
  (38*x**3)*(7*x**3) = 266*x**6
  21*7*x**3 = 147*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 266*x**6 - 553*x**5 - 1368*x**3 + 147*x**3 + 2844*x**2 - 756</replace>
Combining like terms, got 266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756
<replace-#Step 5>#Step 6:
Current expression: 266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756</replace>
No more calculations needed.
<answer>266*x**6 - 553*x**5 - 1221*x**3 + 2844*x**2 - 756</answer>


Question:
Simplify this expression: -21*x**3*(4*x**3 - 27*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: -84*x**6 + 567*x**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -21*x**3*(4*x**3 - 27*x**2)
Expanding the part (4*x**3 - 27*x**2) using the distributive property, and we got: (-27*x**2)*(-21*x**3) + (-21*x**3)*(4*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-27*x**2)*(-21*x**3) + (-21*x**3)*(4*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*x**2)*(-21*x**3) = 567*x**5
  (4*x**3)*(-21*x**3) = -84*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -84*x**6 + 567*x**5</replace>
No more calculations needed.
<answer>-84*x**6 + 567*x**5</answer>


Question:
Simplify this expression: (94 - 44*z**2)*(63*z + 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2772*z**3 - 1892*z**2 + 5922*z + 4042

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: (94 - 44*z**2)*(63*z + 43)
Expanding the part (63*z + 43) using the distributive property, and we got: (63*z)*(94 - 44*z**2) + 43*(94 - 44*z**2)
<replace-#Step 1>#Step 2:
Current expression: (63*z)*(94 - 44*z**2) + 43*(94 - 44*z**2)</replace>
Simplifying the partial expression: 43*(94 - 44*z**2)
Expanding the part (94 - 44*z**2) using the distributive property, and we got: -44*z**2*43 + 94*43
Replacing 43*(94 - 44*z**2) with -44*z**2*43 + 94*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (63*z)*(94 - 44*z**2) - 44*z**2*43 + 4042</replace>
Simplifying the partial expression: (63*z)*(94 - 44*z**2)
Expanding the part (94 - 44*z**2) using the distributive property, and we got: 94*(63*z) + (63*z)*(-44*z**2)
Replacing (63*z)*(94 - 44*z**2) with 94*(63*z) + (63*z)*(-44*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 94*63*z + (63*z)*(-44*z**2) - 44*z**2*43 + 4042</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*z**2)*43 = -1892*z**2
  (-44*z**2)*(63*z) = -2772*z**3
  94*63*z = 5922*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2772*z**3 - 1892*z**2 + 5922*z + 4042</replace>
No more calculations needed.
<answer>-2772*z**3 - 1892*z**2 + 5922*z + 4042</answer>


Question:
Simplify this expression: (27 - 41*x**3)*(25*x**3 - 15*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: -1025*x**6 + 615*x**4 + 675*x**3 - 405*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 - 41*x**3)*(25*x**3 - 15*x)
Expanding the part (27 - 41*x**3) using the distributive property, and we got: (-41*x**3)*(25*x**3 - 15*x) + 27*(25*x**3 - 15*x)
<replace-#Step 1>#Step 2:
Current expression: (-41*x**3)*(25*x**3 - 15*x) + 27*(25*x**3 - 15*x)</replace>
Simplifying the partial expression: 27*(25*x**3 - 15*x)
Expanding the part (25*x**3 - 15*x) using the distributive property, and we got: -15*x*27 + (25*x**3)*27
Replacing 27*(25*x**3 - 15*x) with -15*x*27 + (25*x**3)*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -15*x*27 + (-41*x**3)*(25*x**3 - 15*x) + (25*x**3)*27</replace>
Simplifying the partial expression: (-41*x**3)*(25*x**3 - 15*x)
Expanding the part (25*x**3 - 15*x) using the distributive property, and we got: (-15*x)*(-41*x**3) + (-41*x**3)*(25*x**3)
Replacing (-41*x**3)*(25*x**3 - 15*x) with (-15*x)*(-41*x**3) + (-41*x**3)*(25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-15*x)*(-41*x**3) - 15*x*27 + (-41*x**3)*(25*x**3) + (25*x**3)*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*x)*27 = -405*x
  (-15*x)*(-41*x**3) = 615*x**4
  (25*x**3)*27 = 675*x**3
  (25*x**3)*(-41*x**3) = -1025*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1025*x**6 + 615*x**4 + 675*x**3 - 405*x</replace>
No more calculations needed.
<answer>-1025*x**6 + 615*x**4 + 675*x**3 - 405*x</answer>


Question:
Simplify this expression: -900*z**3 - 460
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -900*z**3 - 460

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: -900*z**3 - 460
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: -900*z**3 - 460</replace>
No more calculations needed.
<answer>-900*z**3 - 460</answer>


Question:
Calculate the following: (-23*z**3 - 10*z)*(-5*z**3 - 30*z + 80)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 115*z**6 + 740*z**4 - 1840*z**3 + 300*z**2 - 800*z


Question:
Calculate the following: (17*x**3 + 8*x)*(-20*x**2 + 11*x + 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: -340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*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: (17*x**3 + 8*x)*(-20*x**2 + 11*x + 33)
Expanding the part (17*x**3 + 8*x) using the distributive property, and we got: (8*x)*(-20*x**2 + 11*x + 33) + (17*x**3)*(-20*x**2 + 11*x + 33)
<replace-#Step 1>#Step 2:
Current expression: (8*x)*(-20*x**2 + 11*x + 33) + (17*x**3)*(-20*x**2 + 11*x + 33)</replace>
Simplifying the partial expression: (8*x)*(-20*x**2 + 11*x + 33)
Expanding the part (-20*x**2 + 11*x + 33) using the distributive property, and we got: 33*(8*x) + (8*x)*(11*x) + (8*x)*(-20*x**2)
Replacing (8*x)*(-20*x**2 + 11*x + 33) with 33*(8*x) + (8*x)*(11*x) + (8*x)*(-20*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 33*8*x + (8*x)*(11*x) + (8*x)*(-20*x**2) + (17*x**3)*(-20*x**2 + 11*x + 33)</replace>
Simplifying the partial expression: (17*x**3)*(-20*x**2 + 11*x + 33)
Expanding the part (-20*x**2 + 11*x + 33) using the distributive property, and we got: 33*(17*x**3) + (11*x)*(17*x**3) + (-20*x**2)*(17*x**3)
Replacing (17*x**3)*(-20*x**2 + 11*x + 33) with 33*(17*x**3) + (11*x)*(17*x**3) + (-20*x**2)*(17*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*17*x**3 + 33*8*x + (8*x)*(11*x) + (8*x)*(-20*x**2) + (11*x)*(17*x**3) + (-20*x**2)*(17*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**2)*(8*x) = -160*x**3
  (-20*x**2)*(17*x**3) = -340*x**5
  (11*x)*(8*x) = 88*x**2
  (11*x)*(17*x**3) = 187*x**4
  33*8*x = 264*x
  33*17*x**3 = 561*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -340*x**5 + 187*x**4 - 160*x**3 + 561*x**3 + 88*x**2 + 264*x</replace>
Combining like terms, got -340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x
<replace-#Step 5>#Step 6:
Current expression: -340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x</replace>
No more calculations needed.
<answer>-340*x**5 + 187*x**4 + 401*x**3 + 88*x**2 + 264*x</answer>


Question:
Simplify this expression: (16*z**3 + 5*z**2)*(49*z**3 - 34*z**2 - 38*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 784*z**6 - 299*z**5 - 778*z**4 - 190*z**3


Question:
Simplify this expression: 29*y**3*(32*y + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 928*y**4 + 986*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: 29*y**3*(32*y + 34)
Expanding the part (32*y + 34) using the distributive property, and we got: 34*(29*y**3) + (32*y)*(29*y**3)
<replace-#Step 1>#Step 2:
Current expression: 34*(29*y**3) + (32*y)*(29*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  34*(29*y**3) = 986*y**3
  (32*y)*(29*y**3) = 928*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 928*y**4 + 986*y**3</replace>
No more calculations needed.
<answer>928*y**4 + 986*y**3</answer>


Question:
Calculate the following: -52*y**3*(-28*y**3 + 86*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: 1456*y**6 - 4472*y**5 - 1040*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: -52*y**3*(-28*y**3 + 86*y**2 + 20)
Expanding the part (-28*y**3 + 86*y**2 + 20) using the distributive property, and we got: 20*(-52*y**3) + (86*y**2)*(-52*y**3) + (-52*y**3)*(-28*y**3)
<replace-#Step 1>#Step 2:
Current expression: 20*(-52*y**3) + (86*y**2)*(-52*y**3) + (-52*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:
  20*(-52*y**3) = -1040*y**3
  (-28*y**3)*(-52*y**3) = 1456*y**6
  (86*y**2)*(-52*y**3) = -4472*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1456*y**6 - 4472*y**5 - 1040*y**3</replace>
No more calculations needed.
<answer>1456*y**6 - 4472*y**5 - 1040*y**3</answer>


Question:
Calculate the following: (43*x + 38)*(13*x**3 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 559*x**4 + 494*x**3 - 1333*x - 1178

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x + 38)*(13*x**3 - 31)
Expanding the part (13*x**3 - 31) using the distributive property, and we got: (13*x**3)*(43*x + 38) - 31*(43*x + 38)
<replace-#Step 1>#Step 2:
Current expression: (13*x**3)*(43*x + 38) - 31*(43*x + 38)</replace>
Simplifying the partial expression: -31*(43*x + 38)
Expanding the part (43*x + 38) using the distributive property, and we got: (43*x)*(-31) + 38*(-31)
Replacing -31*(43*x + 38) with (43*x)*(-31) + 38*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(-31) + (13*x**3)*(43*x + 38) - 1178</replace>
Simplifying the partial expression: (13*x**3)*(43*x + 38)
Expanding the part (43*x + 38) using the distributive property, and we got: 38*(13*x**3) + (43*x)*(13*x**3)
Replacing (13*x**3)*(43*x + 38) with 38*(13*x**3) + (43*x)*(13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 38*13*x**3 + (43*x)*(13*x**3) + (43*x)*(-31) - 1178</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x)*-31 = -1333*x
  (43*x)*(13*x**3) = 559*x**4
  38*13*x**3 = 494*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 559*x**4 + 494*x**3 - 1333*x - 1178</replace>
No more calculations needed.
<answer>559*x**4 + 494*x**3 - 1333*x - 1178</answer>


Question:
Simplify this expression: (10*y - 42)*(7*y**2 - 7*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 70*y**3 - 364*y**2 + 294*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*y - 42)*(7*y**2 - 7*y)
Expanding the part (10*y - 42) using the distributive property, and we got: (10*y)*(7*y**2 - 7*y) - 42*(7*y**2 - 7*y)
<replace-#Step 1>#Step 2:
Current expression: (10*y)*(7*y**2 - 7*y) - 42*(7*y**2 - 7*y)</replace>
Simplifying the partial expression: -42*(7*y**2 - 7*y)
Expanding the part (7*y**2 - 7*y) using the distributive property, and we got: -7*y*(-42) + (7*y**2)*(-42)
Replacing -42*(7*y**2 - 7*y) with -7*y*(-42) + (7*y**2)*(-42) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -7*y*(-42) + (10*y)*(7*y**2 - 7*y) + (7*y**2)*(-42)</replace>
Simplifying the partial expression: (10*y)*(7*y**2 - 7*y)
Expanding the part (7*y**2 - 7*y) using the distributive property, and we got: (-7*y)*(10*y) + (10*y)*(7*y**2)
Replacing (10*y)*(7*y**2 - 7*y) with (-7*y)*(10*y) + (10*y)*(7*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*y)*(10*y) - 7*y*(-42) + (10*y)*(7*y**2) + (7*y**2)*(-42)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*y)*-42 = 294*y
  (-7*y)*(10*y) = -70*y**2
  (7*y**2)*-42 = -294*y**2
  (7*y**2)*(10*y) = 70*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 70*y**3 - 294*y**2 - 70*y**2 + 294*y</replace>
Combining like terms, got 70*y**3 - 364*y**2 + 294*y
<replace-#Step 5>#Step 6:
Current expression: 70*y**3 - 364*y**2 + 294*y</replace>
No more calculations needed.
<answer>70*y**3 - 364*y**2 + 294*y</answer>


Question:
Simplify this expression: (37*z**2 + 17)*(-34*z**3 + 19*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: -1258*z**5 + 703*z**4 - 578*z**3 + 323*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: (37*z**2 + 17)*(-34*z**3 + 19*z**2)
Expanding the part (37*z**2 + 17) using the distributive property, and we got: (37*z**2)*(-34*z**3 + 19*z**2) + 17*(-34*z**3 + 19*z**2)
<replace-#Step 1>#Step 2:
Current expression: (37*z**2)*(-34*z**3 + 19*z**2) + 17*(-34*z**3 + 19*z**2)</replace>
Simplifying the partial expression: 17*(-34*z**3 + 19*z**2)
Expanding the part (-34*z**3 + 19*z**2) using the distributive property, and we got: (19*z**2)*17 - 34*z**3*17
Replacing 17*(-34*z**3 + 19*z**2) with (19*z**2)*17 - 34*z**3*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*z**2)*17 + (37*z**2)*(-34*z**3 + 19*z**2) - 34*z**3*17</replace>
Simplifying the partial expression: (37*z**2)*(-34*z**3 + 19*z**2)
Expanding the part (-34*z**3 + 19*z**2) using the distributive property, and we got: (19*z**2)*(37*z**2) + (37*z**2)*(-34*z**3)
Replacing (37*z**2)*(-34*z**3 + 19*z**2) with (19*z**2)*(37*z**2) + (37*z**2)*(-34*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (19*z**2)*(37*z**2) + (19*z**2)*17 + (37*z**2)*(-34*z**3) - 34*z**3*17</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*z**3)*17 = -578*z**3
  (-34*z**3)*(37*z**2) = -1258*z**5
  (19*z**2)*17 = 323*z**2
  (19*z**2)*(37*z**2) = 703*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2</replace>
No more calculations needed.
<answer>-1258*z**5 + 703*z**4 - 578*z**3 + 323*z**2</answer>


Question:
Simplify this expression: (29*x**2 + 19)*(-11*x**3 - 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -319*x**5 - 209*x**3 - 1363*x**2 - 893

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 + 19)*(-11*x**3 - 47)
Expanding the part (-11*x**3 - 47) using the distributive property, and we got: (-11*x**3)*(29*x**2 + 19) - 47*(29*x**2 + 19)
<replace-#Step 1>#Step 2:
Current expression: (-11*x**3)*(29*x**2 + 19) - 47*(29*x**2 + 19)</replace>
Simplifying the partial expression: -47*(29*x**2 + 19)
Expanding the part (29*x**2 + 19) using the distributive property, and we got: (29*x**2)*(-47) + 19*(-47)
Replacing -47*(29*x**2 + 19) with (29*x**2)*(-47) + 19*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*x**2)*(-47) + (-11*x**3)*(29*x**2 + 19) - 893</replace>
Simplifying the partial expression: (-11*x**3)*(29*x**2 + 19)
Expanding the part (29*x**2 + 19) using the distributive property, and we got: 19*(-11*x**3) + (29*x**2)*(-11*x**3)
Replacing (-11*x**3)*(29*x**2 + 19) with 19*(-11*x**3) + (29*x**2)*(-11*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 19*(-11)*x**3 + (29*x**2)*(-11*x**3) + (29*x**2)*(-47) - 893</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*x**2)*-47 = -1363*x**2
  (29*x**2)*(-11*x**3) = -319*x**5
  19*-11*x**3 = -209*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -319*x**5 - 209*x**3 - 1363*x**2 - 893</replace>
No more calculations needed.
<answer>-319*x**5 - 209*x**3 - 1363*x**2 - 893</answer>


Question:
Calculate the following: (18 - 26*y**3)*(-12*y**3 - 36*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: 312*y**6 + 936*y**4 - 216*y**3 - 648*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: (18 - 26*y**3)*(-12*y**3 - 36*y)
Expanding the part (18 - 26*y**3) using the distributive property, and we got: (-26*y**3)*(-12*y**3 - 36*y) + 18*(-12*y**3 - 36*y)
<replace-#Step 1>#Step 2:
Current expression: (-26*y**3)*(-12*y**3 - 36*y) + 18*(-12*y**3 - 36*y)</replace>
Simplifying the partial expression: 18*(-12*y**3 - 36*y)
Expanding the part (-12*y**3 - 36*y) using the distributive property, and we got: -36*y*18 - 12*y**3*18
Replacing 18*(-12*y**3 - 36*y) with -36*y*18 - 12*y**3*18 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -36*y*18 + (-26*y**3)*(-12*y**3 - 36*y) - 12*y**3*18</replace>
Simplifying the partial expression: (-26*y**3)*(-12*y**3 - 36*y)
Expanding the part (-12*y**3 - 36*y) using the distributive property, and we got: (-36*y)*(-26*y**3) + (-26*y**3)*(-12*y**3)
Replacing (-26*y**3)*(-12*y**3 - 36*y) with (-36*y)*(-26*y**3) + (-26*y**3)*(-12*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*y)*(-26*y**3) - 36*y*18 + (-26*y**3)*(-12*y**3) - 12*y**3*18</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*y)*18 = -648*y
  (-36*y)*(-26*y**3) = 936*y**4
  (-12*y**3)*18 = -216*y**3
  (-12*y**3)*(-26*y**3) = 312*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 312*y**6 + 936*y**4 - 216*y**3 - 648*y</replace>
No more calculations needed.
<answer>312*y**6 + 936*y**4 - 216*y**3 - 648*y</answer>


Question:
Simplify this expression: (29*x**2 - 24*x)*(-10*x**3 - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -290*x**5 + 240*x**4 - 638*x**2 + 528*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: (29*x**2 - 24*x)*(-10*x**3 - 22)
Expanding the part (-10*x**3 - 22) using the distributive property, and we got: (-10*x**3)*(29*x**2 - 24*x) - 22*(29*x**2 - 24*x)
<replace-#Step 1>#Step 2:
Current expression: (-10*x**3)*(29*x**2 - 24*x) - 22*(29*x**2 - 24*x)</replace>
Simplifying the partial expression: -22*(29*x**2 - 24*x)
Expanding the part (29*x**2 - 24*x) using the distributive property, and we got: -24*x*(-22) + (29*x**2)*(-22)
Replacing -22*(29*x**2 - 24*x) with -24*x*(-22) + (29*x**2)*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*x*(-22) + (29*x**2)*(-22) + (-10*x**3)*(29*x**2 - 24*x)</replace>
Simplifying the partial expression: (-10*x**3)*(29*x**2 - 24*x)
Expanding the part (29*x**2 - 24*x) using the distributive property, and we got: (-24*x)*(-10*x**3) + (29*x**2)*(-10*x**3)
Replacing (-10*x**3)*(29*x**2 - 24*x) with (-24*x)*(-10*x**3) + (29*x**2)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*x)*(-10*x**3) - 24*x*(-22) + (29*x**2)*(-10*x**3) + (29*x**2)*(-22)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*x)*-22 = 528*x
  (-24*x)*(-10*x**3) = 240*x**4
  (29*x**2)*-22 = -638*x**2
  (29*x**2)*(-10*x**3) = -290*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -290*x**5 + 240*x**4 - 638*x**2 + 528*x</replace>
No more calculations needed.
<answer>-290*x**5 + 240*x**4 - 638*x**2 + 528*x</answer>


Question:
Simplify this expression: (-26*x - 13)*(37*x + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -962*x**2 - 923*x - 221

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*x - 13)*(37*x + 17)
Expanding the part (-26*x - 13) using the distributive property, and we got: (-26*x)*(37*x + 17) - 13*(37*x + 17)
<replace-#Step 1>#Step 2:
Current expression: (-26*x)*(37*x + 17) - 13*(37*x + 17)</replace>
Simplifying the partial expression: -13*(37*x + 17)
Expanding the part (37*x + 17) using the distributive property, and we got: (37*x)*(-13) + 17*(-13)
Replacing -13*(37*x + 17) with (37*x)*(-13) + 17*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-26*x)*(37*x + 17) + (37*x)*(-13) - 221</replace>
Simplifying the partial expression: (-26*x)*(37*x + 17)
Expanding the part (37*x + 17) using the distributive property, and we got: (-26*x)*(37*x) + 17*(-26*x)
Replacing (-26*x)*(37*x + 17) with (-26*x)*(37*x) + 17*(-26*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*x)*(37*x) + 17*(-26)*x + (37*x)*(-13) - 221</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (37*x)*-13 = -481*x
  (37*x)*(-26*x) = -962*x**2
  17*-26*x = -442*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -962*x**2 - 481*x - 442*x - 221</replace>
Combining like terms, got -962*x**2 - 923*x - 221
<replace-#Step 5>#Step 6:
Current expression: -962*x**2 - 923*x - 221</replace>
No more calculations needed.
<answer>-962*x**2 - 923*x - 221</answer>


Question:
Calculate the following: (45*x**2 + 9)*(11*x**3 + 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: 495*x**5 + 99*x**3 + 1710*x**2 + 342

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45*x**2 + 9)*(11*x**3 + 38)
Expanding the part (45*x**2 + 9) using the distributive property, and we got: (45*x**2)*(11*x**3 + 38) + 9*(11*x**3 + 38)
<replace-#Step 1>#Step 2:
Current expression: (45*x**2)*(11*x**3 + 38) + 9*(11*x**3 + 38)</replace>
Simplifying the partial expression: 9*(11*x**3 + 38)
Expanding the part (11*x**3 + 38) using the distributive property, and we got: (11*x**3)*9 + 38*9
Replacing 9*(11*x**3 + 38) with (11*x**3)*9 + 38*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (45*x**2)*(11*x**3 + 38) + (11*x**3)*9 + 342</replace>
Simplifying the partial expression: (45*x**2)*(11*x**3 + 38)
Expanding the part (11*x**3 + 38) using the distributive property, and we got: 38*(45*x**2) + (45*x**2)*(11*x**3)
Replacing (45*x**2)*(11*x**3 + 38) with 38*(45*x**2) + (45*x**2)*(11*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 38*45*x**2 + (45*x**2)*(11*x**3) + (11*x**3)*9 + 342</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*x**3)*9 = 99*x**3
  (11*x**3)*(45*x**2) = 495*x**5
  38*45*x**2 = 1710*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 495*x**5 + 99*x**3 + 1710*x**2 + 342</replace>
No more calculations needed.
<answer>495*x**5 + 99*x**3 + 1710*x**2 + 342</answer>


Question:
Calculate the following: -27*x**3*(-75*x**3 + 32*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2025*x**6 - 864*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: -27*x**3*(-75*x**3 + 32*x)
Expanding the part (-75*x**3 + 32*x) using the distributive property, and we got: (32*x)*(-27*x**3) + (-75*x**3)*(-27*x**3)
<replace-#Step 1>#Step 2:
Current expression: (32*x)*(-27*x**3) + (-75*x**3)*(-27*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-75*x**3)*(-27*x**3) = 2025*x**6
  (32*x)*(-27*x**3) = -864*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2025*x**6 - 864*x**4</replace>
No more calculations needed.
<answer>2025*x**6 - 864*x**4</answer>


Question:
Simplify this expression: (42 - 8*y**2)*(-15*y**3 - 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 120*y**5 - 630*y**3 + 80*y**2 - 420

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 - 8*y**2)*(-15*y**3 - 10)
Expanding the part (-15*y**3 - 10) using the distributive property, and we got: (-15*y**3)*(42 - 8*y**2) - 10*(42 - 8*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**3)*(42 - 8*y**2) - 10*(42 - 8*y**2)</replace>
Simplifying the partial expression: -10*(42 - 8*y**2)
Expanding the part (42 - 8*y**2) using the distributive property, and we got: -8*y**2*(-10) + 42*(-10)
Replacing -10*(42 - 8*y**2) with -8*y**2*(-10) + 42*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*y**2*(-10) + (-15*y**3)*(42 - 8*y**2) - 420</replace>
Simplifying the partial expression: (-15*y**3)*(42 - 8*y**2)
Expanding the part (42 - 8*y**2) using the distributive property, and we got: 42*(-15*y**3) + (-8*y**2)*(-15*y**3)
Replacing (-15*y**3)*(42 - 8*y**2) with 42*(-15*y**3) + (-8*y**2)*(-15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*(-15)*y**3 + (-8*y**2)*(-15*y**3) - 8*y**2*(-10) - 420</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*y**2)*-10 = 80*y**2
  (-8*y**2)*(-15*y**3) = 120*y**5
  42*-15*y**3 = -630*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 120*y**5 - 630*y**3 + 80*y**2 - 420</replace>
No more calculations needed.
<answer>120*y**5 - 630*y**3 + 80*y**2 - 420</answer>


Question:
Calculate the following: 29*y**2*(13*y**3 - 21*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 377*y**5 - 609*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: 29*y**2*(13*y**3 - 21*y)
Expanding the part (13*y**3 - 21*y) using the distributive property, and we got: (-21*y)*(29*y**2) + (29*y**2)*(13*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-21*y)*(29*y**2) + (29*y**2)*(13*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*y)*(29*y**2) = -609*y**3
  (13*y**3)*(29*y**2) = 377*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 377*y**5 - 609*y**3</replace>
No more calculations needed.
<answer>377*y**5 - 609*y**3</answer>


Question:
Simplify this expression: -66*z**2*(50*z**3 - 37*z**2 + 3*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: -3300*z**5 + 2442*z**4 - 198*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: -66*z**2*(50*z**3 - 37*z**2 + 3*z)
Expanding the part (50*z**3 - 37*z**2 + 3*z) using the distributive property, and we got: (3*z)*(-66*z**2) + (-66*z**2)*(-37*z**2) + (-66*z**2)*(50*z**3)
<replace-#Step 1>#Step 2:
Current expression: (3*z)*(-66*z**2) + (-66*z**2)*(-37*z**2) + (-66*z**2)*(50*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z**2)*(-66*z**2) = 2442*z**4
  (3*z)*(-66*z**2) = -198*z**3
  (50*z**3)*(-66*z**2) = -3300*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3300*z**5 + 2442*z**4 - 198*z**3</replace>
No more calculations needed.
<answer>-3300*z**5 + 2442*z**4 - 198*z**3</answer>


Question:
Calculate the following: -14*x*(36*x**3 + 35*x**2 + 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -504*x**4 - 490*x**3 - 406*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: -14*x*(36*x**3 + 35*x**2 + 29)
Expanding the part (36*x**3 + 35*x**2 + 29) using the distributive property, and we got: (-14*x)*(35*x**2) + (-14*x)*(36*x**3) + 29*(-14*x)
<replace-#Step 1>#Step 2:
Current expression: (-14*x)*(35*x**2) + (-14*x)*(36*x**3) + 29*(-14*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  29*(-14*x) = -406*x
  (35*x**2)*(-14*x) = -490*x**3
  (36*x**3)*(-14*x) = -504*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -504*x**4 - 490*x**3 - 406*x</replace>
No more calculations needed.
<answer>-504*x**4 - 490*x**3 - 406*x</answer>


Question:
Simplify this expression: (47*y**2 + 4*y)*(20*y**3 - 37*y - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*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: (47*y**2 + 4*y)*(20*y**3 - 37*y - 29)
Expanding the part (47*y**2 + 4*y) using the distributive property, and we got: (4*y)*(20*y**3 - 37*y - 29) + (47*y**2)*(20*y**3 - 37*y - 29)
<replace-#Step 1>#Step 2:
Current expression: (4*y)*(20*y**3 - 37*y - 29) + (47*y**2)*(20*y**3 - 37*y - 29)</replace>
Simplifying the partial expression: (4*y)*(20*y**3 - 37*y - 29)
Expanding the part (20*y**3 - 37*y - 29) using the distributive property, and we got: (-37*y)*(4*y) - 116*y + (4*y)*(20*y**3)
Replacing (4*y)*(20*y**3 - 37*y - 29) with (-37*y)*(4*y) - 116*y + (4*y)*(20*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*y)*(4*y) - 29*4*y + (4*y)*(20*y**3) + (47*y**2)*(20*y**3 - 37*y - 29)</replace>
Simplifying the partial expression: (47*y**2)*(20*y**3 - 37*y - 29)
Expanding the part (20*y**3 - 37*y - 29) using the distributive property, and we got: (-37*y)*(47*y**2) - 1363*y**2 + (47*y**2)*(20*y**3)
Replacing (47*y**2)*(20*y**3 - 37*y - 29) with (-37*y)*(47*y**2) - 1363*y**2 + (47*y**2)*(20*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*y)*(4*y) + (-37*y)*(47*y**2) - 29*47*y**2 - 29*4*y + (4*y)*(20*y**3) + (47*y**2)*(20*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*y)*(4*y) = -148*y**2
  (-37*y)*(47*y**2) = -1739*y**3
  (20*y**3)*(4*y) = 80*y**4
  (20*y**3)*(47*y**2) = 940*y**5
  -29*4*y = -116*y
  -29*47*y**2 = -1363*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 940*y**5 + 80*y**4 - 1739*y**3 - 1363*y**2 - 148*y**2 - 116*y</replace>
Combining like terms, got 940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y
<replace-#Step 5>#Step 6:
Current expression: 940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y</replace>
No more calculations needed.
<answer>940*y**5 + 80*y**4 - 1739*y**3 - 1511*y**2 - 116*y</answer>


Question:
Calculate the following: (28*z**3 + 31)*(-14*z**3 + 31*z**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: -392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (28*z**3 + 31)*(-14*z**3 + 31*z**2 - 23)
Expanding the part (28*z**3 + 31) using the distributive property, and we got: (28*z**3)*(-14*z**3 + 31*z**2 - 23) + 31*(-14*z**3 + 31*z**2 - 23)
<replace-#Step 1>#Step 2:
Current expression: (28*z**3)*(-14*z**3 + 31*z**2 - 23) + 31*(-14*z**3 + 31*z**2 - 23)</replace>
Simplifying the partial expression: 31*(-14*z**3 + 31*z**2 - 23)
Expanding the part (-14*z**3 + 31*z**2 - 23) using the distributive property, and we got: (31*z**2)*31 - 14*z**3*31 - 23*31
Replacing 31*(-14*z**3 + 31*z**2 - 23) with (31*z**2)*31 - 14*z**3*31 - 23*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (31*z**2)*31 - 14*z**3*31 + (28*z**3)*(-14*z**3 + 31*z**2 - 23) - 713</replace>
Simplifying the partial expression: (28*z**3)*(-14*z**3 + 31*z**2 - 23)
Expanding the part (-14*z**3 + 31*z**2 - 23) using the distributive property, and we got: -644*z**3 + (31*z**2)*(28*z**3) + (-14*z**3)*(28*z**3)
Replacing (28*z**3)*(-14*z**3 + 31*z**2 - 23) with -644*z**3 + (31*z**2)*(28*z**3) + (-14*z**3)*(28*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -23*28*z**3 + (31*z**2)*(28*z**3) + (31*z**2)*31 + (-14*z**3)*(28*z**3) - 14*z**3*31 - 713</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**3)*31 = -434*z**3
  (-14*z**3)*(28*z**3) = -392*z**6
  (31*z**2)*31 = 961*z**2
  (31*z**2)*(28*z**3) = 868*z**5
  -23*28*z**3 = -644*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -392*z**6 + 868*z**5 - 644*z**3 - 434*z**3 + 961*z**2 - 713</replace>
Combining like terms, got -392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713
<replace-#Step 5>#Step 6:
Current expression: -392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713</replace>
No more calculations needed.
<answer>-392*z**6 + 868*z**5 - 1078*z**3 + 961*z**2 - 713</answer>


Question:
Calculate the following: (-43*x**2 - 24*x)*(30*x**2 - 37*x + 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: -1290*x**4 + 871*x**3 + 28*x**2 - 480*x


Question:
Calculate the following: (31 - 26*y)*(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: -26*y**4 + 31*y**3 - 156*y**2 + 186*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: (31 - 26*y)*(y**3 + 6*y)
Expanding the part (31 - 26*y) using the distributive property, and we got: (-26*y)*(y**3 + 6*y) + 31*(y**3 + 6*y)
<replace-#Step 1>#Step 2:
Current expression: (-26*y)*(y**3 + 6*y) + 31*(y**3 + 6*y)</replace>
Simplifying the partial expression: 31*(y**3 + 6*y)
Expanding the part (y**3 + 6*y) using the distributive property, and we got: y**3*31 + (6*y)*31
Replacing 31*(y**3 + 6*y) with y**3*31 + (6*y)*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-26*y)*(y**3 + 6*y) + y**3*31 + (6*y)*31</replace>
Simplifying the partial expression: (-26*y)*(y**3 + 6*y)
Expanding the part (y**3 + 6*y) using the distributive property, and we got: (-26*y)*y**3 + (-26*y)*(6*y)
Replacing (-26*y)*(y**3 + 6*y) with (-26*y)*y**3 + (-26*y)*(6*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*y)*y**3 + (-26*y)*(6*y) + y**3*31 + (6*y)*31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**3*31 = 31*y**3
  y**3*(-26*y) = -26*y**4
  (6*y)*31 = 186*y
  (6*y)*(-26*y) = -156*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -26*y**4 + 31*y**3 - 156*y**2 + 186*y</replace>
No more calculations needed.
<answer>-26*y**4 + 31*y**3 - 156*y**2 + 186*y</answer>


Question:
Calculate the following: -945*z**2 - 385
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -945*z**2 - 385

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: -945*z**2 - 385
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: -945*z**2 - 385</replace>
No more calculations needed.
<answer>-945*z**2 - 385</answer>


Question:
Calculate the following: (-54*x**3 + x**2 + 40)*(-25*x**3 - 13*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: 1350*x**6 + 677*x**5 - 13*x**4 - 1216*x**3 - 516*x**2 + 160


Question:
Calculate the following: (-32*x**2 - 37*x)*(-52*x**3 - 30*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1664*x**5 + 1924*x**4 + 960*x**3 + 1110*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: (-32*x**2 - 37*x)*(-52*x**3 - 30*x)
Expanding the part (-52*x**3 - 30*x) using the distributive property, and we got: (-30*x)*(-32*x**2 - 37*x) + (-52*x**3)*(-32*x**2 - 37*x)
<replace-#Step 1>#Step 2:
Current expression: (-30*x)*(-32*x**2 - 37*x) + (-52*x**3)*(-32*x**2 - 37*x)</replace>
Simplifying the partial expression: (-52*x**3)*(-32*x**2 - 37*x)
Expanding the part (-32*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(-52*x**3) + (-32*x**2)*(-52*x**3)
Replacing (-52*x**3)*(-32*x**2 - 37*x) with (-37*x)*(-52*x**3) + (-32*x**2)*(-52*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*x)*(-52*x**3) + (-30*x)*(-32*x**2 - 37*x) + (-32*x**2)*(-52*x**3)</replace>
Simplifying the partial expression: (-30*x)*(-32*x**2 - 37*x)
Expanding the part (-32*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(-30*x) + (-30*x)*(-32*x**2)
Replacing (-30*x)*(-32*x**2 - 37*x) with (-37*x)*(-30*x) + (-30*x)*(-32*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*x)*(-30*x) + (-37*x)*(-52*x**3) + (-30*x)*(-32*x**2) + (-32*x**2)*(-52*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*x)*(-52*x**3) = 1924*x**4
  (-37*x)*(-30*x) = 1110*x**2
  (-32*x**2)*(-52*x**3) = 1664*x**5
  (-32*x**2)*(-30*x) = 960*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2</replace>
No more calculations needed.
<answer>1664*x**5 + 1924*x**4 + 960*x**3 + 1110*x**2</answer>


Question:
Simplify this expression: (-33*x**2 + 40*x - 35)*(42*x**3 + 20*x + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1386*x**5 + 1680*x**4 - 2130*x**3 - 586*x**2 + 980*x - 1470


Question:
Simplify this expression: (29*z**3 + 76*z)*(54*z**3 - 19*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: 1566*z**6 - 551*z**5 + 4104*z**4 - 1444*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: (29*z**3 + 76*z)*(54*z**3 - 19*z**2)
Expanding the part (54*z**3 - 19*z**2) using the distributive property, and we got: (-19*z**2)*(29*z**3 + 76*z) + (54*z**3)*(29*z**3 + 76*z)
<replace-#Step 1>#Step 2:
Current expression: (-19*z**2)*(29*z**3 + 76*z) + (54*z**3)*(29*z**3 + 76*z)</replace>
Simplifying the partial expression: (-19*z**2)*(29*z**3 + 76*z)
Expanding the part (29*z**3 + 76*z) using the distributive property, and we got: (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3)
Replacing (-19*z**2)*(29*z**3 + 76*z) with (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (76*z)*(-19*z**2) + (-19*z**2)*(29*z**3) + (54*z**3)*(29*z**3 + 76*z)</replace>
Simplifying the partial expression: (54*z**3)*(29*z**3 + 76*z)
Expanding the part (29*z**3 + 76*z) using the distributive property, and we got: (76*z)*(54*z**3) + (29*z**3)*(54*z**3)
Replacing (54*z**3)*(29*z**3 + 76*z) with (76*z)*(54*z**3) + (29*z**3)*(54*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (76*z)*(-19*z**2) + (76*z)*(54*z**3) + (-19*z**2)*(29*z**3) + (29*z**3)*(54*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*z**3)*(-19*z**2) = -551*z**5
  (29*z**3)*(54*z**3) = 1566*z**6
  (76*z)*(-19*z**2) = -1444*z**3
  (76*z)*(54*z**3) = 4104*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3</replace>
No more calculations needed.
<answer>1566*z**6 - 551*z**5 + 4104*z**4 - 1444*z**3</answer>


Question:
Simplify this expression: (-18*x**3 + 15*x - 34)*(-46*x**3 + 34*x**2 - 32*x + 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 828*x**6 - 612*x**5 - 114*x**4 + 1642*x**3 - 1636*x**2 + 1448*x - 816


Question:
Simplify this expression: (-40*x**2 + 19*x + 7)*(-13*x**3 + 32*x**2 + 30*x + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 520*x**5 - 1527*x**4 - 683*x**3 + 474*x**2 + 362*x + 56


Question:
Calculate the following: (-44*y**2 + 11*y)*(-y**2 + 42*y + 76)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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*y**4 - 1859*y**3 - 2882*y**2 + 836*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-44*y**2 + 11*y)*(-y**2 + 42*y + 76)
Expanding the part (-44*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-y**2 + 42*y + 76) + (-44*y**2)*(-y**2 + 42*y + 76)
<replace-#Step 1>#Step 2:
Current expression: (11*y)*(-y**2 + 42*y + 76) + (-44*y**2)*(-y**2 + 42*y + 76)</replace>
Simplifying the partial expression: (-44*y**2)*(-y**2 + 42*y + 76)
Expanding the part (-y**2 + 42*y + 76) using the distributive property, and we got: 76*(-44*y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)
Replacing (-44*y**2)*(-y**2 + 42*y + 76) with 76*(-44*y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 76*(-44)*y**2 + (11*y)*(-y**2 + 42*y + 76) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)</replace>
Simplifying the partial expression: (11*y)*(-y**2 + 42*y + 76)
Expanding the part (-y**2 + 42*y + 76) using the distributive property, and we got: 76*(11*y) + (11*y)*(42*y) + (11*y)*(-y**2)
Replacing (11*y)*(-y**2 + 42*y + 76) with 76*(11*y) + (11*y)*(42*y) + (11*y)*(-y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 76*(-44)*y**2 + 76*11*y + (11*y)*(42*y) + (11*y)*(-y**2) + (42*y)*(-44*y**2) + (-44*y**2)*(-y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y**2)*(-44*y**2) = 44*y**4
  (-y**2)*(11*y) = -11*y**3
  (42*y)*(-44*y**2) = -1848*y**3
  (42*y)*(11*y) = 462*y**2
  76*-44*y**2 = -3344*y**2
  76*11*y = 836*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 44*y**4 - 1848*y**3 - 11*y**3 - 3344*y**2 + 462*y**2 + 836*y</replace>
Combining like terms, got 44*y**4 - 1859*y**3 - 2882*y**2 + 836*y
<replace-#Step 5>#Step 6:
Current expression: 44*y**4 - 1859*y**3 - 2882*y**2 + 836*y</replace>
No more calculations needed.
<answer>44*y**4 - 1859*y**3 - 2882*y**2 + 836*y</answer>