Question:
Simplify this expression: (46 - 6*x**3)*(45*x**2 + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -270*x**5 - 186*x**3 + 2070*x**2 + 1426

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46 - 6*x**3)*(45*x**2 + 31)
Expanding the part (45*x**2 + 31) using the distributive property, and we got: (45*x**2)*(46 - 6*x**3) + 31*(46 - 6*x**3)
<replace-#Step 1>#Step 2:
Current expression: (45*x**2)*(46 - 6*x**3) + 31*(46 - 6*x**3)</replace>
Simplifying the partial expression: 31*(46 - 6*x**3)
Expanding the part (46 - 6*x**3) using the distributive property, and we got: -6*x**3*31 + 46*31
Replacing 31*(46 - 6*x**3) with -6*x**3*31 + 46*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (45*x**2)*(46 - 6*x**3) - 6*x**3*31 + 1426</replace>
Simplifying the partial expression: (45*x**2)*(46 - 6*x**3)
Expanding the part (46 - 6*x**3) using the distributive property, and we got: 46*(45*x**2) + (45*x**2)*(-6*x**3)
Replacing (45*x**2)*(46 - 6*x**3) with 46*(45*x**2) + (45*x**2)*(-6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 46*45*x**2 + (45*x**2)*(-6*x**3) - 6*x**3*31 + 1426</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-6*x**3)*31 = -186*x**3
  (-6*x**3)*(45*x**2) = -270*x**5
  46*45*x**2 = 2070*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -270*x**5 - 186*x**3 + 2070*x**2 + 1426</replace>
No more calculations needed.
<answer>-270*x**5 - 186*x**3 + 2070*x**2 + 1426</answer>


Question:
Simplify this expression: (-14*z**2 - 40*z)*(34*z**3 + 49*z**2 + 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -476*z**5 - 2046*z**4 - 1960*z**3 - 168*z**2 - 480*z


Question:
Simplify this expression: (-24*x - 12)*(-5*x**3 + 32*x**2 - 41*x - 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: 120*x**4 - 708*x**3 + 600*x**2 + 1356*x + 432


Question:
Calculate the following: (41*x**3 + 7*x**2)*(2*x**2 - 4*x + 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: 82*x**5 - 150*x**4 + 1530*x**3 + 266*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: (41*x**3 + 7*x**2)*(2*x**2 - 4*x + 38)
Expanding the part (41*x**3 + 7*x**2) using the distributive property, and we got: (7*x**2)*(2*x**2 - 4*x + 38) + (41*x**3)*(2*x**2 - 4*x + 38)
<replace-#Step 1>#Step 2:
Current expression: (7*x**2)*(2*x**2 - 4*x + 38) + (41*x**3)*(2*x**2 - 4*x + 38)</replace>
Simplifying the partial expression: (7*x**2)*(2*x**2 - 4*x + 38)
Expanding the part (2*x**2 - 4*x + 38) using the distributive property, and we got: (-4*x)*(7*x**2) + 38*(7*x**2) + (2*x**2)*(7*x**2)
Replacing (7*x**2)*(2*x**2 - 4*x + 38) with (-4*x)*(7*x**2) + 38*(7*x**2) + (2*x**2)*(7*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-4*x)*(7*x**2) + 38*7*x**2 + (2*x**2)*(7*x**2) + (41*x**3)*(2*x**2 - 4*x + 38)</replace>
Simplifying the partial expression: (41*x**3)*(2*x**2 - 4*x + 38)
Expanding the part (2*x**2 - 4*x + 38) using the distributive property, and we got: (-4*x)*(41*x**3) + 38*(41*x**3) + (2*x**2)*(41*x**3)
Replacing (41*x**3)*(2*x**2 - 4*x + 38) with (-4*x)*(41*x**3) + 38*(41*x**3) + (2*x**2)*(41*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*x)*(7*x**2) + (-4*x)*(41*x**3) + 38*41*x**3 + 38*7*x**2 + (2*x**2)*(7*x**2) + (2*x**2)*(41*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x)*(7*x**2) = -28*x**3
  (-4*x)*(41*x**3) = -164*x**4
  (2*x**2)*(7*x**2) = 14*x**4
  (2*x**2)*(41*x**3) = 82*x**5
  38*7*x**2 = 266*x**2
  38*41*x**3 = 1558*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 82*x**5 - 164*x**4 + 14*x**4 - 28*x**3 + 1558*x**3 + 266*x**2</replace>
Combining like terms, got 82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2
<replace-#Step 5>#Step 6:
Current expression: 82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2</replace>
No more calculations needed.
<answer>82*x**5 - 150*x**4 + 1530*x**3 + 266*x**2</answer>


Question:
Simplify this expression: (-21*y**3 - 8)*(8*y**3 + 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -168*y**6 - 799*y**3 - 280

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-21*y**3 - 8)*(8*y**3 + 35)
Expanding the part (-21*y**3 - 8) using the distributive property, and we got: (-21*y**3)*(8*y**3 + 35) - 8*(8*y**3 + 35)
<replace-#Step 1>#Step 2:
Current expression: (-21*y**3)*(8*y**3 + 35) - 8*(8*y**3 + 35)</replace>
Simplifying the partial expression: -8*(8*y**3 + 35)
Expanding the part (8*y**3 + 35) using the distributive property, and we got: (8*y**3)*(-8) + 35*(-8)
Replacing -8*(8*y**3 + 35) with (8*y**3)*(-8) + 35*(-8) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*y**3)*(8*y**3 + 35) + (8*y**3)*(-8) - 280</replace>
Simplifying the partial expression: (-21*y**3)*(8*y**3 + 35)
Expanding the part (8*y**3 + 35) using the distributive property, and we got: 35*(-21*y**3) + (-21*y**3)*(8*y**3)
Replacing (-21*y**3)*(8*y**3 + 35) with 35*(-21*y**3) + (-21*y**3)*(8*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 35*(-21)*y**3 + (-21*y**3)*(8*y**3) + (8*y**3)*(-8) - 280</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*y**3)*-8 = -64*y**3
  (8*y**3)*(-21*y**3) = -168*y**6
  35*-21*y**3 = -735*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -168*y**6 - 735*y**3 - 64*y**3 - 280</replace>
Combining like terms, got -168*y**6 - 799*y**3 - 280
<replace-#Step 5>#Step 6:
Current expression: -168*y**6 - 799*y**3 - 280</replace>
No more calculations needed.
<answer>-168*y**6 - 799*y**3 - 280</answer>


Question:
Simplify this expression: (16 - 11*z)*(20*z**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: -220*z**4 + 320*z**3 + 242*z - 352

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16 - 11*z)*(20*z**3 - 22)
Expanding the part (20*z**3 - 22) using the distributive property, and we got: (20*z**3)*(16 - 11*z) - 22*(16 - 11*z)
<replace-#Step 1>#Step 2:
Current expression: (20*z**3)*(16 - 11*z) - 22*(16 - 11*z)</replace>
Simplifying the partial expression: -22*(16 - 11*z)
Expanding the part (16 - 11*z) using the distributive property, and we got: -11*z*(-22) + 16*(-22)
Replacing -22*(16 - 11*z) with -11*z*(-22) + 16*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*z*(-22) + (20*z**3)*(16 - 11*z) - 352</replace>
Simplifying the partial expression: (20*z**3)*(16 - 11*z)
Expanding the part (16 - 11*z) using the distributive property, and we got: (-11*z)*(20*z**3) + 16*(20*z**3)
Replacing (20*z**3)*(16 - 11*z) with (-11*z)*(20*z**3) + 16*(20*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(20*z**3) - 11*z*(-22) + 16*20*z**3 - 352</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z)*-22 = 242*z
  (-11*z)*(20*z**3) = -220*z**4
  16*20*z**3 = 320*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -220*z**4 + 320*z**3 + 242*z - 352</replace>
No more calculations needed.
<answer>-220*z**4 + 320*z**3 + 242*z - 352</answer>


Question:
Calculate the following: (16*x**2 + 47)*(-9*x**3 + 12*x**2 - 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*x**2 + 47)*(-9*x**3 + 12*x**2 - 18)
Expanding the part (16*x**2 + 47) using the distributive property, and we got: (16*x**2)*(-9*x**3 + 12*x**2 - 18) + 47*(-9*x**3 + 12*x**2 - 18)
<replace-#Step 1>#Step 2:
Current expression: (16*x**2)*(-9*x**3 + 12*x**2 - 18) + 47*(-9*x**3 + 12*x**2 - 18)</replace>
Simplifying the partial expression: 47*(-9*x**3 + 12*x**2 - 18)
Expanding the part (-9*x**3 + 12*x**2 - 18) using the distributive property, and we got: (12*x**2)*47 - 9*x**3*47 - 18*47
Replacing 47*(-9*x**3 + 12*x**2 - 18) with (12*x**2)*47 - 9*x**3*47 - 18*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*x**2)*47 + (16*x**2)*(-9*x**3 + 12*x**2 - 18) - 9*x**3*47 - 846</replace>
Simplifying the partial expression: (16*x**2)*(-9*x**3 + 12*x**2 - 18)
Expanding the part (-9*x**3 + 12*x**2 - 18) using the distributive property, and we got: -288*x**2 + (12*x**2)*(16*x**2) + (16*x**2)*(-9*x**3)
Replacing (16*x**2)*(-9*x**3 + 12*x**2 - 18) with -288*x**2 + (12*x**2)*(16*x**2) + (16*x**2)*(-9*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -18*16*x**2 + (12*x**2)*(16*x**2) + (12*x**2)*47 + (16*x**2)*(-9*x**3) - 9*x**3*47 - 846</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*x**3)*47 = -423*x**3
  (-9*x**3)*(16*x**2) = -144*x**5
  (12*x**2)*47 = 564*x**2
  (12*x**2)*(16*x**2) = 192*x**4
  -18*16*x**2 = -288*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -144*x**5 + 192*x**4 - 423*x**3 - 288*x**2 + 564*x**2 - 846</replace>
Combining like terms, got -144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846
<replace-#Step 5>#Step 6:
Current expression: -144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846</replace>
No more calculations needed.
<answer>-144*x**5 + 192*x**4 - 423*x**3 + 276*x**2 - 846</answer>


Question:
Simplify this expression: (-38*y**3 + 40*y)*(-19*y**3 + 10*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: 722*y**6 - 1140*y**4 + 1102*y**3 + 400*y**2 - 1160*y


Question:
Simplify this expression: (-2*z**3 + 23*z**2 + 7)*(47*z**3 - 44*z**2 - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -94*z**6 + 1169*z**5 - 1012*z**4 + 389*z**3 - 998*z**2 - 210


Question:
Calculate the following: (20*x**3 + 102*x)*(4*x**2 + 22*x - 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: 80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*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: (20*x**3 + 102*x)*(4*x**2 + 22*x - 13)
Expanding the part (20*x**3 + 102*x) using the distributive property, and we got: (102*x)*(4*x**2 + 22*x - 13) + (20*x**3)*(4*x**2 + 22*x - 13)
<replace-#Step 1>#Step 2:
Current expression: (102*x)*(4*x**2 + 22*x - 13) + (20*x**3)*(4*x**2 + 22*x - 13)</replace>
Simplifying the partial expression: (20*x**3)*(4*x**2 + 22*x - 13)
Expanding the part (4*x**2 + 22*x - 13) using the distributive property, and we got: -260*x**3 + (22*x)*(20*x**3) + (4*x**2)*(20*x**3)
Replacing (20*x**3)*(4*x**2 + 22*x - 13) with -260*x**3 + (22*x)*(20*x**3) + (4*x**2)*(20*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -13*20*x**3 + (22*x)*(20*x**3) + (102*x)*(4*x**2 + 22*x - 13) + (4*x**2)*(20*x**3)</replace>
Simplifying the partial expression: (102*x)*(4*x**2 + 22*x - 13)
Expanding the part (4*x**2 + 22*x - 13) using the distributive property, and we got: -1326*x + (22*x)*(102*x) + (102*x)*(4*x**2)
Replacing (102*x)*(4*x**2 + 22*x - 13) with -1326*x + (22*x)*(102*x) + (102*x)*(4*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*20*x**3 - 13*102*x + (22*x)*(102*x) + (22*x)*(20*x**3) + (102*x)*(4*x**2) + (4*x**2)*(20*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*x**2)*(20*x**3) = 80*x**5
  (4*x**2)*(102*x) = 408*x**3
  (22*x)*(20*x**3) = 440*x**4
  (22*x)*(102*x) = 2244*x**2
  -13*20*x**3 = -260*x**3
  -13*102*x = -1326*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 80*x**5 + 440*x**4 - 260*x**3 + 408*x**3 + 2244*x**2 - 1326*x</replace>
Combining like terms, got 80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x
<replace-#Step 5>#Step 6:
Current expression: 80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x</replace>
No more calculations needed.
<answer>80*x**5 + 440*x**4 + 148*x**3 + 2244*x**2 - 1326*x</answer>


Question:
Calculate the following: 47*y*(27*y**3 - 34*y - 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: 1269*y**4 - 1598*y**2 - 799*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*(27*y**3 - 34*y - 17)
Expanding the part (27*y**3 - 34*y - 17) using the distributive property, and we got: (-34*y)*(47*y) - 799*y + (47*y)*(27*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-34*y)*(47*y) - 799*y + (47*y)*(27*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -17*(47*y) = -799*y
  (-34*y)*(47*y) = -1598*y**2
  (27*y**3)*(47*y) = 1269*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1269*y**4 - 1598*y**2 - 799*y</replace>
No more calculations needed.
<answer>1269*y**4 - 1598*y**2 - 799*y</answer>


Question:
Simplify this expression: (40*x**3 - 16)*(-16*x**3 - 39*x**2 + 6*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: -640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*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: (40*x**3 - 16)*(-16*x**3 - 39*x**2 + 6*x)
Expanding the part (40*x**3 - 16) using the distributive property, and we got: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) - 16*(-16*x**3 - 39*x**2 + 6*x)
<replace-#Step 1>#Step 2:
Current expression: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) - 16*(-16*x**3 - 39*x**2 + 6*x)</replace>
Simplifying the partial expression: -16*(-16*x**3 - 39*x**2 + 6*x)
Expanding the part (-16*x**3 - 39*x**2 + 6*x) using the distributive property, and we got: (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16)
Replacing -16*(-16*x**3 - 39*x**2 + 6*x) with (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*x)*(-16) - 39*x**2*(-16) - 16*x**3*(-16) + (40*x**3)*(-16*x**3 - 39*x**2 + 6*x)</replace>
Simplifying the partial expression: (40*x**3)*(-16*x**3 - 39*x**2 + 6*x)
Expanding the part (-16*x**3 - 39*x**2 + 6*x) using the distributive property, and we got: (6*x)*(40*x**3) + (-39*x**2)*(40*x**3) + (-16*x**3)*(40*x**3)
Replacing (40*x**3)*(-16*x**3 - 39*x**2 + 6*x) with (6*x)*(40*x**3) + (-39*x**2)*(40*x**3) + (-16*x**3)*(40*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*x)*(40*x**3) + (6*x)*(-16) + (-39*x**2)*(40*x**3) - 39*x**2*(-16) + (-16*x**3)*(40*x**3) - 16*x**3*(-16)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**2)*-16 = 624*x**2
  (-39*x**2)*(40*x**3) = -1560*x**5
  (-16*x**3)*-16 = 256*x**3
  (-16*x**3)*(40*x**3) = -640*x**6
  (6*x)*-16 = -96*x
  (6*x)*(40*x**3) = 240*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x</replace>
No more calculations needed.
<answer>-640*x**6 - 1560*x**5 + 240*x**4 + 256*x**3 + 624*x**2 - 96*x</answer>


Question:
Simplify this expression: (-25*y**2 - y)*(11*y**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: -275*y**4 - 11*y**3 + 25*y**2 + y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-25*y**2 - y)*(11*y**2 - 1)
Expanding the part (11*y**2 - 1) using the distributive property, and we got: (11*y**2)*(-25*y**2 - y) - (-25*y**2 - y)
<replace-#Step 1>#Step 2:
Current expression: (11*y**2)*(-25*y**2 - y) - (-25*y**2 - y)</replace>
Simplifying the partial expression: -(-25*y**2 - y)
Expanding the part (-25*y**2 - y) using the distributive property, and we got: -y*(-1) - 25*y**2*(-1)
Replacing -(-25*y**2 - y) with -y*(-1) - 25*y**2*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -y*(-1) - 25*y**2*(-1) + (11*y**2)*(-25*y**2 - y)</replace>
Simplifying the partial expression: (11*y**2)*(-25*y**2 - y)
Expanding the part (-25*y**2 - y) using the distributive property, and we got: (-y)*(11*y**2) + (-25*y**2)*(11*y**2)
Replacing (11*y**2)*(-25*y**2 - y) with (-y)*(11*y**2) + (-25*y**2)*(11*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y)*(11*y**2) - y*(-1) + (-25*y**2)*(11*y**2) - 25*y**2*(-1)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-y)*-1 = y
  (-y)*(11*y**2) = -11*y**3
  (-25*y**2)*-1 = 25*y**2
  (-25*y**2)*(11*y**2) = -275*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -275*y**4 - 11*y**3 + 25*y**2 + y</replace>
No more calculations needed.
<answer>-275*y**4 - 11*y**3 + 25*y**2 + y</answer>


Question:
Simplify this expression: 4826*y**5
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 4826*y**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 4826*y**5
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: 4826*y**5</replace>
No more calculations needed.
<answer>4826*y**5</answer>


Question:
Simplify this expression: (-41*z**3 - 2*z)*(-40*z**3 + 34*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1640*z**6 - 1314*z**4 - 68*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: (-41*z**3 - 2*z)*(-40*z**3 + 34*z)
Expanding the part (-41*z**3 - 2*z) using the distributive property, and we got: (-2*z)*(-40*z**3 + 34*z) + (-41*z**3)*(-40*z**3 + 34*z)
<replace-#Step 1>#Step 2:
Current expression: (-2*z)*(-40*z**3 + 34*z) + (-41*z**3)*(-40*z**3 + 34*z)</replace>
Simplifying the partial expression: (-41*z**3)*(-40*z**3 + 34*z)
Expanding the part (-40*z**3 + 34*z) using the distributive property, and we got: (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)
Replacing (-41*z**3)*(-40*z**3 + 34*z) with (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*z)*(-40*z**3 + 34*z) + (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)</replace>
Simplifying the partial expression: (-2*z)*(-40*z**3 + 34*z)
Expanding the part (-40*z**3 + 34*z) using the distributive property, and we got: (-2*z)*(34*z) + (-2*z)*(-40*z**3)
Replacing (-2*z)*(-40*z**3 + 34*z) with (-2*z)*(34*z) + (-2*z)*(-40*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(34*z) + (-2*z)*(-40*z**3) + (34*z)*(-41*z**3) + (-41*z**3)*(-40*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*z**3)*(-41*z**3) = 1640*z**6
  (-40*z**3)*(-2*z) = 80*z**4
  (34*z)*(-41*z**3) = -1394*z**4
  (34*z)*(-2*z) = -68*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1640*z**6 - 1394*z**4 + 80*z**4 - 68*z**2</replace>
Combining like terms, got 1640*z**6 - 1314*z**4 - 68*z**2
<replace-#Step 5>#Step 6:
Current expression: 1640*z**6 - 1314*z**4 - 68*z**2</replace>
No more calculations needed.
<answer>1640*z**6 - 1314*z**4 - 68*z**2</answer>


Question:
Simplify this expression: 23*y**2*(-31*y**3 - 55*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: -713*y**5 - 1265*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: 23*y**2*(-31*y**3 - 55*y)
Expanding the part (-31*y**3 - 55*y) using the distributive property, and we got: (-55*y)*(23*y**2) + (23*y**2)*(-31*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-55*y)*(23*y**2) + (23*y**2)*(-31*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-55*y)*(23*y**2) = -1265*y**3
  (-31*y**3)*(23*y**2) = -713*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -713*y**5 - 1265*y**3</replace>
No more calculations needed.
<answer>-713*y**5 - 1265*y**3</answer>


Question:
Calculate the following: 14*x**2*(-41*x**2 - 46*x + 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -574*x**4 - 644*x**3 + 518*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: 14*x**2*(-41*x**2 - 46*x + 37)
Expanding the part (-41*x**2 - 46*x + 37) using the distributive property, and we got: (-46*x)*(14*x**2) + 37*(14*x**2) + (-41*x**2)*(14*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-46*x)*(14*x**2) + 37*(14*x**2) + (-41*x**2)*(14*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  37*(14*x**2) = 518*x**2
  (-46*x)*(14*x**2) = -644*x**3
  (-41*x**2)*(14*x**2) = -574*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -574*x**4 - 644*x**3 + 518*x**2</replace>
No more calculations needed.
<answer>-574*x**4 - 644*x**3 + 518*x**2</answer>


Question:
Simplify this expression: (-5*x - 40)*(19*x**3 + 42*x**2 + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-5*x - 40)*(19*x**3 + 42*x**2 + 44)
Expanding the part (-5*x - 40) using the distributive property, and we got: (-5*x)*(19*x**3 + 42*x**2 + 44) - 40*(19*x**3 + 42*x**2 + 44)
<replace-#Step 1>#Step 2:
Current expression: (-5*x)*(19*x**3 + 42*x**2 + 44) - 40*(19*x**3 + 42*x**2 + 44)</replace>
Simplifying the partial expression: -40*(19*x**3 + 42*x**2 + 44)
Expanding the part (19*x**3 + 42*x**2 + 44) using the distributive property, and we got: (42*x**2)*(-40) + (19*x**3)*(-40) + 44*(-40)
Replacing -40*(19*x**3 + 42*x**2 + 44) with (42*x**2)*(-40) + (19*x**3)*(-40) + 44*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-5*x)*(19*x**3 + 42*x**2 + 44) + (42*x**2)*(-40) + (19*x**3)*(-40) - 1760</replace>
Simplifying the partial expression: (-5*x)*(19*x**3 + 42*x**2 + 44)
Expanding the part (19*x**3 + 42*x**2 + 44) using the distributive property, and we got: (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5*x)
Replacing (-5*x)*(19*x**3 + 42*x**2 + 44) with (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*x)*(42*x**2) + (-5*x)*(19*x**3) + 44*(-5)*x + (42*x**2)*(-40) + (19*x**3)*(-40) - 1760</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*x**3)*-40 = -760*x**3
  (19*x**3)*(-5*x) = -95*x**4
  (42*x**2)*-40 = -1680*x**2
  (42*x**2)*(-5*x) = -210*x**3
  44*-5*x = -220*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -95*x**4 - 760*x**3 - 210*x**3 - 1680*x**2 - 220*x - 1760</replace>
Combining like terms, got -95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760
<replace-#Step 5>#Step 6:
Current expression: -95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760</replace>
No more calculations needed.
<answer>-95*x**4 - 970*x**3 - 1680*x**2 - 220*x - 1760</answer>


Question:
Calculate the following: (7 - 42*y**2)*(35*y - 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: -1470*y**3 + 546*y**2 + 245*y - 91

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 - 42*y**2)*(35*y - 13)
Expanding the part (35*y - 13) using the distributive property, and we got: (35*y)*(7 - 42*y**2) - 13*(7 - 42*y**2)
<replace-#Step 1>#Step 2:
Current expression: (35*y)*(7 - 42*y**2) - 13*(7 - 42*y**2)</replace>
Simplifying the partial expression: -13*(7 - 42*y**2)
Expanding the part (7 - 42*y**2) using the distributive property, and we got: -42*y**2*(-13) + 7*(-13)
Replacing -13*(7 - 42*y**2) with -42*y**2*(-13) + 7*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*y)*(7 - 42*y**2) - 42*y**2*(-13) - 91</replace>
Simplifying the partial expression: (35*y)*(7 - 42*y**2)
Expanding the part (7 - 42*y**2) using the distributive property, and we got: 7*(35*y) + (35*y)*(-42*y**2)
Replacing (35*y)*(7 - 42*y**2) with 7*(35*y) + (35*y)*(-42*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 7*35*y + (35*y)*(-42*y**2) - 42*y**2*(-13) - 91</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y**2)*-13 = 546*y**2
  (-42*y**2)*(35*y) = -1470*y**3
  7*35*y = 245*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1470*y**3 + 546*y**2 + 245*y - 91</replace>
No more calculations needed.
<answer>-1470*y**3 + 546*y**2 + 245*y - 91</answer>


Question:
Simplify this expression: (-37*y**3 - 17*y**2)*(-43*y**3 - 84*y**2 - 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: 1591*y**6 + 3839*y**5 + 1428*y**4 + 1739*y**3 + 799*y**2


Question:
Simplify this expression: (27*z**2 - 14)*(38*z**3 - 9*z**2 + 35*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: 1026*z**5 - 243*z**4 + 413*z**3 + 126*z**2 - 490*z


Question:
Calculate the following: (12 - 43*x**2)*(-10*x**3 - 22*x**2 - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (12 - 43*x**2)*(-10*x**3 - 22*x**2 - 39)
Expanding the part (12 - 43*x**2) using the distributive property, and we got: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) + 12*(-10*x**3 - 22*x**2 - 39)
<replace-#Step 1>#Step 2:
Current expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) + 12*(-10*x**3 - 22*x**2 - 39)</replace>
Simplifying the partial expression: 12*(-10*x**3 - 22*x**2 - 39)
Expanding the part (-10*x**3 - 22*x**2 - 39) using the distributive property, and we got: -22*x**2*12 - 10*x**3*12 - 39*12
Replacing 12*(-10*x**3 - 22*x**2 - 39) with -22*x**2*12 - 10*x**3*12 - 39*12 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39) - 22*x**2*12 - 10*x**3*12 - 468</replace>
Simplifying the partial expression: (-43*x**2)*(-10*x**3 - 22*x**2 - 39)
Expanding the part (-10*x**3 - 22*x**2 - 39) using the distributive property, and we got: -(-1)*1677*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3)
Replacing (-43*x**2)*(-10*x**3 - 22*x**2 - 39) with -(-1)*1677*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -39*(-43)*x**2 + (-43*x**2)*(-22*x**2) + (-43*x**2)*(-10*x**3) - 22*x**2*12 - 10*x**3*12 - 468</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x**2)*12 = -264*x**2
  (-22*x**2)*(-43*x**2) = 946*x**4
  (-10*x**3)*12 = -120*x**3
  (-10*x**3)*(-43*x**2) = 430*x**5
  -39*-43*x**2 = 1677*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 430*x**5 + 946*x**4 - 120*x**3 - 264*x**2 + 1677*x**2 - 468</replace>
Combining like terms, got 430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468
<replace-#Step 5>#Step 6:
Current expression: 430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468</replace>
No more calculations needed.
<answer>430*x**5 + 946*x**4 - 120*x**3 + 1413*x**2 - 468</answer>


Question:
Calculate the following: (-17*z**2 - 40)*(-17*z**2 + z + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240

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*z**2 - 40)*(-17*z**2 + z + 6)
Expanding the part (-17*z**2 - 40) using the distributive property, and we got: (-17*z**2)*(-17*z**2 + z + 6) - 40*(-17*z**2 + z + 6)
<replace-#Step 1>#Step 2:
Current expression: (-17*z**2)*(-17*z**2 + z + 6) - 40*(-17*z**2 + z + 6)</replace>
Simplifying the partial expression: -40*(-17*z**2 + z + 6)
Expanding the part (-17*z**2 + z + 6) using the distributive property, and we got: z*(-40) - 17*z**2*(-40) + 6*(-40)
Replacing -40*(-17*z**2 + z + 6) with z*(-40) - 17*z**2*(-40) + 6*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: z*(-40) + (-17*z**2)*(-17*z**2 + z + 6) - 17*z**2*(-40) - 240</replace>
Simplifying the partial expression: (-17*z**2)*(-17*z**2 + z + 6)
Expanding the part (-17*z**2 + z + 6) using the distributive property, and we got: 6*(-17*z**2) + z*(-17*z**2) + (-17*z**2)*(-17*z**2)
Replacing (-17*z**2)*(-17*z**2 + z + 6) with 6*(-17*z**2) + z*(-17*z**2) + (-17*z**2)*(-17*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 6*(-17)*z**2 + z*(-17*z**2) + z*(-40) - 17*z**2*(-40) + (-17*z**2)*(-17*z**2) - 240</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  z*-40 = -40*z
  z*(-17*z**2) = -17*z**3
  (-17*z**2)*-40 = 680*z**2
  (-17*z**2)*(-17*z**2) = 289*z**4
  6*-17*z**2 = -102*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 289*z**4 - 17*z**3 - 102*z**2 + 680*z**2 - 40*z - 240</replace>
Combining like terms, got 289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240
<replace-#Step 5>#Step 6:
Current expression: 289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240</replace>
No more calculations needed.
<answer>289*z**4 - 17*z**3 + 578*z**2 - 40*z - 240</answer>


Question:
Calculate the following: (47 - 92*z**2)*(49*z**3 - 17*z + 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705

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 - 92*z**2)*(49*z**3 - 17*z + 15)
Expanding the part (47 - 92*z**2) using the distributive property, and we got: (-92*z**2)*(49*z**3 - 17*z + 15) + 47*(49*z**3 - 17*z + 15)
<replace-#Step 1>#Step 2:
Current expression: (-92*z**2)*(49*z**3 - 17*z + 15) + 47*(49*z**3 - 17*z + 15)</replace>
Simplifying the partial expression: 47*(49*z**3 - 17*z + 15)
Expanding the part (49*z**3 - 17*z + 15) using the distributive property, and we got: -17*z*47 + (49*z**3)*47 + 15*47
Replacing 47*(49*z**3 - 17*z + 15) with -17*z*47 + (49*z**3)*47 + 15*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -17*z*47 + (-92*z**2)*(49*z**3 - 17*z + 15) + (49*z**3)*47 + 705</replace>
Simplifying the partial expression: (-92*z**2)*(49*z**3 - 17*z + 15)
Expanding the part (49*z**3 - 17*z + 15) using the distributive property, and we got: (-17*z)*(-92*z**2) + 15*(-92*z**2) + (-92*z**2)*(49*z**3)
Replacing (-92*z**2)*(49*z**3 - 17*z + 15) with (-17*z)*(-92*z**2) + 15*(-92*z**2) + (-92*z**2)*(49*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-17*z)*(-92*z**2) - 17*z*47 + 15*(-92)*z**2 + (-92*z**2)*(49*z**3) + (49*z**3)*47 + 705</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*z)*47 = -799*z
  (-17*z)*(-92*z**2) = 1564*z**3
  (49*z**3)*47 = 2303*z**3
  (49*z**3)*(-92*z**2) = -4508*z**5
  15*-92*z**2 = -1380*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -4508*z**5 + 1564*z**3 + 2303*z**3 - 1380*z**2 - 799*z + 705</replace>
Combining like terms, got -4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705
<replace-#Step 5>#Step 6:
Current expression: -4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705</replace>
No more calculations needed.
<answer>-4508*z**5 + 3867*z**3 - 1380*z**2 - 799*z + 705</answer>


Question:
Calculate the following: (17*z**2 - 45)*(-50*z**3 + 16*z**2 - 4*z - 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: -850*z**5 + 272*z**4 + 2182*z**3 - 1128*z**2 + 180*z + 1080


Question:
Calculate the following: (13 - 29*z)*(69*z**3 - 33*z - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (13 - 29*z)*(69*z**3 - 33*z - 7)
Expanding the part (13 - 29*z) using the distributive property, and we got: (-29*z)*(69*z**3 - 33*z - 7) + 13*(69*z**3 - 33*z - 7)
<replace-#Step 1>#Step 2:
Current expression: (-29*z)*(69*z**3 - 33*z - 7) + 13*(69*z**3 - 33*z - 7)</replace>
Simplifying the partial expression: 13*(69*z**3 - 33*z - 7)
Expanding the part (69*z**3 - 33*z - 7) using the distributive property, and we got: -33*z*13 + (69*z**3)*13 - 7*13
Replacing 13*(69*z**3 - 33*z - 7) with -33*z*13 + (69*z**3)*13 - 7*13 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*z*13 + (-29*z)*(69*z**3 - 33*z - 7) + (69*z**3)*13 - 91</replace>
Simplifying the partial expression: (-29*z)*(69*z**3 - 33*z - 7)
Expanding the part (69*z**3 - 33*z - 7) using the distributive property, and we got: (-33*z)*(-29*z) + (-29*z)*(69*z**3) - (-1)*203*z
Replacing (-29*z)*(69*z**3 - 33*z - 7) with (-33*z)*(-29*z) + (-29*z)*(69*z**3) - (-1)*203*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*z)*(-29*z) - 33*z*13 + (-29*z)*(69*z**3) - 7*(-29)*z + (69*z**3)*13 - 91</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*z)*13 = -429*z
  (-33*z)*(-29*z) = 957*z**2
  (69*z**3)*13 = 897*z**3
  (69*z**3)*(-29*z) = -2001*z**4
  -7*-29*z = 203*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2001*z**4 + 897*z**3 + 957*z**2 - 429*z + 203*z - 91</replace>
Combining like terms, got -2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91
<replace-#Step 5>#Step 6:
Current expression: -2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91</replace>
No more calculations needed.
<answer>-2001*z**4 + 897*z**3 + 957*z**2 - 226*z - 91</answer>


Question:
Simplify this expression: (6*y**2 + 10*y - 22)*(-41*y**3 + 37*y - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -246*y**5 - 410*y**4 + 1124*y**3 + 190*y**2 - 1114*y + 660


Question:
Calculate the following: 15*y*(29*y**2 + 88*y - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 435*y**3 + 1320*y**2 - 240*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 15*y*(29*y**2 + 88*y - 16)
Expanding the part (29*y**2 + 88*y - 16) using the distributive property, and we got: -240*y + (15*y)*(88*y) + (15*y)*(29*y**2)
<replace-#Step 1>#Step 2:
Current expression: -240*y + (15*y)*(88*y) + (15*y)*(29*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(15*y) = -240*y
  (29*y**2)*(15*y) = 435*y**3
  (88*y)*(15*y) = 1320*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 435*y**3 + 1320*y**2 - 240*y</replace>
No more calculations needed.
<answer>435*y**3 + 1320*y**2 - 240*y</answer>


Question:
Simplify this expression: (-66*x - 45)*(-20*x - 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: 1320*x**2 + 3738*x + 1935

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*x - 45)*(-20*x - 43)
Expanding the part (-66*x - 45) using the distributive property, and we got: (-66*x)*(-20*x - 43) - 45*(-20*x - 43)
<replace-#Step 1>#Step 2:
Current expression: (-66*x)*(-20*x - 43) - 45*(-20*x - 43)</replace>
Simplifying the partial expression: -45*(-20*x - 43)
Expanding the part (-20*x - 43) using the distributive property, and we got: -20*x*(-45) - 43*(-45)
Replacing -45*(-20*x - 43) with -20*x*(-45) - 43*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-66*x)*(-20*x - 43) - 20*x*(-45) + 1935</replace>
Simplifying the partial expression: (-66*x)*(-20*x - 43)
Expanding the part (-20*x - 43) using the distributive property, and we got: (-66*x)*(-20*x) - (-1)*2838*x
Replacing (-66*x)*(-20*x - 43) with (-66*x)*(-20*x) - (-1)*2838*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-66*x)*(-20*x) - 20*x*(-45) - 43*(-66)*x + 1935</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x)*-45 = 900*x
  (-20*x)*(-66*x) = 1320*x**2
  -43*-66*x = 2838*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1320*x**2 + 900*x + 2838*x + 1935</replace>
Combining like terms, got 1320*x**2 + 3738*x + 1935
<replace-#Step 5>#Step 6:
Current expression: 1320*x**2 + 3738*x + 1935</replace>
No more calculations needed.
<answer>1320*x**2 + 3738*x + 1935</answer>


Question:
Calculate the following: (62*z**3 - 3)*(-4*z**3 + 39*z**2 - 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (62*z**3 - 3)*(-4*z**3 + 39*z**2 - 28)
Expanding the part (62*z**3 - 3) using the distributive property, and we got: (62*z**3)*(-4*z**3 + 39*z**2 - 28) - 3*(-4*z**3 + 39*z**2 - 28)
<replace-#Step 1>#Step 2:
Current expression: (62*z**3)*(-4*z**3 + 39*z**2 - 28) - 3*(-4*z**3 + 39*z**2 - 28)</replace>
Simplifying the partial expression: -3*(-4*z**3 + 39*z**2 - 28)
Expanding the part (-4*z**3 + 39*z**2 - 28) using the distributive property, and we got: (39*z**2)*(-3) - 4*z**3*(-3) - 28*(-3)
Replacing -3*(-4*z**3 + 39*z**2 - 28) with (39*z**2)*(-3) - 4*z**3*(-3) - 28*(-3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*z**2)*(-3) - 4*z**3*(-3) + (62*z**3)*(-4*z**3 + 39*z**2 - 28) + 84</replace>
Simplifying the partial expression: (62*z**3)*(-4*z**3 + 39*z**2 - 28)
Expanding the part (-4*z**3 + 39*z**2 - 28) using the distributive property, and we got: -1736*z**3 + (39*z**2)*(62*z**3) + (-4*z**3)*(62*z**3)
Replacing (62*z**3)*(-4*z**3 + 39*z**2 - 28) with -1736*z**3 + (39*z**2)*(62*z**3) + (-4*z**3)*(62*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -28*62*z**3 + (39*z**2)*(62*z**3) + (39*z**2)*(-3) + (-4*z**3)*(62*z**3) - 4*z**3*(-3) + 84</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*z**3)*-3 = 12*z**3
  (-4*z**3)*(62*z**3) = -248*z**6
  (39*z**2)*-3 = -117*z**2
  (39*z**2)*(62*z**3) = 2418*z**5
  -28*62*z**3 = -1736*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -248*z**6 + 2418*z**5 - 1736*z**3 + 12*z**3 - 117*z**2 + 84</replace>
Combining like terms, got -248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84
<replace-#Step 5>#Step 6:
Current expression: -248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84</replace>
No more calculations needed.
<answer>-248*z**6 + 2418*z**5 - 1724*z**3 - 117*z**2 + 84</answer>


Question:
Simplify this expression: (z**2 - 45)*(22*z**2 - 13*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: 22*z**4 - 13*z**3 - 990*z**2 + 585*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (z**2 - 45)*(22*z**2 - 13*z)
Expanding the part (z**2 - 45) using the distributive property, and we got: z**2*(22*z**2 - 13*z) - 45*(22*z**2 - 13*z)
<replace-#Step 1>#Step 2:
Current expression: z**2*(22*z**2 - 13*z) - 45*(22*z**2 - 13*z)</replace>
Simplifying the partial expression: -45*(22*z**2 - 13*z)
Expanding the part (22*z**2 - 13*z) using the distributive property, and we got: -13*z*(-45) + (22*z**2)*(-45)
Replacing -45*(22*z**2 - 13*z) with -13*z*(-45) + (22*z**2)*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -13*z*(-45) + z**2*(22*z**2 - 13*z) + (22*z**2)*(-45)</replace>
Simplifying the partial expression: z**2*(22*z**2 - 13*z)
Expanding the part (22*z**2 - 13*z) using the distributive property, and we got: (-13*z)*z**2 + z**2*(22*z**2)
Replacing z**2*(22*z**2 - 13*z) with (-13*z)*z**2 + z**2*(22*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-13*z)*z**2 - 13*z*(-45) + z**2*(22*z**2) + (22*z**2)*(-45)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z)*-45 = 585*z
  (-13*z)*z**2 = -13*z**3
  (22*z**2)*-45 = -990*z**2
  (22*z**2)*z**2 = 22*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 22*z**4 - 13*z**3 - 990*z**2 + 585*z</replace>
No more calculations needed.
<answer>22*z**4 - 13*z**3 - 990*z**2 + 585*z</answer>


Question:
Simplify this expression: -22*z**3*(66 - 12*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 264*z**4 - 1452*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: -22*z**3*(66 - 12*z)
Expanding the part (66 - 12*z) using the distributive property, and we got: (-12*z)*(-22*z**3) + 66*(-22*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-12*z)*(-22*z**3) + 66*(-22*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  66*(-22*z**3) = -1452*z**3
  (-12*z)*(-22*z**3) = 264*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 264*z**4 - 1452*z**3</replace>
No more calculations needed.
<answer>264*z**4 - 1452*z**3</answer>


Question:
Simplify this expression: (27*z**3 - 2*z**2 + z)*(17*z**3 - 47*z**2 + 11*z - 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: 459*z**6 - 1303*z**5 + 408*z**4 - 609*z**3 + 51*z**2 - 20*z


Question:
Simplify this expression: (-5*x**3 + 42*x**2 + 14*x)*(21*x**3 - 61*x**2 + 9*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: -105*x**6 + 1187*x**5 - 2313*x**4 - 476*x**3 + 126*x**2


Question:
Calculate the following: (-6*y**3 - 18)*(3*y**3 + 18*y**2 + 19*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-6*y**3 - 18)*(3*y**3 + 18*y**2 + 19*y)
Expanding the part (-6*y**3 - 18) using the distributive property, and we got: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) - 18*(3*y**3 + 18*y**2 + 19*y)
<replace-#Step 1>#Step 2:
Current expression: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) - 18*(3*y**3 + 18*y**2 + 19*y)</replace>
Simplifying the partial expression: -18*(3*y**3 + 18*y**2 + 19*y)
Expanding the part (3*y**3 + 18*y**2 + 19*y) using the distributive property, and we got: (19*y)*(-18) + (18*y**2)*(-18) + (3*y**3)*(-18)
Replacing -18*(3*y**3 + 18*y**2 + 19*y) with (19*y)*(-18) + (18*y**2)*(-18) + (3*y**3)*(-18) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*y)*(-18) + (18*y**2)*(-18) + (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) + (3*y**3)*(-18)</replace>
Simplifying the partial expression: (-6*y**3)*(3*y**3 + 18*y**2 + 19*y)
Expanding the part (3*y**3 + 18*y**2 + 19*y) using the distributive property, and we got: (19*y)*(-6*y**3) + (18*y**2)*(-6*y**3) + (-6*y**3)*(3*y**3)
Replacing (-6*y**3)*(3*y**3 + 18*y**2 + 19*y) with (19*y)*(-6*y**3) + (18*y**2)*(-6*y**3) + (-6*y**3)*(3*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (19*y)*(-6*y**3) + (19*y)*(-18) + (18*y**2)*(-6*y**3) + (18*y**2)*(-18) + (-6*y**3)*(3*y**3) + (3*y**3)*(-18)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**3)*-18 = -54*y**3
  (3*y**3)*(-6*y**3) = -18*y**6
  (18*y**2)*-18 = -324*y**2
  (18*y**2)*(-6*y**3) = -108*y**5
  (19*y)*-18 = -342*y
  (19*y)*(-6*y**3) = -114*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y</replace>
No more calculations needed.
<answer>-18*y**6 - 108*y**5 - 114*y**4 - 54*y**3 - 324*y**2 - 342*y</answer>


Question:
Simplify this expression: (y**2 + 33)*(-50*y**3 + 2*y + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (y**2 + 33)*(-50*y**3 + 2*y + 36)
Expanding the part (y**2 + 33) using the distributive property, and we got: y**2*(-50*y**3 + 2*y + 36) + 33*(-50*y**3 + 2*y + 36)
<replace-#Step 1>#Step 2:
Current expression: y**2*(-50*y**3 + 2*y + 36) + 33*(-50*y**3 + 2*y + 36)</replace>
Simplifying the partial expression: 33*(-50*y**3 + 2*y + 36)
Expanding the part (-50*y**3 + 2*y + 36) using the distributive property, and we got: (2*y)*33 - 50*y**3*33 + 36*33
Replacing 33*(-50*y**3 + 2*y + 36) with (2*y)*33 - 50*y**3*33 + 36*33 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*(-50*y**3 + 2*y + 36) + (2*y)*33 - 50*y**3*33 + 1188</replace>
Simplifying the partial expression: y**2*(-50*y**3 + 2*y + 36)
Expanding the part (-50*y**3 + 2*y + 36) using the distributive property, and we got: (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2
Replacing y**2*(-50*y**3 + 2*y + 36) with (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (2*y)*y**2 + y**2*(-50*y**3) + 36*y**2 + (2*y)*33 - 50*y**3*33 + 1188</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y**3)*33 = -1650*y**3
  (-50*y**3)*y**2 = -50*y**5
  (2*y)*33 = 66*y
  (2*y)*y**2 = 2*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -50*y**5 - 1650*y**3 + 2*y**3 + 36*y**2 + 66*y + 1188</replace>
Combining like terms, got -50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188
<replace-#Step 5>#Step 6:
Current expression: -50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188</replace>
No more calculations needed.
<answer>-50*y**5 - 1648*y**3 + 36*y**2 + 66*y + 1188</answer>


Question:
Simplify this expression: (-50*y**2 - 71*y)*(27*y**3 + 49*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*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: (-50*y**2 - 71*y)*(27*y**3 + 49*y)
Expanding the part (-50*y**2 - 71*y) using the distributive property, and we got: (-71*y)*(27*y**3 + 49*y) + (-50*y**2)*(27*y**3 + 49*y)
<replace-#Step 1>#Step 2:
Current expression: (-71*y)*(27*y**3 + 49*y) + (-50*y**2)*(27*y**3 + 49*y)</replace>
Simplifying the partial expression: (-71*y)*(27*y**3 + 49*y)
Expanding the part (27*y**3 + 49*y) using the distributive property, and we got: (-71*y)*(49*y) + (-71*y)*(27*y**3)
Replacing (-71*y)*(27*y**3 + 49*y) with (-71*y)*(49*y) + (-71*y)*(27*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-71*y)*(49*y) + (-71*y)*(27*y**3) + (-50*y**2)*(27*y**3 + 49*y)</replace>
Simplifying the partial expression: (-50*y**2)*(27*y**3 + 49*y)
Expanding the part (27*y**3 + 49*y) using the distributive property, and we got: (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3)
Replacing (-50*y**2)*(27*y**3 + 49*y) with (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-71*y)*(49*y) + (-71*y)*(27*y**3) + (49*y)*(-50*y**2) + (-50*y**2)*(27*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (27*y**3)*(-71*y) = -1917*y**4
  (27*y**3)*(-50*y**2) = -1350*y**5
  (49*y)*(-71*y) = -3479*y**2
  (49*y)*(-50*y**2) = -2450*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2</replace>
No more calculations needed.
<answer>-1350*y**5 - 1917*y**4 - 2450*y**3 - 3479*y**2</answer>


Question:
Calculate the following: (-50*z**3 + 11*z**2 + 13*z)*(31*z**3 - 14*z**2 + 43*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: -1550*z**6 + 1041*z**5 - 1901*z**4 + 291*z**3 + 559*z**2


Question:
Calculate the following: (-32*z**3 - 23)*(-11*z**2 + 36*z - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-32*z**3 - 23)*(-11*z**2 + 36*z - 44)
Expanding the part (-32*z**3 - 23) using the distributive property, and we got: (-32*z**3)*(-11*z**2 + 36*z - 44) - 23*(-11*z**2 + 36*z - 44)
<replace-#Step 1>#Step 2:
Current expression: (-32*z**3)*(-11*z**2 + 36*z - 44) - 23*(-11*z**2 + 36*z - 44)</replace>
Simplifying the partial expression: -23*(-11*z**2 + 36*z - 44)
Expanding the part (-11*z**2 + 36*z - 44) using the distributive property, and we got: (36*z)*(-23) - 11*z**2*(-23) - 44*(-23)
Replacing -23*(-11*z**2 + 36*z - 44) with (36*z)*(-23) - 11*z**2*(-23) - 44*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*z)*(-23) - 11*z**2*(-23) + (-32*z**3)*(-11*z**2 + 36*z - 44) + 1012</replace>
Simplifying the partial expression: (-32*z**3)*(-11*z**2 + 36*z - 44)
Expanding the part (-11*z**2 + 36*z - 44) using the distributive property, and we got: -(-1)*1408*z**3 + (36*z)*(-32*z**3) + (-11*z**2)*(-32*z**3)
Replacing (-32*z**3)*(-11*z**2 + 36*z - 44) with -(-1)*1408*z**3 + (36*z)*(-32*z**3) + (-11*z**2)*(-32*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -44*(-32)*z**3 + (36*z)*(-32*z**3) + (36*z)*(-23) + (-11*z**2)*(-32*z**3) - 11*z**2*(-23) + 1012</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z**2)*-23 = 253*z**2
  (-11*z**2)*(-32*z**3) = 352*z**5
  (36*z)*-23 = -828*z
  (36*z)*(-32*z**3) = -1152*z**4
  -44*-32*z**3 = 1408*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012</replace>
No more calculations needed.
<answer>352*z**5 - 1152*z**4 + 1408*z**3 + 253*z**2 - 828*z + 1012</answer>


Question:
Simplify this expression: (7*x**3 + 48*x**2 + 23)*(9*x**3 - 21*x**2 - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 63*x**6 + 285*x**5 - 1008*x**4 + 172*x**3 - 723*x**2 - 115


Question:
Simplify this expression: (7*y**2 - 7*y + 46)*(24*y**3 - 7*y**2 + 21*y - 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 168*y**5 - 217*y**4 + 1300*y**3 - 602*y**2 + 1099*y - 874


Question:
Calculate the following: (-25*x**3 + 5*x**2 - 42)*(23*x**3 + 11*x**2 + 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -575*x**6 - 160*x**5 + 55*x**4 - 1416*x**3 - 372*x**2 - 756


Question:
Calculate the following: -73*z*(-19*z**3 - 53*z + 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: 1387*z**4 + 3869*z**2 - 3431*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: -73*z*(-19*z**3 - 53*z + 47)
Expanding the part (-19*z**3 - 53*z + 47) using the distributive property, and we got: (-73*z)*(-53*z) + (-73*z)*(-19*z**3) + 47*(-73*z)
<replace-#Step 1>#Step 2:
Current expression: (-73*z)*(-53*z) + (-73*z)*(-19*z**3) + 47*(-73*z)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  47*(-73*z) = -3431*z
  (-53*z)*(-73*z) = 3869*z**2
  (-19*z**3)*(-73*z) = 1387*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1387*z**4 + 3869*z**2 - 3431*z</replace>
No more calculations needed.
<answer>1387*z**4 + 3869*z**2 - 3431*z</answer>


Question:
Calculate the following: -92*z**3*(-36*z**3 - 23*z**2 + 35*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: 3312*z**6 + 2116*z**5 - 3220*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -92*z**3*(-36*z**3 - 23*z**2 + 35*z)
Expanding the part (-36*z**3 - 23*z**2 + 35*z) using the distributive property, and we got: (35*z)*(-92*z**3) + (-23*z**2)*(-92*z**3) + (-92*z**3)*(-36*z**3)
<replace-#Step 1>#Step 2:
Current expression: (35*z)*(-92*z**3) + (-23*z**2)*(-92*z**3) + (-92*z**3)*(-36*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*z**3)*(-92*z**3) = 3312*z**6
  (-23*z**2)*(-92*z**3) = 2116*z**5
  (35*z)*(-92*z**3) = -3220*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 3312*z**6 + 2116*z**5 - 3220*z**4</replace>
No more calculations needed.
<answer>3312*z**6 + 2116*z**5 - 3220*z**4</answer>


Question:
Simplify this expression: (-56*z**3 - 4*z)*(23*z**2 + 31*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: -1288*z**5 - 1736*z**4 + 4388*z**3 - 124*z**2 + 320*z


Question:
Calculate the following: (-27*y**3 - 37*y**2 - 55*y)*(-7*y**3 - 20*y - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 189*y**6 + 259*y**5 + 925*y**4 + 1604*y**3 + 2284*y**2 + 1760*y


Question:
Calculate the following: (-7*y**2 - 41*y)*(-16*y**3 - 46*y**2 + 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 112*y**5 + 978*y**4 + 1886*y**3 - 63*y**2 - 369*y


Question:
Calculate the following: 68*z*(-34*z**3 - 12*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2312*z**4 - 816*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: 68*z*(-34*z**3 - 12*z)
Expanding the part (-34*z**3 - 12*z) using the distributive property, and we got: (-12*z)*(68*z) + (68*z)*(-34*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-12*z)*(68*z) + (68*z)*(-34*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*z**3)*(68*z) = -2312*z**4
  (-12*z)*(68*z) = -816*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2312*z**4 - 816*z**2</replace>
No more calculations needed.
<answer>-2312*z**4 - 816*z**2</answer>


Question:
Simplify this expression: (55 - 31*x**2)*(11*x**2 + 19*x + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540

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: (55 - 31*x**2)*(11*x**2 + 19*x + 28)
Expanding the part (55 - 31*x**2) using the distributive property, and we got: (-31*x**2)*(11*x**2 + 19*x + 28) + 55*(11*x**2 + 19*x + 28)
<replace-#Step 1>#Step 2:
Current expression: (-31*x**2)*(11*x**2 + 19*x + 28) + 55*(11*x**2 + 19*x + 28)</replace>
Simplifying the partial expression: 55*(11*x**2 + 19*x + 28)
Expanding the part (11*x**2 + 19*x + 28) using the distributive property, and we got: (19*x)*55 + (11*x**2)*55 + 28*55
Replacing 55*(11*x**2 + 19*x + 28) with (19*x)*55 + (11*x**2)*55 + 28*55 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*x)*55 + (-31*x**2)*(11*x**2 + 19*x + 28) + (11*x**2)*55 + 1540</replace>
Simplifying the partial expression: (-31*x**2)*(11*x**2 + 19*x + 28)
Expanding the part (11*x**2 + 19*x + 28) using the distributive property, and we got: 28*(-31*x**2) + (19*x)*(-31*x**2) + (-31*x**2)*(11*x**2)
Replacing (-31*x**2)*(11*x**2 + 19*x + 28) with 28*(-31*x**2) + (19*x)*(-31*x**2) + (-31*x**2)*(11*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 28*(-31)*x**2 + (19*x)*(-31*x**2) + (19*x)*55 + (-31*x**2)*(11*x**2) + (11*x**2)*55 + 1540</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*x**2)*55 = 605*x**2
  (11*x**2)*(-31*x**2) = -341*x**4
  (19*x)*55 = 1045*x
  (19*x)*(-31*x**2) = -589*x**3
  28*-31*x**2 = -868*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -341*x**4 - 589*x**3 - 868*x**2 + 605*x**2 + 1045*x + 1540</replace>
Combining like terms, got -341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540
<replace-#Step 5>#Step 6:
Current expression: -341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540</replace>
No more calculations needed.
<answer>-341*x**4 - 589*x**3 - 263*x**2 + 1045*x + 1540</answer>


Question:
Calculate the following: (20*z**3 + z)*(24*z**3 + 42*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 480*z**6 + 864*z**4 + 42*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: (20*z**3 + z)*(24*z**3 + 42*z)
Expanding the part (20*z**3 + z) using the distributive property, and we got: z*(24*z**3 + 42*z) + (20*z**3)*(24*z**3 + 42*z)
<replace-#Step 1>#Step 2:
Current expression: z*(24*z**3 + 42*z) + (20*z**3)*(24*z**3 + 42*z)</replace>
Simplifying the partial expression: z*(24*z**3 + 42*z)
Expanding the part (24*z**3 + 42*z) using the distributive property, and we got: z*(42*z) + z*(24*z**3)
Replacing z*(24*z**3 + 42*z) with z*(42*z) + z*(24*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: z*(42*z) + z*(24*z**3) + (20*z**3)*(24*z**3 + 42*z)</replace>
Simplifying the partial expression: (20*z**3)*(24*z**3 + 42*z)
Expanding the part (24*z**3 + 42*z) using the distributive property, and we got: (42*z)*(20*z**3) + (20*z**3)*(24*z**3)
Replacing (20*z**3)*(24*z**3 + 42*z) with (42*z)*(20*z**3) + (20*z**3)*(24*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: z*(42*z) + z*(24*z**3) + (42*z)*(20*z**3) + (20*z**3)*(24*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (24*z**3)*z = 24*z**4
  (24*z**3)*(20*z**3) = 480*z**6
  (42*z)*z = 42*z**2
  (42*z)*(20*z**3) = 840*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 480*z**6 + 24*z**4 + 840*z**4 + 42*z**2</replace>
Combining like terms, got 480*z**6 + 864*z**4 + 42*z**2
<replace-#Step 5>#Step 6:
Current expression: 480*z**6 + 864*z**4 + 42*z**2</replace>
No more calculations needed.
<answer>480*z**6 + 864*z**4 + 42*z**2</answer>


Question:
Calculate the following: (24*x**3 + 30*x)*(-30*x**3 - 10*x**2 - 13*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: -720*x**6 - 240*x**5 - 1212*x**4 - 300*x**3 - 390*x**2


Question:
Simplify this expression: -5*y*(-34*y**3 - 20*y**2 - 18*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: 170*y**4 + 100*y**3 + 90*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: -5*y*(-34*y**3 - 20*y**2 - 18*y)
Expanding the part (-34*y**3 - 20*y**2 - 18*y) using the distributive property, and we got: (-18*y)*(-5*y) + (-5*y)*(-20*y**2) + (-5*y)*(-34*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-18*y)*(-5*y) + (-5*y)*(-20*y**2) + (-5*y)*(-34*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*y**3)*(-5*y) = 170*y**4
  (-20*y**2)*(-5*y) = 100*y**3
  (-18*y)*(-5*y) = 90*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 170*y**4 + 100*y**3 + 90*y**2</replace>
No more calculations needed.
<answer>170*y**4 + 100*y**3 + 90*y**2</answer>


Question:
Calculate the following: (-10*z**2 - 11*z)*(-6*z**3 - 36*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: 60*z**5 + 66*z**4 + 360*z**3 + 396*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: (-10*z**2 - 11*z)*(-6*z**3 - 36*z)
Expanding the part (-6*z**3 - 36*z) using the distributive property, and we got: (-36*z)*(-10*z**2 - 11*z) + (-6*z**3)*(-10*z**2 - 11*z)
<replace-#Step 1>#Step 2:
Current expression: (-36*z)*(-10*z**2 - 11*z) + (-6*z**3)*(-10*z**2 - 11*z)</replace>
Simplifying the partial expression: (-36*z)*(-10*z**2 - 11*z)
Expanding the part (-10*z**2 - 11*z) using the distributive property, and we got: (-36*z)*(-11*z) + (-36*z)*(-10*z**2)
Replacing (-36*z)*(-10*z**2 - 11*z) with (-36*z)*(-11*z) + (-36*z)*(-10*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*z)*(-11*z) + (-36*z)*(-10*z**2) + (-6*z**3)*(-10*z**2 - 11*z)</replace>
Simplifying the partial expression: (-6*z**3)*(-10*z**2 - 11*z)
Expanding the part (-10*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3)
Replacing (-6*z**3)*(-10*z**2 - 11*z) with (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*z)*(-11*z) + (-36*z)*(-10*z**2) + (-11*z)*(-6*z**3) + (-10*z**2)*(-6*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z)*(-36*z) = 396*z**2
  (-11*z)*(-6*z**3) = 66*z**4
  (-10*z**2)*(-36*z) = 360*z**3
  (-10*z**2)*(-6*z**3) = 60*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 60*z**5 + 66*z**4 + 360*z**3 + 396*z**2</replace>
No more calculations needed.
<answer>60*z**5 + 66*z**4 + 360*z**3 + 396*z**2</answer>


Question:
Calculate the following: -44*y*(-36*y**3 - 2*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: 1584*y**4 + 88*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: -44*y*(-36*y**3 - 2*y**2)
Expanding the part (-36*y**3 - 2*y**2) using the distributive property, and we got: (-44*y)*(-2*y**2) + (-44*y)*(-36*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-44*y)*(-2*y**2) + (-44*y)*(-36*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*y**3)*(-44*y) = 1584*y**4
  (-2*y**2)*(-44*y) = 88*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1584*y**4 + 88*y**3</replace>
No more calculations needed.
<answer>1584*y**4 + 88*y**3</answer>


Question:
Simplify this expression: (-16*y - 23)*(20*y**2 - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -320*y**3 - 460*y**2 + 224*y + 322

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-16*y - 23)*(20*y**2 - 14)
Expanding the part (-16*y - 23) using the distributive property, and we got: (-16*y)*(20*y**2 - 14) - 23*(20*y**2 - 14)
<replace-#Step 1>#Step 2:
Current expression: (-16*y)*(20*y**2 - 14) - 23*(20*y**2 - 14)</replace>
Simplifying the partial expression: -23*(20*y**2 - 14)
Expanding the part (20*y**2 - 14) using the distributive property, and we got: (20*y**2)*(-23) - 14*(-23)
Replacing -23*(20*y**2 - 14) with (20*y**2)*(-23) - 14*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-16*y)*(20*y**2 - 14) + (20*y**2)*(-23) + 322</replace>
Simplifying the partial expression: (-16*y)*(20*y**2 - 14)
Expanding the part (20*y**2 - 14) using the distributive property, and we got: (-16*y)*(20*y**2) - (-1)*224*y
Replacing (-16*y)*(20*y**2 - 14) with (-16*y)*(20*y**2) - (-1)*224*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*y)*(20*y**2) - 14*(-16)*y + (20*y**2)*(-23) + 322</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*y**2)*-23 = -460*y**2
  (20*y**2)*(-16*y) = -320*y**3
  -14*-16*y = 224*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -320*y**3 - 460*y**2 + 224*y + 322</replace>
No more calculations needed.
<answer>-320*y**3 - 460*y**2 + 224*y + 322</answer>


Question:
Simplify this expression: (40 - 20*z**2)*(51*z**3 + 36*z**2 + 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (40 - 20*z**2)*(51*z**3 + 36*z**2 + 5)
Expanding the part (40 - 20*z**2) using the distributive property, and we got: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + 40*(51*z**3 + 36*z**2 + 5)
<replace-#Step 1>#Step 2:
Current expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + 40*(51*z**3 + 36*z**2 + 5)</replace>
Simplifying the partial expression: 40*(51*z**3 + 36*z**2 + 5)
Expanding the part (51*z**3 + 36*z**2 + 5) using the distributive property, and we got: (36*z**2)*40 + (51*z**3)*40 + 5*40
Replacing 40*(51*z**3 + 36*z**2 + 5) with (36*z**2)*40 + (51*z**3)*40 + 5*40 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5) + (36*z**2)*40 + (51*z**3)*40 + 200</replace>
Simplifying the partial expression: (-20*z**2)*(51*z**3 + 36*z**2 + 5)
Expanding the part (51*z**3 + 36*z**2 + 5) using the distributive property, and we got: 5*(-20*z**2) + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3)
Replacing (-20*z**2)*(51*z**3 + 36*z**2 + 5) with 5*(-20*z**2) + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 5*(-20)*z**2 + (-20*z**2)*(36*z**2) + (-20*z**2)*(51*z**3) + (36*z**2)*40 + (51*z**3)*40 + 200</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (36*z**2)*40 = 1440*z**2
  (36*z**2)*(-20*z**2) = -720*z**4
  (51*z**3)*40 = 2040*z**3
  (51*z**3)*(-20*z**2) = -1020*z**5
  5*-20*z**2 = -100*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1020*z**5 - 720*z**4 + 2040*z**3 - 100*z**2 + 1440*z**2 + 200</replace>
Combining like terms, got -1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200
<replace-#Step 5>#Step 6:
Current expression: -1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200</replace>
No more calculations needed.
<answer>-1020*z**5 - 720*z**4 + 2040*z**3 + 1340*z**2 + 200</answer>


Question:
Simplify this expression: (41*z**3 + 8)*(-3*z**3 + 17*z**2 - 46*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*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: (41*z**3 + 8)*(-3*z**3 + 17*z**2 - 46*z)
Expanding the part (41*z**3 + 8) using the distributive property, and we got: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) + 8*(-3*z**3 + 17*z**2 - 46*z)
<replace-#Step 1>#Step 2:
Current expression: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) + 8*(-3*z**3 + 17*z**2 - 46*z)</replace>
Simplifying the partial expression: 8*(-3*z**3 + 17*z**2 - 46*z)
Expanding the part (-3*z**3 + 17*z**2 - 46*z) using the distributive property, and we got: -46*z*8 + (17*z**2)*8 - 3*z**3*8
Replacing 8*(-3*z**3 + 17*z**2 - 46*z) with -46*z*8 + (17*z**2)*8 - 3*z**3*8 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*z*8 + (17*z**2)*8 - 3*z**3*8 + (41*z**3)*(-3*z**3 + 17*z**2 - 46*z)</replace>
Simplifying the partial expression: (41*z**3)*(-3*z**3 + 17*z**2 - 46*z)
Expanding the part (-3*z**3 + 17*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(41*z**3) + (17*z**2)*(41*z**3) + (-3*z**3)*(41*z**3)
Replacing (41*z**3)*(-3*z**3 + 17*z**2 - 46*z) with (-46*z)*(41*z**3) + (17*z**2)*(41*z**3) + (-3*z**3)*(41*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(41*z**3) - 46*z*8 + (17*z**2)*(41*z**3) + (17*z**2)*8 + (-3*z**3)*(41*z**3) - 3*z**3*8</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*z)*8 = -368*z
  (-46*z)*(41*z**3) = -1886*z**4
  (-3*z**3)*8 = -24*z**3
  (-3*z**3)*(41*z**3) = -123*z**6
  (17*z**2)*8 = 136*z**2
  (17*z**2)*(41*z**3) = 697*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z</replace>
No more calculations needed.
<answer>-123*z**6 + 697*z**5 - 1886*z**4 - 24*z**3 + 136*z**2 - 368*z</answer>


Question:
Calculate the following: (-29*z - 20)*(6*z + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -174*z**2 - 294*z - 120

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-29*z - 20)*(6*z + 6)
Expanding the part (-29*z - 20) using the distributive property, and we got: (-29*z)*(6*z + 6) - 20*(6*z + 6)
<replace-#Step 1>#Step 2:
Current expression: (-29*z)*(6*z + 6) - 20*(6*z + 6)</replace>
Simplifying the partial expression: -20*(6*z + 6)
Expanding the part (6*z + 6) using the distributive property, and we got: (6*z)*(-20) + 6*(-20)
Replacing -20*(6*z + 6) with (6*z)*(-20) + 6*(-20) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-29*z)*(6*z + 6) + (6*z)*(-20) - 120</replace>
Simplifying the partial expression: (-29*z)*(6*z + 6)
Expanding the part (6*z + 6) using the distributive property, and we got: (-29*z)*(6*z) + 6*(-29*z)
Replacing (-29*z)*(6*z + 6) with (-29*z)*(6*z) + 6*(-29*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*z)*(6*z) + 6*(-29)*z + (6*z)*(-20) - 120</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*z)*-20 = -120*z
  (6*z)*(-29*z) = -174*z**2
  6*-29*z = -174*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -174*z**2 - 174*z - 120*z - 120</replace>
Combining like terms, got -174*z**2 - 294*z - 120
<replace-#Step 5>#Step 6:
Current expression: -174*z**2 - 294*z - 120</replace>
No more calculations needed.
<answer>-174*z**2 - 294*z - 120</answer>


Question:
Calculate the following: (z**2 - 13)*(10*z**3 - 7*z**2 - 33*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: 10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (z**2 - 13)*(10*z**3 - 7*z**2 - 33*z)
Expanding the part (z**2 - 13) using the distributive property, and we got: z**2*(10*z**3 - 7*z**2 - 33*z) - 13*(10*z**3 - 7*z**2 - 33*z)
<replace-#Step 1>#Step 2:
Current expression: z**2*(10*z**3 - 7*z**2 - 33*z) - 13*(10*z**3 - 7*z**2 - 33*z)</replace>
Simplifying the partial expression: -13*(10*z**3 - 7*z**2 - 33*z)
Expanding the part (10*z**3 - 7*z**2 - 33*z) using the distributive property, and we got: -33*z*(-13) - 7*z**2*(-13) + (10*z**3)*(-13)
Replacing -13*(10*z**3 - 7*z**2 - 33*z) with -33*z*(-13) - 7*z**2*(-13) + (10*z**3)*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*z*(-13) + z**2*(10*z**3 - 7*z**2 - 33*z) - 7*z**2*(-13) + (10*z**3)*(-13)</replace>
Simplifying the partial expression: z**2*(10*z**3 - 7*z**2 - 33*z)
Expanding the part (10*z**3 - 7*z**2 - 33*z) using the distributive property, and we got: (-33*z)*z**2 + (-7*z**2)*z**2 + z**2*(10*z**3)
Replacing z**2*(10*z**3 - 7*z**2 - 33*z) with (-33*z)*z**2 + (-7*z**2)*z**2 + z**2*(10*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*z)*z**2 - 33*z*(-13) + (-7*z**2)*z**2 + z**2*(10*z**3) - 7*z**2*(-13) + (10*z**3)*(-13)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*z)*-13 = 429*z
  (-33*z)*z**2 = -33*z**3
  (-7*z**2)*-13 = 91*z**2
  (-7*z**2)*z**2 = -7*z**4
  (10*z**3)*-13 = -130*z**3
  (10*z**3)*z**2 = 10*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 10*z**5 - 7*z**4 - 130*z**3 - 33*z**3 + 91*z**2 + 429*z</replace>
Combining like terms, got 10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z
<replace-#Step 5>#Step 6:
Current expression: 10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z</replace>
No more calculations needed.
<answer>10*z**5 - 7*z**4 - 163*z**3 + 91*z**2 + 429*z</answer>


Question:
Simplify this expression: (-y**2 - 82*y)*(32*y**3 + 50*y + 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-y**2 - 82*y)*(32*y**3 + 50*y + 40)
Expanding the part (-y**2 - 82*y) using the distributive property, and we got: (-82*y)*(32*y**3 + 50*y + 40) + (-y**2)*(32*y**3 + 50*y + 40)
<replace-#Step 1>#Step 2:
Current expression: (-82*y)*(32*y**3 + 50*y + 40) + (-y**2)*(32*y**3 + 50*y + 40)</replace>
Simplifying the partial expression: (-y**2)*(32*y**3 + 50*y + 40)
Expanding the part (32*y**3 + 50*y + 40) using the distributive property, and we got: 40*(-y**2) + (50*y)*(-y**2) + (-y**2)*(32*y**3)
Replacing (-y**2)*(32*y**3 + 50*y + 40) with 40*(-y**2) + (50*y)*(-y**2) + (-y**2)*(32*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-82*y)*(32*y**3 + 50*y + 40) + 40*(-1)*y**2 + (50*y)*(-y**2) + (-y**2)*(32*y**3)</replace>
Simplifying the partial expression: (-82*y)*(32*y**3 + 50*y + 40)
Expanding the part (32*y**3 + 50*y + 40) using the distributive property, and we got: (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-82*y)
Replacing (-82*y)*(32*y**3 + 50*y + 40) with (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-82*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-82*y)*(50*y) + (-82*y)*(32*y**3) + 40*(-1)*y**2 + 40*(-82)*y + (50*y)*(-y**2) + (-y**2)*(32*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*y**3)*(-y**2) = -32*y**5
  (32*y**3)*(-82*y) = -2624*y**4
  (50*y)*(-y**2) = -50*y**3
  (50*y)*(-82*y) = -4100*y**2
  40*-1*y**2 = -40*y**2
  40*-82*y = -3280*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -32*y**5 - 2624*y**4 - 50*y**3 - 4100*y**2 - 40*y**2 - 3280*y</replace>
Combining like terms, got -32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y
<replace-#Step 5>#Step 6:
Current expression: -32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y</replace>
No more calculations needed.
<answer>-32*y**5 - 2624*y**4 - 50*y**3 - 4140*y**2 - 3280*y</answer>