Question:
Calculate the following: (2*x + 15)*(-20*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: -40*x**3 - 318*x**2 - 135*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: (2*x + 15)*(-20*x**2 - 9*x)
Expanding the part (2*x + 15) using the distributive property, and we got: (2*x)*(-20*x**2 - 9*x) + 15*(-20*x**2 - 9*x)
<replace-#Step 1>#Step 2:
Current expression: (2*x)*(-20*x**2 - 9*x) + 15*(-20*x**2 - 9*x)</replace>
Simplifying the partial expression: 15*(-20*x**2 - 9*x)
Expanding the part (-20*x**2 - 9*x) using the distributive property, and we got: -9*x*15 - 20*x**2*15
Replacing 15*(-20*x**2 - 9*x) with -9*x*15 - 20*x**2*15 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -9*x*15 + (2*x)*(-20*x**2 - 9*x) - 20*x**2*15</replace>
Simplifying the partial expression: (2*x)*(-20*x**2 - 9*x)
Expanding the part (-20*x**2 - 9*x) using the distributive property, and we got: (-9*x)*(2*x) + (2*x)*(-20*x**2)
Replacing (2*x)*(-20*x**2 - 9*x) with (-9*x)*(2*x) + (2*x)*(-20*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*x)*(2*x) - 9*x*15 + (2*x)*(-20*x**2) - 20*x**2*15</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x**2)*15 = -300*x**2
  (-20*x**2)*(2*x) = -40*x**3
  (-9*x)*15 = -135*x
  (-9*x)*(2*x) = -18*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -40*x**3 - 300*x**2 - 18*x**2 - 135*x</replace>
Combining like terms, got -40*x**3 - 318*x**2 - 135*x
<replace-#Step 5>#Step 6:
Current expression: -40*x**3 - 318*x**2 - 135*x</replace>
No more calculations needed.
<answer>-40*x**3 - 318*x**2 - 135*x</answer>


Question:
Simplify this expression: (-49*y - 5)*(-67*y**3 - 38*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3283*y**4 + 335*y**3 + 1862*y**2 + 190*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: (-49*y - 5)*(-67*y**3 - 38*y)
Expanding the part (-49*y - 5) using the distributive property, and we got: (-49*y)*(-67*y**3 - 38*y) - 5*(-67*y**3 - 38*y)
<replace-#Step 1>#Step 2:
Current expression: (-49*y)*(-67*y**3 - 38*y) - 5*(-67*y**3 - 38*y)</replace>
Simplifying the partial expression: -5*(-67*y**3 - 38*y)
Expanding the part (-67*y**3 - 38*y) using the distributive property, and we got: -38*y*(-5) - 67*y**3*(-5)
Replacing -5*(-67*y**3 - 38*y) with -38*y*(-5) - 67*y**3*(-5) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*y)*(-67*y**3 - 38*y) - 38*y*(-5) - 67*y**3*(-5)</replace>
Simplifying the partial expression: (-49*y)*(-67*y**3 - 38*y)
Expanding the part (-67*y**3 - 38*y) using the distributive property, and we got: (-49*y)*(-38*y) + (-49*y)*(-67*y**3)
Replacing (-49*y)*(-67*y**3 - 38*y) with (-49*y)*(-38*y) + (-49*y)*(-67*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y)*(-38*y) + (-49*y)*(-67*y**3) - 38*y*(-5) - 67*y**3*(-5)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-67*y**3)*-5 = 335*y**3
  (-67*y**3)*(-49*y) = 3283*y**4
  (-38*y)*-5 = 190*y
  (-38*y)*(-49*y) = 1862*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3283*y**4 + 335*y**3 + 1862*y**2 + 190*y</replace>
No more calculations needed.
<answer>3283*y**4 + 335*y**3 + 1862*y**2 + 190*y</answer>


Question:
Simplify this expression: (-y**3 - y**2)*(-4*y**3 + 28*y - 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: 4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*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: (-y**3 - y**2)*(-4*y**3 + 28*y - 7)
Expanding the part (-y**3 - y**2) using the distributive property, and we got: (-y**2)*(-4*y**3 + 28*y - 7) + (-y**3)*(-4*y**3 + 28*y - 7)
<replace-#Step 1>#Step 2:
Current expression: (-y**2)*(-4*y**3 + 28*y - 7) + (-y**3)*(-4*y**3 + 28*y - 7)</replace>
Simplifying the partial expression: (-y**2)*(-4*y**3 + 28*y - 7)
Expanding the part (-4*y**3 + 28*y - 7) using the distributive property, and we got: -(-1)*7*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3)
Replacing (-y**2)*(-4*y**3 + 28*y - 7) with -(-1)*7*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -7*(-1)*y**2 + (28*y)*(-y**2) + (-y**2)*(-4*y**3) + (-y**3)*(-4*y**3 + 28*y - 7)</replace>
Simplifying the partial expression: (-y**3)*(-4*y**3 + 28*y - 7)
Expanding the part (-4*y**3 + 28*y - 7) using the distributive property, and we got: -(-1)*7*y**3 + (28*y)*(-y**3) + (-4*y**3)*(-y**3)
Replacing (-y**3)*(-4*y**3 + 28*y - 7) with -(-1)*7*y**3 + (28*y)*(-y**3) + (-4*y**3)*(-y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -7*(-1)*y**3 - 7*(-1)*y**2 + (28*y)*(-y**2) + (28*y)*(-y**3) + (-y**2)*(-4*y**3) + (-4*y**3)*(-y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*y**3)*(-y**2) = 4*y**5
  (-4*y**3)*(-y**3) = 4*y**6
  (28*y)*(-y**2) = -28*y**3
  (28*y)*(-y**3) = -28*y**4
  -7*-1*y**2 = 7*y**2
  -7*-1*y**3 = 7*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 4*y**6 + 4*y**5 - 28*y**4 - 28*y**3 + 7*y**3 + 7*y**2</replace>
Combining like terms, got 4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2
<replace-#Step 5>#Step 6:
Current expression: 4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2</replace>
No more calculations needed.
<answer>4*y**6 + 4*y**5 - 28*y**4 - 21*y**3 + 7*y**2</answer>


Question:
Calculate the following: (22*z**2 - 21)*(-35*z**2 - 8*z + 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546

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**2 - 21)*(-35*z**2 - 8*z + 26)
Expanding the part (22*z**2 - 21) using the distributive property, and we got: (22*z**2)*(-35*z**2 - 8*z + 26) - 21*(-35*z**2 - 8*z + 26)
<replace-#Step 1>#Step 2:
Current expression: (22*z**2)*(-35*z**2 - 8*z + 26) - 21*(-35*z**2 - 8*z + 26)</replace>
Simplifying the partial expression: -21*(-35*z**2 - 8*z + 26)
Expanding the part (-35*z**2 - 8*z + 26) using the distributive property, and we got: -8*z*(-21) - 35*z**2*(-21) + 26*(-21)
Replacing -21*(-35*z**2 - 8*z + 26) with -8*z*(-21) - 35*z**2*(-21) + 26*(-21) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*z*(-21) - 35*z**2*(-21) + (22*z**2)*(-35*z**2 - 8*z + 26) - 546</replace>
Simplifying the partial expression: (22*z**2)*(-35*z**2 - 8*z + 26)
Expanding the part (-35*z**2 - 8*z + 26) using the distributive property, and we got: (-8*z)*(22*z**2) + 26*(22*z**2) + (-35*z**2)*(22*z**2)
Replacing (22*z**2)*(-35*z**2 - 8*z + 26) with (-8*z)*(22*z**2) + 26*(22*z**2) + (-35*z**2)*(22*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*z)*(22*z**2) - 8*z*(-21) + 26*22*z**2 + (-35*z**2)*(22*z**2) - 35*z**2*(-21) - 546</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*z**2)*-21 = 735*z**2
  (-35*z**2)*(22*z**2) = -770*z**4
  (-8*z)*-21 = 168*z
  (-8*z)*(22*z**2) = -176*z**3
  26*22*z**2 = 572*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -770*z**4 - 176*z**3 + 572*z**2 + 735*z**2 + 168*z - 546</replace>
Combining like terms, got -770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546
<replace-#Step 5>#Step 6:
Current expression: -770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546</replace>
No more calculations needed.
<answer>-770*z**4 - 176*z**3 + 1307*z**2 + 168*z - 546</answer>


Question:
Simplify this expression: -67*y**2*(-33*y**3 - 2*y**2 + 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2211*y**5 + 134*y**4 - 2546*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: -67*y**2*(-33*y**3 - 2*y**2 + 38)
Expanding the part (-33*y**3 - 2*y**2 + 38) using the distributive property, and we got: 38*(-67*y**2) + (-67*y**2)*(-2*y**2) + (-67*y**2)*(-33*y**3)
<replace-#Step 1>#Step 2:
Current expression: 38*(-67*y**2) + (-67*y**2)*(-2*y**2) + (-67*y**2)*(-33*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  38*(-67*y**2) = -2546*y**2
  (-33*y**3)*(-67*y**2) = 2211*y**5
  (-2*y**2)*(-67*y**2) = 134*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2211*y**5 + 134*y**4 - 2546*y**2</replace>
No more calculations needed.
<answer>2211*y**5 + 134*y**4 - 2546*y**2</answer>


Question:
Simplify this expression: (21*y**3 - 28*y)*(26*y**3 + 12*y + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*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: (21*y**3 - 28*y)*(26*y**3 + 12*y + 48)
Expanding the part (21*y**3 - 28*y) using the distributive property, and we got: (-28*y)*(26*y**3 + 12*y + 48) + (21*y**3)*(26*y**3 + 12*y + 48)
<replace-#Step 1>#Step 2:
Current expression: (-28*y)*(26*y**3 + 12*y + 48) + (21*y**3)*(26*y**3 + 12*y + 48)</replace>
Simplifying the partial expression: (-28*y)*(26*y**3 + 12*y + 48)
Expanding the part (26*y**3 + 12*y + 48) using the distributive property, and we got: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28*y)
Replacing (-28*y)*(26*y**3 + 12*y + 48) with (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*(-28)*y + (21*y**3)*(26*y**3 + 12*y + 48)</replace>
Simplifying the partial expression: (21*y**3)*(26*y**3 + 12*y + 48)
Expanding the part (26*y**3 + 12*y + 48) using the distributive property, and we got: 48*(21*y**3) + (12*y)*(21*y**3) + (21*y**3)*(26*y**3)
Replacing (21*y**3)*(26*y**3 + 12*y + 48) with 48*(21*y**3) + (12*y)*(21*y**3) + (21*y**3)*(26*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*y)*(12*y) + (-28*y)*(26*y**3) + 48*21*y**3 + 48*(-28)*y + (12*y)*(21*y**3) + (21*y**3)*(26*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*y)*(-28*y) = -336*y**2
  (12*y)*(21*y**3) = 252*y**4
  (26*y**3)*(-28*y) = -728*y**4
  (26*y**3)*(21*y**3) = 546*y**6
  48*-28*y = -1344*y
  48*21*y**3 = 1008*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 546*y**6 - 728*y**4 + 252*y**4 + 1008*y**3 - 336*y**2 - 1344*y</replace>
Combining like terms, got 546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y
<replace-#Step 5>#Step 6:
Current expression: 546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y</replace>
No more calculations needed.
<answer>546*y**6 - 476*y**4 + 1008*y**3 - 336*y**2 - 1344*y</answer>


Question:
Simplify this expression: -174*z**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: -174*z**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -174*z**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: -174*z**5</replace>
No more calculations needed.
<answer>-174*z**5</answer>


Question:
Calculate the following: (40*x**3 + 22*x + 5)*(56*x**3 - 11*x**2 + 5*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2240*x**6 - 440*x**5 + 1432*x**4 + 38*x**3 + 55*x**2 + 25*x


Question:
Simplify this expression: -66*z**3*(-12*z**3 + 80*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 792*z**6 - 5280*z**5

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -66*z**3*(-12*z**3 + 80*z**2)
Expanding the part (-12*z**3 + 80*z**2) using the distributive property, and we got: (80*z**2)*(-66*z**3) + (-66*z**3)*(-12*z**3)
<replace-#Step 1>#Step 2:
Current expression: (80*z**2)*(-66*z**3) + (-66*z**3)*(-12*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*z**3)*(-66*z**3) = 792*z**6
  (80*z**2)*(-66*z**3) = -5280*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 792*z**6 - 5280*z**5</replace>
No more calculations needed.
<answer>792*z**6 - 5280*z**5</answer>


Question:
Calculate the following: 15*z**3*(4*z - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 60*z**4 - 195*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: 15*z**3*(4*z - 13)
Expanding the part (4*z - 13) using the distributive property, and we got: -195*z**3 + (4*z)*(15*z**3)
<replace-#Step 1>#Step 2:
Current expression: -195*z**3 + (4*z)*(15*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -13*(15*z**3) = -195*z**3
  (4*z)*(15*z**3) = 60*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 60*z**4 - 195*z**3</replace>
No more calculations needed.
<answer>60*z**4 - 195*z**3</answer>


Question:
Calculate the following: (20 - 17*y**2)*(23*y**2 - 50*y + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620

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 - 17*y**2)*(23*y**2 - 50*y + 31)
Expanding the part (20 - 17*y**2) using the distributive property, and we got: (-17*y**2)*(23*y**2 - 50*y + 31) + 20*(23*y**2 - 50*y + 31)
<replace-#Step 1>#Step 2:
Current expression: (-17*y**2)*(23*y**2 - 50*y + 31) + 20*(23*y**2 - 50*y + 31)</replace>
Simplifying the partial expression: 20*(23*y**2 - 50*y + 31)
Expanding the part (23*y**2 - 50*y + 31) using the distributive property, and we got: -50*y*20 + (23*y**2)*20 + 31*20
Replacing 20*(23*y**2 - 50*y + 31) with -50*y*20 + (23*y**2)*20 + 31*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -50*y*20 + (-17*y**2)*(23*y**2 - 50*y + 31) + (23*y**2)*20 + 620</replace>
Simplifying the partial expression: (-17*y**2)*(23*y**2 - 50*y + 31)
Expanding the part (23*y**2 - 50*y + 31) using the distributive property, and we got: (-50*y)*(-17*y**2) + 31*(-17*y**2) + (-17*y**2)*(23*y**2)
Replacing (-17*y**2)*(23*y**2 - 50*y + 31) with (-50*y)*(-17*y**2) + 31*(-17*y**2) + (-17*y**2)*(23*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*y)*(-17*y**2) - 50*y*20 + 31*(-17)*y**2 + (-17*y**2)*(23*y**2) + (23*y**2)*20 + 620</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y)*20 = -1000*y
  (-50*y)*(-17*y**2) = 850*y**3
  (23*y**2)*20 = 460*y**2
  (23*y**2)*(-17*y**2) = -391*y**4
  31*-17*y**2 = -527*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -391*y**4 + 850*y**3 - 527*y**2 + 460*y**2 - 1000*y + 620</replace>
Combining like terms, got -391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620
<replace-#Step 5>#Step 6:
Current expression: -391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620</replace>
No more calculations needed.
<answer>-391*y**4 + 850*y**3 - 67*y**2 - 1000*y + 620</answer>


Question:
Simplify this expression: (38*x**3 + 39*x + 22)*(15*x**3 + 14*x**2 + 45*x - 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: 570*x**6 + 532*x**5 + 2295*x**4 + 40*x**3 + 2063*x**2 + 132*x - 484


Question:
Simplify this expression: (13*z**3 + 3*z)*(-42*z**3 + 37*z**2 - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -546*z**6 + 481*z**5 - 126*z**4 - 344*z**3 - 105*z


Question:
Simplify this expression: (23 - 54*z**2)*(61*z**3 - 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3294*z**5 + 1403*z**3 + 810*z**2 - 345

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 - 54*z**2)*(61*z**3 - 15)
Expanding the part (61*z**3 - 15) using the distributive property, and we got: (61*z**3)*(23 - 54*z**2) - 15*(23 - 54*z**2)
<replace-#Step 1>#Step 2:
Current expression: (61*z**3)*(23 - 54*z**2) - 15*(23 - 54*z**2)</replace>
Simplifying the partial expression: -15*(23 - 54*z**2)
Expanding the part (23 - 54*z**2) using the distributive property, and we got: -54*z**2*(-15) + 23*(-15)
Replacing -15*(23 - 54*z**2) with -54*z**2*(-15) + 23*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -54*z**2*(-15) + (61*z**3)*(23 - 54*z**2) - 345</replace>
Simplifying the partial expression: (61*z**3)*(23 - 54*z**2)
Expanding the part (23 - 54*z**2) using the distributive property, and we got: 23*(61*z**3) + (-54*z**2)*(61*z**3)
Replacing (61*z**3)*(23 - 54*z**2) with 23*(61*z**3) + (-54*z**2)*(61*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 23*61*z**3 + (-54*z**2)*(61*z**3) - 54*z**2*(-15) - 345</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-54*z**2)*-15 = 810*z**2
  (-54*z**2)*(61*z**3) = -3294*z**5
  23*61*z**3 = 1403*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3294*z**5 + 1403*z**3 + 810*z**2 - 345</replace>
No more calculations needed.
<answer>-3294*z**5 + 1403*z**3 + 810*z**2 - 345</answer>


Question:
Calculate the following: (-68*x**3 - 40*x)*(-19*x**3 - 3*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1292*x**6 + 964*x**4 + 120*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: (-68*x**3 - 40*x)*(-19*x**3 - 3*x)
Expanding the part (-68*x**3 - 40*x) using the distributive property, and we got: (-40*x)*(-19*x**3 - 3*x) + (-68*x**3)*(-19*x**3 - 3*x)
<replace-#Step 1>#Step 2:
Current expression: (-40*x)*(-19*x**3 - 3*x) + (-68*x**3)*(-19*x**3 - 3*x)</replace>
Simplifying the partial expression: (-68*x**3)*(-19*x**3 - 3*x)
Expanding the part (-19*x**3 - 3*x) using the distributive property, and we got: (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)
Replacing (-68*x**3)*(-19*x**3 - 3*x) with (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-40*x)*(-19*x**3 - 3*x) + (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)</replace>
Simplifying the partial expression: (-40*x)*(-19*x**3 - 3*x)
Expanding the part (-19*x**3 - 3*x) using the distributive property, and we got: (-40*x)*(-3*x) + (-40*x)*(-19*x**3)
Replacing (-40*x)*(-19*x**3 - 3*x) with (-40*x)*(-3*x) + (-40*x)*(-19*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*x)*(-3*x) + (-40*x)*(-19*x**3) + (-3*x)*(-68*x**3) + (-68*x**3)*(-19*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**3)*(-68*x**3) = 1292*x**6
  (-19*x**3)*(-40*x) = 760*x**4
  (-3*x)*(-68*x**3) = 204*x**4
  (-3*x)*(-40*x) = 120*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1292*x**6 + 204*x**4 + 760*x**4 + 120*x**2</replace>
Combining like terms, got 1292*x**6 + 964*x**4 + 120*x**2
<replace-#Step 5>#Step 6:
Current expression: 1292*x**6 + 964*x**4 + 120*x**2</replace>
No more calculations needed.
<answer>1292*x**6 + 964*x**4 + 120*x**2</answer>


Question:
Simplify this expression: (-92*y**2 - 1)*(-50*y**3 + 71*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: 4600*y**5 - 6482*y**3 - 71*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: (-92*y**2 - 1)*(-50*y**3 + 71*y)
Expanding the part (-92*y**2 - 1) using the distributive property, and we got: (-92*y**2)*(-50*y**3 + 71*y) - (-50*y**3 + 71*y)
<replace-#Step 1>#Step 2:
Current expression: (-92*y**2)*(-50*y**3 + 71*y) - (-50*y**3 + 71*y)</replace>
Simplifying the partial expression: -(-50*y**3 + 71*y)
Expanding the part (-50*y**3 + 71*y) using the distributive property, and we got: (71*y)*(-1) - 50*y**3*(-1)
Replacing -(-50*y**3 + 71*y) with (71*y)*(-1) - 50*y**3*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (71*y)*(-1) + (-92*y**2)*(-50*y**3 + 71*y) - 50*y**3*(-1)</replace>
Simplifying the partial expression: (-92*y**2)*(-50*y**3 + 71*y)
Expanding the part (-50*y**3 + 71*y) using the distributive property, and we got: (71*y)*(-92*y**2) + (-92*y**2)*(-50*y**3)
Replacing (-92*y**2)*(-50*y**3 + 71*y) with (71*y)*(-92*y**2) + (-92*y**2)*(-50*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (71*y)*(-92*y**2) + (71*y)*(-1) + (-92*y**2)*(-50*y**3) - 50*y**3*(-1)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y**3)*-1 = 50*y**3
  (-50*y**3)*(-92*y**2) = 4600*y**5
  (71*y)*-1 = -71*y
  (71*y)*(-92*y**2) = -6532*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 4600*y**5 - 6532*y**3 + 50*y**3 - 71*y</replace>
Combining like terms, got 4600*y**5 - 6482*y**3 - 71*y
<replace-#Step 5>#Step 6:
Current expression: 4600*y**5 - 6482*y**3 - 71*y</replace>
No more calculations needed.
<answer>4600*y**5 - 6482*y**3 - 71*y</answer>


Question:
Calculate the following: (19*y**2 + 42*y)*(14*y**3 + 48*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: 266*y**5 + 588*y**4 + 912*y**3 + 2016*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: (19*y**2 + 42*y)*(14*y**3 + 48*y)
Expanding the part (14*y**3 + 48*y) using the distributive property, and we got: (48*y)*(19*y**2 + 42*y) + (14*y**3)*(19*y**2 + 42*y)
<replace-#Step 1>#Step 2:
Current expression: (48*y)*(19*y**2 + 42*y) + (14*y**3)*(19*y**2 + 42*y)</replace>
Simplifying the partial expression: (14*y**3)*(19*y**2 + 42*y)
Expanding the part (19*y**2 + 42*y) using the distributive property, and we got: (42*y)*(14*y**3) + (19*y**2)*(14*y**3)
Replacing (14*y**3)*(19*y**2 + 42*y) with (42*y)*(14*y**3) + (19*y**2)*(14*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*y)*(14*y**3) + (48*y)*(19*y**2 + 42*y) + (19*y**2)*(14*y**3)</replace>
Simplifying the partial expression: (48*y)*(19*y**2 + 42*y)
Expanding the part (19*y**2 + 42*y) using the distributive property, and we got: (42*y)*(48*y) + (48*y)*(19*y**2)
Replacing (48*y)*(19*y**2 + 42*y) with (42*y)*(48*y) + (48*y)*(19*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (42*y)*(48*y) + (42*y)*(14*y**3) + (48*y)*(19*y**2) + (19*y**2)*(14*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*y**2)*(14*y**3) = 266*y**5
  (19*y**2)*(48*y) = 912*y**3
  (42*y)*(14*y**3) = 588*y**4
  (42*y)*(48*y) = 2016*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2</replace>
No more calculations needed.
<answer>266*y**5 + 588*y**4 + 912*y**3 + 2016*y**2</answer>


Question:
Calculate the following: (21*z - 45)*(-17*z**2 + 28*z - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -357*z**3 + 1353*z**2 - 2268*z + 2160

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*z - 45)*(-17*z**2 + 28*z - 48)
Expanding the part (21*z - 45) using the distributive property, and we got: (21*z)*(-17*z**2 + 28*z - 48) - 45*(-17*z**2 + 28*z - 48)
<replace-#Step 1>#Step 2:
Current expression: (21*z)*(-17*z**2 + 28*z - 48) - 45*(-17*z**2 + 28*z - 48)</replace>
Simplifying the partial expression: -45*(-17*z**2 + 28*z - 48)
Expanding the part (-17*z**2 + 28*z - 48) using the distributive property, and we got: (28*z)*(-45) - 17*z**2*(-45) - 48*(-45)
Replacing -45*(-17*z**2 + 28*z - 48) with (28*z)*(-45) - 17*z**2*(-45) - 48*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*z)*(-17*z**2 + 28*z - 48) + (28*z)*(-45) - 17*z**2*(-45) + 2160</replace>
Simplifying the partial expression: (21*z)*(-17*z**2 + 28*z - 48)
Expanding the part (-17*z**2 + 28*z - 48) using the distributive property, and we got: -1008*z + (21*z)*(28*z) + (21*z)*(-17*z**2)
Replacing (21*z)*(-17*z**2 + 28*z - 48) with -1008*z + (21*z)*(28*z) + (21*z)*(-17*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -48*21*z + (21*z)*(28*z) + (21*z)*(-17*z**2) + (28*z)*(-45) - 17*z**2*(-45) + 2160</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*z**2)*-45 = 765*z**2
  (-17*z**2)*(21*z) = -357*z**3
  (28*z)*-45 = -1260*z
  (28*z)*(21*z) = 588*z**2
  -48*21*z = -1008*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -357*z**3 + 588*z**2 + 765*z**2 - 1260*z - 1008*z + 2160</replace>
Combining like terms, got -357*z**3 + 1353*z**2 - 2268*z + 2160
<replace-#Step 5>#Step 6:
Current expression: -357*z**3 + 1353*z**2 - 2268*z + 2160</replace>
No more calculations needed.
<answer>-357*z**3 + 1353*z**2 - 2268*z + 2160</answer>


Question:
Calculate the following: x**3*(-20*x**2 - 35*x + 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -20*x**5 - 35*x**4 + 11*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: x**3*(-20*x**2 - 35*x + 11)
Expanding the part (-20*x**2 - 35*x + 11) using the distributive property, and we got: (-35*x)*x**3 + (-20*x**2)*x**3 + 11*x**3
<replace-#Step 1>#Step 2:
Current expression: (-35*x)*x**3 + (-20*x**2)*x**3 + 11*x**3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x)*x**3 = -35*x**4
  (-20*x**2)*x**3 = -20*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*x**5 - 35*x**4 + 11*x**3</replace>
No more calculations needed.
<answer>-20*x**5 - 35*x**4 + 11*x**3</answer>


Question:
Calculate the following: -2*x**3*(-23*x**3 + 9*x**2 - 46*x - 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 46*x**6 - 18*x**5 + 92*x**4 + 22*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -2*x**3*(-23*x**3 + 9*x**2 - 46*x - 11)
Expanding the part (-23*x**3 + 9*x**2 - 46*x - 11) using the distributive property, and we got: (-46*x)*(-2*x**3) - (-1)*22*x**3 + (9*x**2)*(-2*x**3) + (-23*x**3)*(-2*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-46*x)*(-2*x**3) - (-1)*22*x**3 + (9*x**2)*(-2*x**3) + (-23*x**3)*(-2*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -11*(-2*x**3) = 22*x**3
  (-46*x)*(-2*x**3) = 92*x**4
  (-23*x**3)*(-2*x**3) = 46*x**6
  (9*x**2)*(-2*x**3) = -18*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 46*x**6 - 18*x**5 + 92*x**4 + 22*x**3</replace>
No more calculations needed.
<answer>46*x**6 - 18*x**5 + 92*x**4 + 22*x**3</answer>


Question:
Simplify this expression: (34 - 43*z)*(-25*z**3 + 18*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1075*z**4 - 1624*z**3 + 612*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (34 - 43*z)*(-25*z**3 + 18*z**2)
Expanding the part (34 - 43*z) using the distributive property, and we got: (-43*z)*(-25*z**3 + 18*z**2) + 34*(-25*z**3 + 18*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-43*z)*(-25*z**3 + 18*z**2) + 34*(-25*z**3 + 18*z**2)</replace>
Simplifying the partial expression: 34*(-25*z**3 + 18*z**2)
Expanding the part (-25*z**3 + 18*z**2) using the distributive property, and we got: (18*z**2)*34 - 25*z**3*34
Replacing 34*(-25*z**3 + 18*z**2) with (18*z**2)*34 - 25*z**3*34 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*z)*(-25*z**3 + 18*z**2) + (18*z**2)*34 - 25*z**3*34</replace>
Simplifying the partial expression: (-43*z)*(-25*z**3 + 18*z**2)
Expanding the part (-25*z**3 + 18*z**2) using the distributive property, and we got: (-43*z)*(18*z**2) + (-43*z)*(-25*z**3)
Replacing (-43*z)*(-25*z**3 + 18*z**2) with (-43*z)*(18*z**2) + (-43*z)*(-25*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*z)*(18*z**2) + (-43*z)*(-25*z**3) + (18*z**2)*34 - 25*z**3*34</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*z**3)*34 = -850*z**3
  (-25*z**3)*(-43*z) = 1075*z**4
  (18*z**2)*34 = 612*z**2
  (18*z**2)*(-43*z) = -774*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1075*z**4 - 850*z**3 - 774*z**3 + 612*z**2</replace>
Combining like terms, got 1075*z**4 - 1624*z**3 + 612*z**2
<replace-#Step 5>#Step 6:
Current expression: 1075*z**4 - 1624*z**3 + 612*z**2</replace>
No more calculations needed.
<answer>1075*z**4 - 1624*z**3 + 612*z**2</answer>


Question:
Calculate the following: 3*y*(-27*y**2 - 12*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: -81*y**3 - 36*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: 3*y*(-27*y**2 - 12*y)
Expanding the part (-27*y**2 - 12*y) using the distributive property, and we got: (-12*y)*(3*y) + (3*y)*(-27*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-12*y)*(3*y) + (3*y)*(-27*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**2)*(3*y) = -81*y**3
  (-12*y)*(3*y) = -36*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -81*y**3 - 36*y**2</replace>
No more calculations needed.
<answer>-81*y**3 - 36*y**2</answer>


Question:
Simplify this expression: (-19*z**2 - 53*z + 9)*(52*z**3 - 19*z**2 + 3*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -988*z**5 - 2395*z**4 + 1418*z**3 - 330*z**2 + 27*z


Question:
Calculate the following: (8*y**2 - 18)*(43*y**3 - 42*y**2 - 8*y + 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: 344*y**5 - 336*y**4 - 838*y**3 + 916*y**2 + 144*y - 360


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

Answer: 24*y**6 + 24*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 12*y**3*(2*y**3 + 2*y)
Expanding the part (2*y**3 + 2*y) using the distributive property, and we got: (2*y)*(12*y**3) + (2*y**3)*(12*y**3)
<replace-#Step 1>#Step 2:
Current expression: (2*y)*(12*y**3) + (2*y**3)*(12*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*y)*(12*y**3) = 24*y**4
  (2*y**3)*(12*y**3) = 24*y**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 24*y**6 + 24*y**4</replace>
No more calculations needed.
<answer>24*y**6 + 24*y**4</answer>


Question:
Calculate the following: (-38*z**2 + 19*z + 28)*(-2*z**3 + 45*z**2 + 30*z + 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: 76*z**5 - 1748*z**4 - 341*z**3 + 994*z**2 + 1258*z + 616


Question:
Simplify this expression: (31 - 49*z**3)*(22*z**3 - 40*z**2 - 26*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*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: (31 - 49*z**3)*(22*z**3 - 40*z**2 - 26*z)
Expanding the part (31 - 49*z**3) using the distributive property, and we got: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + 31*(22*z**3 - 40*z**2 - 26*z)
<replace-#Step 1>#Step 2:
Current expression: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + 31*(22*z**3 - 40*z**2 - 26*z)</replace>
Simplifying the partial expression: 31*(22*z**3 - 40*z**2 - 26*z)
Expanding the part (22*z**3 - 40*z**2 - 26*z) using the distributive property, and we got: -26*z*31 - 40*z**2*31 + (22*z**3)*31
Replacing 31*(22*z**3 - 40*z**2 - 26*z) with -26*z*31 - 40*z**2*31 + (22*z**3)*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -26*z*31 - 40*z**2*31 + (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) + (22*z**3)*31</replace>
Simplifying the partial expression: (-49*z**3)*(22*z**3 - 40*z**2 - 26*z)
Expanding the part (22*z**3 - 40*z**2 - 26*z) using the distributive property, and we got: (-26*z)*(-49*z**3) + (-40*z**2)*(-49*z**3) + (-49*z**3)*(22*z**3)
Replacing (-49*z**3)*(22*z**3 - 40*z**2 - 26*z) with (-26*z)*(-49*z**3) + (-40*z**2)*(-49*z**3) + (-49*z**3)*(22*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*z)*(-49*z**3) - 26*z*31 + (-40*z**2)*(-49*z**3) - 40*z**2*31 + (-49*z**3)*(22*z**3) + (22*z**3)*31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*z**2)*31 = -1240*z**2
  (-40*z**2)*(-49*z**3) = 1960*z**5
  (-26*z)*31 = -806*z
  (-26*z)*(-49*z**3) = 1274*z**4
  (22*z**3)*31 = 682*z**3
  (22*z**3)*(-49*z**3) = -1078*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z</replace>
No more calculations needed.
<answer>-1078*z**6 + 1960*z**5 + 1274*z**4 + 682*z**3 - 1240*z**2 - 806*z</answer>


Question:
Simplify this expression: (40*x**2 + 11)*(-35*x**3 + 17*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1400*x**5 + 680*x**4 - 385*x**3 + 187*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: (40*x**2 + 11)*(-35*x**3 + 17*x**2)
Expanding the part (40*x**2 + 11) using the distributive property, and we got: (40*x**2)*(-35*x**3 + 17*x**2) + 11*(-35*x**3 + 17*x**2)
<replace-#Step 1>#Step 2:
Current expression: (40*x**2)*(-35*x**3 + 17*x**2) + 11*(-35*x**3 + 17*x**2)</replace>
Simplifying the partial expression: 11*(-35*x**3 + 17*x**2)
Expanding the part (-35*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*11 - 35*x**3*11
Replacing 11*(-35*x**3 + 17*x**2) with (17*x**2)*11 - 35*x**3*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*x**2)*11 + (40*x**2)*(-35*x**3 + 17*x**2) - 35*x**3*11</replace>
Simplifying the partial expression: (40*x**2)*(-35*x**3 + 17*x**2)
Expanding the part (-35*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*(40*x**2) + (40*x**2)*(-35*x**3)
Replacing (40*x**2)*(-35*x**3 + 17*x**2) with (17*x**2)*(40*x**2) + (40*x**2)*(-35*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (17*x**2)*(40*x**2) + (17*x**2)*11 + (40*x**2)*(-35*x**3) - 35*x**3*11</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x**3)*11 = -385*x**3
  (-35*x**3)*(40*x**2) = -1400*x**5
  (17*x**2)*11 = 187*x**2
  (17*x**2)*(40*x**2) = 680*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2</replace>
No more calculations needed.
<answer>-1400*x**5 + 680*x**4 - 385*x**3 + 187*x**2</answer>


Question:
Calculate the following: -63*x**2*(21*x**3 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1323*x**5 + 2079*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: -63*x**2*(21*x**3 - 33)
Expanding the part (21*x**3 - 33) using the distributive property, and we got: -(-1)*2079*x**2 + (-63*x**2)*(21*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*2079*x**2 + (-63*x**2)*(21*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -33*(-63*x**2) = 2079*x**2
  (21*x**3)*(-63*x**2) = -1323*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1323*x**5 + 2079*x**2</replace>
No more calculations needed.
<answer>-1323*x**5 + 2079*x**2</answer>


Question:
Simplify this expression: (-15*x**2 - 2*x - 31)*(27*x**3 - 48*x**2 - 21*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -405*x**5 + 666*x**4 - 426*x**3 + 1530*x**2 + 651*x


Question:
Calculate the following: (-38*z**3 + 20*z**2)*(-6*z**3 - 39*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: 228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-38*z**3 + 20*z**2)*(-6*z**3 - 39*z)
Expanding the part (-6*z**3 - 39*z) using the distributive property, and we got: (-39*z)*(-38*z**3 + 20*z**2) + (-6*z**3)*(-38*z**3 + 20*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-39*z)*(-38*z**3 + 20*z**2) + (-6*z**3)*(-38*z**3 + 20*z**2)</replace>
Simplifying the partial expression: (-39*z)*(-38*z**3 + 20*z**2)
Expanding the part (-38*z**3 + 20*z**2) using the distributive property, and we got: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3)
Replacing (-39*z)*(-38*z**3 + 20*z**2) with (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) + (-6*z**3)*(-38*z**3 + 20*z**2)</replace>
Simplifying the partial expression: (-6*z**3)*(-38*z**3 + 20*z**2)
Expanding the part (-38*z**3 + 20*z**2) using the distributive property, and we got: (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3)
Replacing (-6*z**3)*(-38*z**3 + 20*z**2) with (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*z)*(20*z**2) + (-39*z)*(-38*z**3) + (20*z**2)*(-6*z**3) + (-38*z**3)*(-6*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*z**3)*(-39*z) = 1482*z**4
  (-38*z**3)*(-6*z**3) = 228*z**6
  (20*z**2)*(-39*z) = -780*z**3
  (20*z**2)*(-6*z**3) = -120*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3</replace>
No more calculations needed.
<answer>228*z**6 - 120*z**5 + 1482*z**4 - 780*z**3</answer>


Question:
Calculate the following: (30*z**2 - 34*z)*(46*z**2 + 19*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: 1380*z**4 - 994*z**3 - 646*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: (30*z**2 - 34*z)*(46*z**2 + 19*z)
Expanding the part (30*z**2 - 34*z) using the distributive property, and we got: (-34*z)*(46*z**2 + 19*z) + (30*z**2)*(46*z**2 + 19*z)
<replace-#Step 1>#Step 2:
Current expression: (-34*z)*(46*z**2 + 19*z) + (30*z**2)*(46*z**2 + 19*z)</replace>
Simplifying the partial expression: (-34*z)*(46*z**2 + 19*z)
Expanding the part (46*z**2 + 19*z) using the distributive property, and we got: (-34*z)*(19*z) + (-34*z)*(46*z**2)
Replacing (-34*z)*(46*z**2 + 19*z) with (-34*z)*(19*z) + (-34*z)*(46*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*z)*(19*z) + (-34*z)*(46*z**2) + (30*z**2)*(46*z**2 + 19*z)</replace>
Simplifying the partial expression: (30*z**2)*(46*z**2 + 19*z)
Expanding the part (46*z**2 + 19*z) using the distributive property, and we got: (19*z)*(30*z**2) + (30*z**2)*(46*z**2)
Replacing (30*z**2)*(46*z**2 + 19*z) with (19*z)*(30*z**2) + (30*z**2)*(46*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*z)*(19*z) + (-34*z)*(46*z**2) + (19*z)*(30*z**2) + (30*z**2)*(46*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*z)*(-34*z) = -646*z**2
  (19*z)*(30*z**2) = 570*z**3
  (46*z**2)*(-34*z) = -1564*z**3
  (46*z**2)*(30*z**2) = 1380*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1380*z**4 - 1564*z**3 + 570*z**3 - 646*z**2</replace>
Combining like terms, got 1380*z**4 - 994*z**3 - 646*z**2
<replace-#Step 5>#Step 6:
Current expression: 1380*z**4 - 994*z**3 - 646*z**2</replace>
No more calculations needed.
<answer>1380*z**4 - 994*z**3 - 646*z**2</answer>


Question:
Calculate the following: (-45*x**3 + 11*x**2)*(-61*x**3 - 33*x**2 - 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2745*x**6 + 814*x**5 - 363*x**4 + 2070*x**3 - 506*x**2


Question:
Calculate the following: (19*z**2 - 35)*(-47*z**3 + 2*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: -893*z**5 + 38*z**4 + 1892*z**3 - 70*z**2 - 455*z


Question:
Calculate the following: (-54*y**2 - 23)*(35*y**2 + 50*y - 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: -1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-54*y**2 - 23)*(35*y**2 + 50*y - 38)
Expanding the part (-54*y**2 - 23) using the distributive property, and we got: (-54*y**2)*(35*y**2 + 50*y - 38) - 23*(35*y**2 + 50*y - 38)
<replace-#Step 1>#Step 2:
Current expression: (-54*y**2)*(35*y**2 + 50*y - 38) - 23*(35*y**2 + 50*y - 38)</replace>
Simplifying the partial expression: -23*(35*y**2 + 50*y - 38)
Expanding the part (35*y**2 + 50*y - 38) using the distributive property, and we got: (50*y)*(-23) + (35*y**2)*(-23) - 38*(-23)
Replacing -23*(35*y**2 + 50*y - 38) with (50*y)*(-23) + (35*y**2)*(-23) - 38*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (50*y)*(-23) + (-54*y**2)*(35*y**2 + 50*y - 38) + (35*y**2)*(-23) + 874</replace>
Simplifying the partial expression: (-54*y**2)*(35*y**2 + 50*y - 38)
Expanding the part (35*y**2 + 50*y - 38) using the distributive property, and we got: -(-1)*2052*y**2 + (50*y)*(-54*y**2) + (-54*y**2)*(35*y**2)
Replacing (-54*y**2)*(35*y**2 + 50*y - 38) with -(-1)*2052*y**2 + (50*y)*(-54*y**2) + (-54*y**2)*(35*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -38*(-54)*y**2 + (50*y)*(-54*y**2) + (50*y)*(-23) + (-54*y**2)*(35*y**2) + (35*y**2)*(-23) + 874</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*y**2)*-23 = -805*y**2
  (35*y**2)*(-54*y**2) = -1890*y**4
  (50*y)*-23 = -1150*y
  (50*y)*(-54*y**2) = -2700*y**3
  -38*-54*y**2 = 2052*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1890*y**4 - 2700*y**3 - 805*y**2 + 2052*y**2 - 1150*y + 874</replace>
Combining like terms, got -1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874
<replace-#Step 5>#Step 6:
Current expression: -1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874</replace>
No more calculations needed.
<answer>-1890*y**4 - 2700*y**3 + 1247*y**2 - 1150*y + 874</answer>


Question:
Calculate the following: (-41*z**2 - 40)*(48*z**2 + 48*z + 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: -1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-41*z**2 - 40)*(48*z**2 + 48*z + 9)
Expanding the part (-41*z**2 - 40) using the distributive property, and we got: (-41*z**2)*(48*z**2 + 48*z + 9) - 40*(48*z**2 + 48*z + 9)
<replace-#Step 1>#Step 2:
Current expression: (-41*z**2)*(48*z**2 + 48*z + 9) - 40*(48*z**2 + 48*z + 9)</replace>
Simplifying the partial expression: -40*(48*z**2 + 48*z + 9)
Expanding the part (48*z**2 + 48*z + 9) using the distributive property, and we got: (48*z)*(-40) + (48*z**2)*(-40) + 9*(-40)
Replacing -40*(48*z**2 + 48*z + 9) with (48*z)*(-40) + (48*z**2)*(-40) + 9*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*z)*(-40) + (-41*z**2)*(48*z**2 + 48*z + 9) + (48*z**2)*(-40) - 360</replace>
Simplifying the partial expression: (-41*z**2)*(48*z**2 + 48*z + 9)
Expanding the part (48*z**2 + 48*z + 9) using the distributive property, and we got: 9*(-41*z**2) + (48*z)*(-41*z**2) + (-41*z**2)*(48*z**2)
Replacing (-41*z**2)*(48*z**2 + 48*z + 9) with 9*(-41*z**2) + (48*z)*(-41*z**2) + (-41*z**2)*(48*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 9*(-41)*z**2 + (48*z)*(-41*z**2) + (48*z)*(-40) + (-41*z**2)*(48*z**2) + (48*z**2)*(-40) - 360</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*z)*-40 = -1920*z
  (48*z)*(-41*z**2) = -1968*z**3
  (48*z**2)*-40 = -1920*z**2
  (48*z**2)*(-41*z**2) = -1968*z**4
  9*-41*z**2 = -369*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1968*z**4 - 1968*z**3 - 1920*z**2 - 369*z**2 - 1920*z - 360</replace>
Combining like terms, got -1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360
<replace-#Step 5>#Step 6:
Current expression: -1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360</replace>
No more calculations needed.
<answer>-1968*z**4 - 1968*z**3 - 2289*z**2 - 1920*z - 360</answer>


Question:
Calculate the following: (21*x**2 - 46)*(-7*x**3 - 9*x**2 + 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: -147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (21*x**2 - 46)*(-7*x**3 - 9*x**2 + 16)
Expanding the part (21*x**2 - 46) using the distributive property, and we got: (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 46*(-7*x**3 - 9*x**2 + 16)
<replace-#Step 1>#Step 2:
Current expression: (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 46*(-7*x**3 - 9*x**2 + 16)</replace>
Simplifying the partial expression: -46*(-7*x**3 - 9*x**2 + 16)
Expanding the part (-7*x**3 - 9*x**2 + 16) using the distributive property, and we got: -9*x**2*(-46) - 7*x**3*(-46) + 16*(-46)
Replacing -46*(-7*x**3 - 9*x**2 + 16) with -9*x**2*(-46) - 7*x**3*(-46) + 16*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -9*x**2*(-46) + (21*x**2)*(-7*x**3 - 9*x**2 + 16) - 7*x**3*(-46) - 736</replace>
Simplifying the partial expression: (21*x**2)*(-7*x**3 - 9*x**2 + 16)
Expanding the part (-7*x**3 - 9*x**2 + 16) using the distributive property, and we got: 16*(21*x**2) + (-9*x**2)*(21*x**2) + (21*x**2)*(-7*x**3)
Replacing (21*x**2)*(-7*x**3 - 9*x**2 + 16) with 16*(21*x**2) + (-9*x**2)*(21*x**2) + (21*x**2)*(-7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 16*21*x**2 + (-9*x**2)*(21*x**2) - 9*x**2*(-46) + (21*x**2)*(-7*x**3) - 7*x**3*(-46) - 736</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*x**2)*-46 = 414*x**2
  (-9*x**2)*(21*x**2) = -189*x**4
  (-7*x**3)*-46 = 322*x**3
  (-7*x**3)*(21*x**2) = -147*x**5
  16*21*x**2 = 336*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -147*x**5 - 189*x**4 + 322*x**3 + 336*x**2 + 414*x**2 - 736</replace>
Combining like terms, got -147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736
<replace-#Step 5>#Step 6:
Current expression: -147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736</replace>
No more calculations needed.
<answer>-147*x**5 - 189*x**4 + 322*x**3 + 750*x**2 - 736</answer>


Question:
Calculate the following: (60*x**2 + 46*x)*(9*x**3 + 15*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 540*x**5 + 1314*x**4 + 690*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (60*x**2 + 46*x)*(9*x**3 + 15*x**2)
Expanding the part (9*x**3 + 15*x**2) using the distributive property, and we got: (15*x**2)*(60*x**2 + 46*x) + (9*x**3)*(60*x**2 + 46*x)
<replace-#Step 1>#Step 2:
Current expression: (15*x**2)*(60*x**2 + 46*x) + (9*x**3)*(60*x**2 + 46*x)</replace>
Simplifying the partial expression: (9*x**3)*(60*x**2 + 46*x)
Expanding the part (60*x**2 + 46*x) using the distributive property, and we got: (46*x)*(9*x**3) + (60*x**2)*(9*x**3)
Replacing (9*x**3)*(60*x**2 + 46*x) with (46*x)*(9*x**3) + (60*x**2)*(9*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (46*x)*(9*x**3) + (15*x**2)*(60*x**2 + 46*x) + (60*x**2)*(9*x**3)</replace>
Simplifying the partial expression: (15*x**2)*(60*x**2 + 46*x)
Expanding the part (60*x**2 + 46*x) using the distributive property, and we got: (46*x)*(15*x**2) + (15*x**2)*(60*x**2)
Replacing (15*x**2)*(60*x**2 + 46*x) with (46*x)*(15*x**2) + (15*x**2)*(60*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (46*x)*(15*x**2) + (46*x)*(9*x**3) + (15*x**2)*(60*x**2) + (60*x**2)*(9*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (46*x)*(9*x**3) = 414*x**4
  (46*x)*(15*x**2) = 690*x**3
  (60*x**2)*(9*x**3) = 540*x**5
  (60*x**2)*(15*x**2) = 900*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 540*x**5 + 414*x**4 + 900*x**4 + 690*x**3</replace>
Combining like terms, got 540*x**5 + 1314*x**4 + 690*x**3
<replace-#Step 5>#Step 6:
Current expression: 540*x**5 + 1314*x**4 + 690*x**3</replace>
No more calculations needed.
<answer>540*x**5 + 1314*x**4 + 690*x**3</answer>


Question:
Calculate the following: (-48*z**2 + 43*z)*(-23*z**3 + 50*z**2 + 20*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: 1104*z**5 - 3389*z**4 + 1190*z**3 + 860*z**2


Question:
Simplify this expression: (49 - 2*z)*(51 - 39*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: 78*z**2 - 2013*z + 2499

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49 - 2*z)*(51 - 39*z)
Expanding the part (49 - 2*z) using the distributive property, and we got: (-2*z)*(51 - 39*z) + 49*(51 - 39*z)
<replace-#Step 1>#Step 2:
Current expression: (-2*z)*(51 - 39*z) + 49*(51 - 39*z)</replace>
Simplifying the partial expression: 49*(51 - 39*z)
Expanding the part (51 - 39*z) using the distributive property, and we got: -39*z*49 + 51*49
Replacing 49*(51 - 39*z) with -39*z*49 + 51*49 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*z*49 + (-2*z)*(51 - 39*z) + 2499</replace>
Simplifying the partial expression: (-2*z)*(51 - 39*z)
Expanding the part (51 - 39*z) using the distributive property, and we got: (-39*z)*(-2*z) + 51*(-2*z)
Replacing (-2*z)*(51 - 39*z) with (-39*z)*(-2*z) + 51*(-2*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*z)*(-2*z) - 39*z*49 + 51*(-2)*z + 2499</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*z)*49 = -1911*z
  (-39*z)*(-2*z) = 78*z**2
  51*-2*z = -102*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 78*z**2 - 1911*z - 102*z + 2499</replace>
Combining like terms, got 78*z**2 - 2013*z + 2499
<replace-#Step 5>#Step 6:
Current expression: 78*z**2 - 2013*z + 2499</replace>
No more calculations needed.
<answer>78*z**2 - 2013*z + 2499</answer>


Question:
Simplify this expression: (31*x**2 + 40*x)*(48*x**3 - 21*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31*x**2 + 40*x)*(48*x**3 - 21*x)
Expanding the part (48*x**3 - 21*x) using the distributive property, and we got: (-21*x)*(31*x**2 + 40*x) + (48*x**3)*(31*x**2 + 40*x)
<replace-#Step 1>#Step 2:
Current expression: (-21*x)*(31*x**2 + 40*x) + (48*x**3)*(31*x**2 + 40*x)</replace>
Simplifying the partial expression: (-21*x)*(31*x**2 + 40*x)
Expanding the part (31*x**2 + 40*x) using the distributive property, and we got: (-21*x)*(40*x) + (-21*x)*(31*x**2)
Replacing (-21*x)*(31*x**2 + 40*x) with (-21*x)*(40*x) + (-21*x)*(31*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*x)*(40*x) + (-21*x)*(31*x**2) + (48*x**3)*(31*x**2 + 40*x)</replace>
Simplifying the partial expression: (48*x**3)*(31*x**2 + 40*x)
Expanding the part (31*x**2 + 40*x) using the distributive property, and we got: (40*x)*(48*x**3) + (31*x**2)*(48*x**3)
Replacing (48*x**3)*(31*x**2 + 40*x) with (40*x)*(48*x**3) + (31*x**2)*(48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*x)*(40*x) + (-21*x)*(31*x**2) + (40*x)*(48*x**3) + (31*x**2)*(48*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*x**2)*(-21*x) = -651*x**3
  (31*x**2)*(48*x**3) = 1488*x**5
  (40*x)*(-21*x) = -840*x**2
  (40*x)*(48*x**3) = 1920*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2</replace>
No more calculations needed.
<answer>1488*x**5 + 1920*x**4 - 651*x**3 - 840*x**2</answer>


Question:
Calculate the following: (-48*z**2 - 30*z - 24)*(-34*z**2 + 32*z + 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1632*z**4 - 516*z**3 - 1392*z**2 - 1548*z - 624


Question:
Calculate the following: (5*y**2 + 46*y)*(34*y**2 - 39*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 + 1369*y**3 - 1794*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**2 + 46*y)*(34*y**2 - 39*y)
Expanding the part (34*y**2 - 39*y) using the distributive property, and we got: (-39*y)*(5*y**2 + 46*y) + (34*y**2)*(5*y**2 + 46*y)
<replace-#Step 1>#Step 2:
Current expression: (-39*y)*(5*y**2 + 46*y) + (34*y**2)*(5*y**2 + 46*y)</replace>
Simplifying the partial expression: (-39*y)*(5*y**2 + 46*y)
Expanding the part (5*y**2 + 46*y) using the distributive property, and we got: (-39*y)*(46*y) + (-39*y)*(5*y**2)
Replacing (-39*y)*(5*y**2 + 46*y) with (-39*y)*(46*y) + (-39*y)*(5*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-39*y)*(46*y) + (-39*y)*(5*y**2) + (34*y**2)*(5*y**2 + 46*y)</replace>
Simplifying the partial expression: (34*y**2)*(5*y**2 + 46*y)
Expanding the part (5*y**2 + 46*y) using the distributive property, and we got: (46*y)*(34*y**2) + (5*y**2)*(34*y**2)
Replacing (34*y**2)*(5*y**2 + 46*y) with (46*y)*(34*y**2) + (5*y**2)*(34*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*y)*(46*y) + (-39*y)*(5*y**2) + (46*y)*(34*y**2) + (5*y**2)*(34*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (5*y**2)*(-39*y) = -195*y**3
  (5*y**2)*(34*y**2) = 170*y**4
  (46*y)*(-39*y) = -1794*y**2
  (46*y)*(34*y**2) = 1564*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 170*y**4 - 195*y**3 + 1564*y**3 - 1794*y**2</replace>
Combining like terms, got 170*y**4 + 1369*y**3 - 1794*y**2
<replace-#Step 5>#Step 6:
Current expression: 170*y**4 + 1369*y**3 - 1794*y**2</replace>
No more calculations needed.
<answer>170*y**4 + 1369*y**3 - 1794*y**2</answer>


Question:
Calculate the following: (-20*z**3 - 22*z)*(47*z**3 - 40*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -940*z**6 + 800*z**5 - 1034*z**4 + 880*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: (-20*z**3 - 22*z)*(47*z**3 - 40*z**2)
Expanding the part (47*z**3 - 40*z**2) using the distributive property, and we got: (-40*z**2)*(-20*z**3 - 22*z) + (47*z**3)*(-20*z**3 - 22*z)
<replace-#Step 1>#Step 2:
Current expression: (-40*z**2)*(-20*z**3 - 22*z) + (47*z**3)*(-20*z**3 - 22*z)</replace>
Simplifying the partial expression: (-40*z**2)*(-20*z**3 - 22*z)
Expanding the part (-20*z**3 - 22*z) using the distributive property, and we got: (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3)
Replacing (-40*z**2)*(-20*z**3 - 22*z) with (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-22*z)*(-40*z**2) + (-40*z**2)*(-20*z**3) + (47*z**3)*(-20*z**3 - 22*z)</replace>
Simplifying the partial expression: (47*z**3)*(-20*z**3 - 22*z)
Expanding the part (-20*z**3 - 22*z) using the distributive property, and we got: (-22*z)*(47*z**3) + (-20*z**3)*(47*z**3)
Replacing (47*z**3)*(-20*z**3 - 22*z) with (-22*z)*(47*z**3) + (-20*z**3)*(47*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*z)*(-40*z**2) + (-22*z)*(47*z**3) + (-40*z**2)*(-20*z**3) + (-20*z**3)*(47*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*z)*(-40*z**2) = 880*z**3
  (-22*z)*(47*z**3) = -1034*z**4
  (-20*z**3)*(-40*z**2) = 800*z**5
  (-20*z**3)*(47*z**3) = -940*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3</replace>
No more calculations needed.
<answer>-940*z**6 + 800*z**5 - 1034*z**4 + 880*z**3</answer>


Question:
Calculate the following: (4*y**2 + 30)*(-38*y**3 + 75*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: -152*y**5 - 840*y**3 + 2250*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: (4*y**2 + 30)*(-38*y**3 + 75*y)
Expanding the part (4*y**2 + 30) using the distributive property, and we got: (4*y**2)*(-38*y**3 + 75*y) + 30*(-38*y**3 + 75*y)
<replace-#Step 1>#Step 2:
Current expression: (4*y**2)*(-38*y**3 + 75*y) + 30*(-38*y**3 + 75*y)</replace>
Simplifying the partial expression: 30*(-38*y**3 + 75*y)
Expanding the part (-38*y**3 + 75*y) using the distributive property, and we got: (75*y)*30 - 38*y**3*30
Replacing 30*(-38*y**3 + 75*y) with (75*y)*30 - 38*y**3*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (75*y)*30 + (4*y**2)*(-38*y**3 + 75*y) - 38*y**3*30</replace>
Simplifying the partial expression: (4*y**2)*(-38*y**3 + 75*y)
Expanding the part (-38*y**3 + 75*y) using the distributive property, and we got: (75*y)*(4*y**2) + (4*y**2)*(-38*y**3)
Replacing (4*y**2)*(-38*y**3 + 75*y) with (75*y)*(4*y**2) + (4*y**2)*(-38*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (75*y)*(4*y**2) + (75*y)*30 + (4*y**2)*(-38*y**3) - 38*y**3*30</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*y**3)*30 = -1140*y**3
  (-38*y**3)*(4*y**2) = -152*y**5
  (75*y)*30 = 2250*y
  (75*y)*(4*y**2) = 300*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -152*y**5 - 1140*y**3 + 300*y**3 + 2250*y</replace>
Combining like terms, got -152*y**5 - 840*y**3 + 2250*y
<replace-#Step 5>#Step 6:
Current expression: -152*y**5 - 840*y**3 + 2250*y</replace>
No more calculations needed.
<answer>-152*y**5 - 840*y**3 + 2250*y</answer>


Question:
Simplify this expression: (-8*y**2 - 29*y)*(25*y**3 + 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: -200*y**5 - 725*y**4 - 224*y**2 - 812*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-8*y**2 - 29*y)*(25*y**3 + 28)
Expanding the part (25*y**3 + 28) using the distributive property, and we got: (25*y**3)*(-8*y**2 - 29*y) + 28*(-8*y**2 - 29*y)
<replace-#Step 1>#Step 2:
Current expression: (25*y**3)*(-8*y**2 - 29*y) + 28*(-8*y**2 - 29*y)</replace>
Simplifying the partial expression: 28*(-8*y**2 - 29*y)
Expanding the part (-8*y**2 - 29*y) using the distributive property, and we got: -29*y*28 - 8*y**2*28
Replacing 28*(-8*y**2 - 29*y) with -29*y*28 - 8*y**2*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -29*y*28 - 8*y**2*28 + (25*y**3)*(-8*y**2 - 29*y)</replace>
Simplifying the partial expression: (25*y**3)*(-8*y**2 - 29*y)
Expanding the part (-8*y**2 - 29*y) using the distributive property, and we got: (-29*y)*(25*y**3) + (-8*y**2)*(25*y**3)
Replacing (25*y**3)*(-8*y**2 - 29*y) with (-29*y)*(25*y**3) + (-8*y**2)*(25*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*y)*(25*y**3) - 29*y*28 + (-8*y**2)*(25*y**3) - 8*y**2*28</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y)*28 = -812*y
  (-29*y)*(25*y**3) = -725*y**4
  (-8*y**2)*28 = -224*y**2
  (-8*y**2)*(25*y**3) = -200*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -200*y**5 - 725*y**4 - 224*y**2 - 812*y</replace>
No more calculations needed.
<answer>-200*y**5 - 725*y**4 - 224*y**2 - 812*y</answer>


Question:
Calculate the following: (35*z**2 + 28*z)*(65*z**3 - 39*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: 2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*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: (35*z**2 + 28*z)*(65*z**3 - 39*z)
Expanding the part (65*z**3 - 39*z) using the distributive property, and we got: (-39*z)*(35*z**2 + 28*z) + (65*z**3)*(35*z**2 + 28*z)
<replace-#Step 1>#Step 2:
Current expression: (-39*z)*(35*z**2 + 28*z) + (65*z**3)*(35*z**2 + 28*z)</replace>
Simplifying the partial expression: (-39*z)*(35*z**2 + 28*z)
Expanding the part (35*z**2 + 28*z) using the distributive property, and we got: (-39*z)*(28*z) + (-39*z)*(35*z**2)
Replacing (-39*z)*(35*z**2 + 28*z) with (-39*z)*(28*z) + (-39*z)*(35*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-39*z)*(28*z) + (-39*z)*(35*z**2) + (65*z**3)*(35*z**2 + 28*z)</replace>
Simplifying the partial expression: (65*z**3)*(35*z**2 + 28*z)
Expanding the part (35*z**2 + 28*z) using the distributive property, and we got: (28*z)*(65*z**3) + (35*z**2)*(65*z**3)
Replacing (65*z**3)*(35*z**2 + 28*z) with (28*z)*(65*z**3) + (35*z**2)*(65*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*z)*(28*z) + (-39*z)*(35*z**2) + (28*z)*(65*z**3) + (35*z**2)*(65*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*z)*(-39*z) = -1092*z**2
  (28*z)*(65*z**3) = 1820*z**4
  (35*z**2)*(-39*z) = -1365*z**3
  (35*z**2)*(65*z**3) = 2275*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2</replace>
No more calculations needed.
<answer>2275*z**5 + 1820*z**4 - 1365*z**3 - 1092*z**2</answer>


Question:
Simplify this expression: (40*z - 23)*(31*z**3 + 30*z**2 - 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: 1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299

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*z - 23)*(31*z**3 + 30*z**2 - 13)
Expanding the part (40*z - 23) using the distributive property, and we got: (40*z)*(31*z**3 + 30*z**2 - 13) - 23*(31*z**3 + 30*z**2 - 13)
<replace-#Step 1>#Step 2:
Current expression: (40*z)*(31*z**3 + 30*z**2 - 13) - 23*(31*z**3 + 30*z**2 - 13)</replace>
Simplifying the partial expression: -23*(31*z**3 + 30*z**2 - 13)
Expanding the part (31*z**3 + 30*z**2 - 13) using the distributive property, and we got: (30*z**2)*(-23) + (31*z**3)*(-23) - 13*(-23)
Replacing -23*(31*z**3 + 30*z**2 - 13) with (30*z**2)*(-23) + (31*z**3)*(-23) - 13*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*z)*(31*z**3 + 30*z**2 - 13) + (30*z**2)*(-23) + (31*z**3)*(-23) + 299</replace>
Simplifying the partial expression: (40*z)*(31*z**3 + 30*z**2 - 13)
Expanding the part (31*z**3 + 30*z**2 - 13) using the distributive property, and we got: -520*z + (40*z)*(30*z**2) + (40*z)*(31*z**3)
Replacing (40*z)*(31*z**3 + 30*z**2 - 13) with -520*z + (40*z)*(30*z**2) + (40*z)*(31*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*40*z + (40*z)*(30*z**2) + (40*z)*(31*z**3) + (30*z**2)*(-23) + (31*z**3)*(-23) + 299</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*z**2)*-23 = -690*z**2
  (30*z**2)*(40*z) = 1200*z**3
  (31*z**3)*-23 = -713*z**3
  (31*z**3)*(40*z) = 1240*z**4
  -13*40*z = -520*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1240*z**4 - 713*z**3 + 1200*z**3 - 690*z**2 - 520*z + 299</replace>
Combining like terms, got 1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299
<replace-#Step 5>#Step 6:
Current expression: 1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299</replace>
No more calculations needed.
<answer>1240*z**4 + 487*z**3 - 690*z**2 - 520*z + 299</answer>


Question:
Calculate the following: (2*x**3 + 20*x)*(-34*x**2 - 33*x + 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: -68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*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: (2*x**3 + 20*x)*(-34*x**2 - 33*x + 22)
Expanding the part (2*x**3 + 20*x) using the distributive property, and we got: (20*x)*(-34*x**2 - 33*x + 22) + (2*x**3)*(-34*x**2 - 33*x + 22)
<replace-#Step 1>#Step 2:
Current expression: (20*x)*(-34*x**2 - 33*x + 22) + (2*x**3)*(-34*x**2 - 33*x + 22)</replace>
Simplifying the partial expression: (2*x**3)*(-34*x**2 - 33*x + 22)
Expanding the part (-34*x**2 - 33*x + 22) using the distributive property, and we got: (-33*x)*(2*x**3) + 22*(2*x**3) + (-34*x**2)*(2*x**3)
Replacing (2*x**3)*(-34*x**2 - 33*x + 22) with (-33*x)*(2*x**3) + 22*(2*x**3) + (-34*x**2)*(2*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-33*x)*(2*x**3) + 22*2*x**3 + (20*x)*(-34*x**2 - 33*x + 22) + (-34*x**2)*(2*x**3)</replace>
Simplifying the partial expression: (20*x)*(-34*x**2 - 33*x + 22)
Expanding the part (-34*x**2 - 33*x + 22) using the distributive property, and we got: (-33*x)*(20*x) + 22*(20*x) + (20*x)*(-34*x**2)
Replacing (20*x)*(-34*x**2 - 33*x + 22) with (-33*x)*(20*x) + 22*(20*x) + (20*x)*(-34*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*x)*(20*x) + (-33*x)*(2*x**3) + 22*2*x**3 + 22*20*x + (20*x)*(-34*x**2) + (-34*x**2)*(2*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**2)*(2*x**3) = -68*x**5
  (-34*x**2)*(20*x) = -680*x**3
  (-33*x)*(2*x**3) = -66*x**4
  (-33*x)*(20*x) = -660*x**2
  22*2*x**3 = 44*x**3
  22*20*x = 440*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -68*x**5 - 66*x**4 - 680*x**3 + 44*x**3 - 660*x**2 + 440*x</replace>
Combining like terms, got -68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x
<replace-#Step 5>#Step 6:
Current expression: -68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x</replace>
No more calculations needed.
<answer>-68*x**5 - 66*x**4 - 636*x**3 - 660*x**2 + 440*x</answer>


Question:
Simplify this expression: (-31*y - 37)*(3*y**2 + 25*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: -93*y**3 - 886*y**2 + 5*y + 1110

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-31*y - 37)*(3*y**2 + 25*y - 30)
Expanding the part (-31*y - 37) using the distributive property, and we got: (-31*y)*(3*y**2 + 25*y - 30) - 37*(3*y**2 + 25*y - 30)
<replace-#Step 1>#Step 2:
Current expression: (-31*y)*(3*y**2 + 25*y - 30) - 37*(3*y**2 + 25*y - 30)</replace>
Simplifying the partial expression: -37*(3*y**2 + 25*y - 30)
Expanding the part (3*y**2 + 25*y - 30) using the distributive property, and we got: (25*y)*(-37) + (3*y**2)*(-37) - 30*(-37)
Replacing -37*(3*y**2 + 25*y - 30) with (25*y)*(-37) + (3*y**2)*(-37) - 30*(-37) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*y)*(3*y**2 + 25*y - 30) + (25*y)*(-37) + (3*y**2)*(-37) + 1110</replace>
Simplifying the partial expression: (-31*y)*(3*y**2 + 25*y - 30)
Expanding the part (3*y**2 + 25*y - 30) using the distributive property, and we got: (-31*y)*(25*y) + (-31*y)*(3*y**2) - (-1)*930*y
Replacing (-31*y)*(3*y**2 + 25*y - 30) with (-31*y)*(25*y) + (-31*y)*(3*y**2) - (-1)*930*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*y)*(25*y) + (-31*y)*(3*y**2) - 30*(-31)*y + (25*y)*(-37) + (3*y**2)*(-37) + 1110</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y**2)*-37 = -111*y**2
  (3*y**2)*(-31*y) = -93*y**3
  (25*y)*-37 = -925*y
  (25*y)*(-31*y) = -775*y**2
  -30*-31*y = 930*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -93*y**3 - 775*y**2 - 111*y**2 - 925*y + 930*y + 1110</replace>
Combining like terms, got -93*y**3 - 886*y**2 + 5*y + 1110
<replace-#Step 5>#Step 6:
Current expression: -93*y**3 - 886*y**2 + 5*y + 1110</replace>
No more calculations needed.
<answer>-93*y**3 - 886*y**2 + 5*y + 1110</answer>


Question:
Calculate the following: (12*x**2 - 29*x + 38)*(-28*x**3 + 13*x**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: -336*x**5 + 968*x**4 - 1441*x**3 - 70*x**2 + 1363*x - 1786


Question:
Simplify this expression: (49 - 28*x**2)*(4*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: -112*x**3 + 364*x**2 + 196*x - 637

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49 - 28*x**2)*(4*x - 13)
Expanding the part (4*x - 13) using the distributive property, and we got: (4*x)*(49 - 28*x**2) - 13*(49 - 28*x**2)
<replace-#Step 1>#Step 2:
Current expression: (4*x)*(49 - 28*x**2) - 13*(49 - 28*x**2)</replace>
Simplifying the partial expression: -13*(49 - 28*x**2)
Expanding the part (49 - 28*x**2) using the distributive property, and we got: -28*x**2*(-13) + 49*(-13)
Replacing -13*(49 - 28*x**2) with -28*x**2*(-13) + 49*(-13) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*x)*(49 - 28*x**2) - 28*x**2*(-13) - 637</replace>
Simplifying the partial expression: (4*x)*(49 - 28*x**2)
Expanding the part (49 - 28*x**2) using the distributive property, and we got: 49*(4*x) + (4*x)*(-28*x**2)
Replacing (4*x)*(49 - 28*x**2) with 49*(4*x) + (4*x)*(-28*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 49*4*x + (4*x)*(-28*x**2) - 28*x**2*(-13) - 637</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*x**2)*-13 = 364*x**2
  (-28*x**2)*(4*x) = -112*x**3
  49*4*x = 196*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -112*x**3 + 364*x**2 + 196*x - 637</replace>
No more calculations needed.
<answer>-112*x**3 + 364*x**2 + 196*x - 637</answer>


Question:
Calculate the following: (-25*x - 13)*(33*x**3 - 10*x**2 + 28*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -825*x**4 - 179*x**3 - 570*x**2 - 364*x


Question:
Calculate the following: (34*x**3 + 51*x)*(14*x**2 - 43*x + 65)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*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: (34*x**3 + 51*x)*(14*x**2 - 43*x + 65)
Expanding the part (34*x**3 + 51*x) using the distributive property, and we got: (51*x)*(14*x**2 - 43*x + 65) + (34*x**3)*(14*x**2 - 43*x + 65)
<replace-#Step 1>#Step 2:
Current expression: (51*x)*(14*x**2 - 43*x + 65) + (34*x**3)*(14*x**2 - 43*x + 65)</replace>
Simplifying the partial expression: (34*x**3)*(14*x**2 - 43*x + 65)
Expanding the part (14*x**2 - 43*x + 65) using the distributive property, and we got: (-43*x)*(34*x**3) + 65*(34*x**3) + (14*x**2)*(34*x**3)
Replacing (34*x**3)*(14*x**2 - 43*x + 65) with (-43*x)*(34*x**3) + 65*(34*x**3) + (14*x**2)*(34*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*x)*(34*x**3) + 65*34*x**3 + (51*x)*(14*x**2 - 43*x + 65) + (14*x**2)*(34*x**3)</replace>
Simplifying the partial expression: (51*x)*(14*x**2 - 43*x + 65)
Expanding the part (14*x**2 - 43*x + 65) using the distributive property, and we got: (-43*x)*(51*x) + 65*(51*x) + (51*x)*(14*x**2)
Replacing (51*x)*(14*x**2 - 43*x + 65) with (-43*x)*(51*x) + 65*(51*x) + (51*x)*(14*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*x)*(51*x) + (-43*x)*(34*x**3) + 65*34*x**3 + 65*51*x + (51*x)*(14*x**2) + (14*x**2)*(34*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*x)*(34*x**3) = -1462*x**4
  (-43*x)*(51*x) = -2193*x**2
  (14*x**2)*(34*x**3) = 476*x**5
  (14*x**2)*(51*x) = 714*x**3
  65*34*x**3 = 2210*x**3
  65*51*x = 3315*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 476*x**5 - 1462*x**4 + 714*x**3 + 2210*x**3 - 2193*x**2 + 3315*x</replace>
Combining like terms, got 476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x
<replace-#Step 5>#Step 6:
Current expression: 476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x</replace>
No more calculations needed.
<answer>476*x**5 - 1462*x**4 + 2924*x**3 - 2193*x**2 + 3315*x</answer>


Question:
Calculate the following: (39*x**3 - 31*x**2)*(-32*x**3 + 4*x**2 - 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1248*x**6 + 1148*x**5 - 904*x**4 + 620*x**3


Question:
Calculate the following: (-2*x**2 + 35*x - 27)*(6*x**3 + 45*x**2 + 28*x + 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -12*x**5 + 120*x**4 + 1357*x**3 - 313*x**2 + 609*x - 1053


Question:
Calculate the following: (-5*z**3 - 50*z**2)*(66*z**3 + 30*z**2 + 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -330*z**6 - 3450*z**5 - 1500*z**4 - 100*z**3 - 1000*z**2