Question:
Calculate the following: -71*z*(-4*z**3 - 42*z - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 284*z**4 + 2982*z**2 + 1136*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: -71*z*(-4*z**3 - 42*z - 16)
Expanding the part (-4*z**3 - 42*z - 16) using the distributive property, and we got: (-71*z)*(-42*z) + (-71*z)*(-4*z**3) - (-1)*1136*z
<replace-#Step 1>#Step 2:
Current expression: (-71*z)*(-42*z) + (-71*z)*(-4*z**3) - (-1)*1136*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(-71*z) = 1136*z
  (-42*z)*(-71*z) = 2982*z**2
  (-4*z**3)*(-71*z) = 284*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 284*z**4 + 2982*z**2 + 1136*z</replace>
No more calculations needed.
<answer>284*z**4 + 2982*z**2 + 1136*z</answer>


Question:
Simplify this expression: -25*y*(32*y**3 + 33*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -800*y**4 - 825*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -25*y*(32*y**3 + 33*y**2)
Expanding the part (32*y**3 + 33*y**2) using the distributive property, and we got: (-25*y)*(33*y**2) + (-25*y)*(32*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-25*y)*(33*y**2) + (-25*y)*(32*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*y**3)*(-25*y) = -800*y**4
  (33*y**2)*(-25*y) = -825*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -800*y**4 - 825*y**3</replace>
No more calculations needed.
<answer>-800*y**4 - 825*y**3</answer>


Question:
Calculate the following: (28*y**3 + 15*y)*(-37*y**3 + 10*y**2 - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1036*y**6 + 280*y**5 - 555*y**4 - 1222*y**3 - 735*y


Question:
Calculate the following: -29*x*(46*x**2 + 53)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1334*x**3 - 1537*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -29*x*(46*x**2 + 53)
Expanding the part (46*x**2 + 53) using the distributive property, and we got: (-29*x)*(46*x**2) + 53*(-29*x)
<replace-#Step 1>#Step 2:
Current expression: (-29*x)*(46*x**2) + 53*(-29*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  53*(-29*x) = -1537*x
  (46*x**2)*(-29*x) = -1334*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1334*x**3 - 1537*x</replace>
No more calculations needed.
<answer>-1334*x**3 - 1537*x</answer>


Question:
Calculate the following: (-40*x**2 + 75*x)*(7*x**3 - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -280*x**5 + 525*x**4 + 1760*x**2 - 3300*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-40*x**2 + 75*x)*(7*x**3 - 44)
Expanding the part (7*x**3 - 44) using the distributive property, and we got: (7*x**3)*(-40*x**2 + 75*x) - 44*(-40*x**2 + 75*x)
<replace-#Step 1>#Step 2:
Current expression: (7*x**3)*(-40*x**2 + 75*x) - 44*(-40*x**2 + 75*x)</replace>
Simplifying the partial expression: -44*(-40*x**2 + 75*x)
Expanding the part (-40*x**2 + 75*x) using the distributive property, and we got: (75*x)*(-44) - 40*x**2*(-44)
Replacing -44*(-40*x**2 + 75*x) with (75*x)*(-44) - 40*x**2*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (75*x)*(-44) - 40*x**2*(-44) + (7*x**3)*(-40*x**2 + 75*x)</replace>
Simplifying the partial expression: (7*x**3)*(-40*x**2 + 75*x)
Expanding the part (-40*x**2 + 75*x) using the distributive property, and we got: (75*x)*(7*x**3) + (-40*x**2)*(7*x**3)
Replacing (7*x**3)*(-40*x**2 + 75*x) with (75*x)*(7*x**3) + (-40*x**2)*(7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (75*x)*(7*x**3) + (75*x)*(-44) + (-40*x**2)*(7*x**3) - 40*x**2*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*x**2)*-44 = 1760*x**2
  (-40*x**2)*(7*x**3) = -280*x**5
  (75*x)*-44 = -3300*x
  (75*x)*(7*x**3) = 525*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -280*x**5 + 525*x**4 + 1760*x**2 - 3300*x</replace>
No more calculations needed.
<answer>-280*x**5 + 525*x**4 + 1760*x**2 - 3300*x</answer>


Question:
Simplify this expression: (-24*z**3 + 67*z**2)*(32*z**3 - 3*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: -768*z**6 + 2216*z**5 - 273*z**4 + 201*z**3


Question:
Simplify this expression: -39*x**2*(-33*x**3 - 8*x**2 + 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1287*x**5 + 312*x**4 - 117*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -39*x**2*(-33*x**3 - 8*x**2 + 3)
Expanding the part (-33*x**3 - 8*x**2 + 3) using the distributive property, and we got: 3*(-39*x**2) + (-39*x**2)*(-8*x**2) + (-39*x**2)*(-33*x**3)
<replace-#Step 1>#Step 2:
Current expression: 3*(-39*x**2) + (-39*x**2)*(-8*x**2) + (-39*x**2)*(-33*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  3*(-39*x**2) = -117*x**2
  (-33*x**3)*(-39*x**2) = 1287*x**5
  (-8*x**2)*(-39*x**2) = 312*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1287*x**5 + 312*x**4 - 117*x**2</replace>
No more calculations needed.
<answer>1287*x**5 + 312*x**4 - 117*x**2</answer>


Question:
Calculate the following: (5*z**2 + 10)*(41*z**3 + 32*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: 205*z**5 + 160*z**4 + 410*z**3 + 320*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: (5*z**2 + 10)*(41*z**3 + 32*z**2)
Expanding the part (5*z**2 + 10) using the distributive property, and we got: (5*z**2)*(41*z**3 + 32*z**2) + 10*(41*z**3 + 32*z**2)
<replace-#Step 1>#Step 2:
Current expression: (5*z**2)*(41*z**3 + 32*z**2) + 10*(41*z**3 + 32*z**2)</replace>
Simplifying the partial expression: 10*(41*z**3 + 32*z**2)
Expanding the part (41*z**3 + 32*z**2) using the distributive property, and we got: (32*z**2)*10 + (41*z**3)*10
Replacing 10*(41*z**3 + 32*z**2) with (32*z**2)*10 + (41*z**3)*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*z**2)*(41*z**3 + 32*z**2) + (32*z**2)*10 + (41*z**3)*10</replace>
Simplifying the partial expression: (5*z**2)*(41*z**3 + 32*z**2)
Expanding the part (41*z**3 + 32*z**2) using the distributive property, and we got: (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3)
Replacing (5*z**2)*(41*z**3 + 32*z**2) with (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (5*z**2)*(32*z**2) + (5*z**2)*(41*z**3) + (32*z**2)*10 + (41*z**3)*10</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*z**2)*10 = 320*z**2
  (32*z**2)*(5*z**2) = 160*z**4
  (41*z**3)*10 = 410*z**3
  (41*z**3)*(5*z**2) = 205*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 205*z**5 + 160*z**4 + 410*z**3 + 320*z**2</replace>
No more calculations needed.
<answer>205*z**5 + 160*z**4 + 410*z**3 + 320*z**2</answer>


Question:
Calculate the following: (9*y**3 + 42)*(-4*y**3 - 5*y**2 + y + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*y**3 + 42)*(-4*y**3 - 5*y**2 + y + 41)
Expanding the part (9*y**3 + 42) using the distributive property, and we got: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 42*(-4*y**3 - 5*y**2 + y + 41)
<replace-#Step 1>#Step 2:
Current expression: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 42*(-4*y**3 - 5*y**2 + y + 41)</replace>
Simplifying the partial expression: 42*(-4*y**3 - 5*y**2 + y + 41)
Expanding the part (-4*y**3 - 5*y**2 + y + 41) using the distributive property, and we got: y*42 - 5*y**2*42 - 4*y**3*42 + 41*42
Replacing 42*(-4*y**3 - 5*y**2 + y + 41) with y*42 - 5*y**2*42 - 4*y**3*42 + 41*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*42 - 5*y**2*42 - 4*y**3*42 + (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) + 1722</replace>
Simplifying the partial expression: (9*y**3)*(-4*y**3 - 5*y**2 + y + 41)
Expanding the part (-4*y**3 - 5*y**2 + y + 41) using the distributive property, and we got: 41*(9*y**3) + y*(9*y**3) + (-5*y**2)*(9*y**3) + (-4*y**3)*(9*y**3)
Replacing (9*y**3)*(-4*y**3 - 5*y**2 + y + 41) with 41*(9*y**3) + y*(9*y**3) + (-5*y**2)*(9*y**3) + (-4*y**3)*(9*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 41*9*y**3 + y*(9*y**3) + y*42 + (-5*y**2)*(9*y**3) - 5*y**2*42 + (-4*y**3)*(9*y**3) - 4*y**3*42 + 1722</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*42 = 42*y
  y*(9*y**3) = 9*y**4
  (-5*y**2)*42 = -210*y**2
  (-5*y**2)*(9*y**3) = -45*y**5
  (-4*y**3)*42 = -168*y**3
  (-4*y**3)*(9*y**3) = -36*y**6
  41*9*y**3 = 369*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -36*y**6 - 45*y**5 + 9*y**4 - 168*y**3 + 369*y**3 - 210*y**2 + 42*y + 1722</replace>
Combining like terms, got -36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722
<replace-#Step 5>#Step 6:
Current expression: -36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722</replace>
No more calculations needed.
<answer>-36*y**6 - 45*y**5 + 9*y**4 + 201*y**3 - 210*y**2 + 42*y + 1722</answer>


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

Answer: -180*x**4 - 1000*x**2 - 460*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 20*x*(-9*x**3 - 50*x - 23)
Expanding the part (-9*x**3 - 50*x - 23) using the distributive property, and we got: (-50*x)*(20*x) - 460*x + (20*x)*(-9*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-50*x)*(20*x) - 460*x + (20*x)*(-9*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -23*(20*x) = -460*x
  (-50*x)*(20*x) = -1000*x**2
  (-9*x**3)*(20*x) = -180*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -180*x**4 - 1000*x**2 - 460*x</replace>
No more calculations needed.
<answer>-180*x**4 - 1000*x**2 - 460*x</answer>


Question:
Simplify this expression: (45 - 32*x)*(-19*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: 608*x**3 - 1527*x**2 + 945*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: (45 - 32*x)*(-19*x**2 + 21*x)
Expanding the part (45 - 32*x) using the distributive property, and we got: (-32*x)*(-19*x**2 + 21*x) + 45*(-19*x**2 + 21*x)
<replace-#Step 1>#Step 2:
Current expression: (-32*x)*(-19*x**2 + 21*x) + 45*(-19*x**2 + 21*x)</replace>
Simplifying the partial expression: 45*(-19*x**2 + 21*x)
Expanding the part (-19*x**2 + 21*x) using the distributive property, and we got: (21*x)*45 - 19*x**2*45
Replacing 45*(-19*x**2 + 21*x) with (21*x)*45 - 19*x**2*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-32*x)*(-19*x**2 + 21*x) + (21*x)*45 - 19*x**2*45</replace>
Simplifying the partial expression: (-32*x)*(-19*x**2 + 21*x)
Expanding the part (-19*x**2 + 21*x) using the distributive property, and we got: (-32*x)*(21*x) + (-32*x)*(-19*x**2)
Replacing (-32*x)*(-19*x**2 + 21*x) with (-32*x)*(21*x) + (-32*x)*(-19*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*x)*(21*x) + (-32*x)*(-19*x**2) + (21*x)*45 - 19*x**2*45</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**2)*45 = -855*x**2
  (-19*x**2)*(-32*x) = 608*x**3
  (21*x)*45 = 945*x
  (21*x)*(-32*x) = -672*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 608*x**3 - 855*x**2 - 672*x**2 + 945*x</replace>
Combining like terms, got 608*x**3 - 1527*x**2 + 945*x
<replace-#Step 5>#Step 6:
Current expression: 608*x**3 - 1527*x**2 + 945*x</replace>
No more calculations needed.
<answer>608*x**3 - 1527*x**2 + 945*x</answer>


Question:
Calculate the following: (-30*x**3 + 9*x**2 - 22)*(14*x**3 + 44*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: -420*x**6 - 1194*x**5 + 396*x**4 + 1102*x**3 - 1391*x**2 + 1034


Question:
Calculate the following: 255*x**3 - 204*x**2 + 782*x + 187
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 255*x**3 - 204*x**2 + 782*x + 187

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: 255*x**3 - 204*x**2 + 782*x + 187
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: 255*x**3 - 204*x**2 + 782*x + 187</replace>
No more calculations needed.
<answer>255*x**3 - 204*x**2 + 782*x + 187</answer>


Question:
Simplify this expression: (-35*y**3 + 87*y**2 + 25*y)*(-2*y**3 + 2*y**2 - 11*y + 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 70*y**6 - 244*y**5 + 509*y**4 - 1397*y**3 + 943*y**2 + 350*y


Question:
Simplify this expression: (49 - 50*x)*(4*x + 94)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -200*x**2 - 4504*x + 4606

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 - 50*x)*(4*x + 94)
Expanding the part (49 - 50*x) using the distributive property, and we got: (-50*x)*(4*x + 94) + 49*(4*x + 94)
<replace-#Step 1>#Step 2:
Current expression: (-50*x)*(4*x + 94) + 49*(4*x + 94)</replace>
Simplifying the partial expression: 49*(4*x + 94)
Expanding the part (4*x + 94) using the distributive property, and we got: (4*x)*49 + 94*49
Replacing 49*(4*x + 94) with (4*x)*49 + 94*49 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-50*x)*(4*x + 94) + (4*x)*49 + 4606</replace>
Simplifying the partial expression: (-50*x)*(4*x + 94)
Expanding the part (4*x + 94) using the distributive property, and we got: (-50*x)*(4*x) + 94*(-50*x)
Replacing (-50*x)*(4*x + 94) with (-50*x)*(4*x) + 94*(-50*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*x)*(4*x) + 94*(-50)*x + (4*x)*49 + 4606</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*x)*49 = 196*x
  (4*x)*(-50*x) = -200*x**2
  94*-50*x = -4700*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -200*x**2 - 4700*x + 196*x + 4606</replace>
Combining like terms, got -200*x**2 - 4504*x + 4606
<replace-#Step 5>#Step 6:
Current expression: -200*x**2 - 4504*x + 4606</replace>
No more calculations needed.
<answer>-200*x**2 - 4504*x + 4606</answer>


Question:
Simplify this expression: (-17*y**3 - 44)*(-44*y**3 + 11*y + 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-17*y**3 - 44)*(-44*y**3 + 11*y + 43)
Expanding the part (-17*y**3 - 44) using the distributive property, and we got: (-17*y**3)*(-44*y**3 + 11*y + 43) - 44*(-44*y**3 + 11*y + 43)
<replace-#Step 1>#Step 2:
Current expression: (-17*y**3)*(-44*y**3 + 11*y + 43) - 44*(-44*y**3 + 11*y + 43)</replace>
Simplifying the partial expression: -44*(-44*y**3 + 11*y + 43)
Expanding the part (-44*y**3 + 11*y + 43) using the distributive property, and we got: (11*y)*(-44) - 44*y**3*(-44) + 43*(-44)
Replacing -44*(-44*y**3 + 11*y + 43) with (11*y)*(-44) - 44*y**3*(-44) + 43*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*y)*(-44) - 44*y**3*(-44) + (-17*y**3)*(-44*y**3 + 11*y + 43) - 1892</replace>
Simplifying the partial expression: (-17*y**3)*(-44*y**3 + 11*y + 43)
Expanding the part (-44*y**3 + 11*y + 43) using the distributive property, and we got: 43*(-17*y**3) + (11*y)*(-17*y**3) + (-44*y**3)*(-17*y**3)
Replacing (-17*y**3)*(-44*y**3 + 11*y + 43) with 43*(-17*y**3) + (11*y)*(-17*y**3) + (-44*y**3)*(-17*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 43*(-17)*y**3 + (11*y)*(-17*y**3) + (11*y)*(-44) + (-44*y**3)*(-17*y**3) - 44*y**3*(-44) - 1892</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*y**3)*-44 = 1936*y**3
  (-44*y**3)*(-17*y**3) = 748*y**6
  (11*y)*-44 = -484*y
  (11*y)*(-17*y**3) = -187*y**4
  43*-17*y**3 = -731*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 748*y**6 - 187*y**4 - 731*y**3 + 1936*y**3 - 484*y - 1892</replace>
Combining like terms, got 748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892
<replace-#Step 5>#Step 6:
Current expression: 748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892</replace>
No more calculations needed.
<answer>748*y**6 - 187*y**4 + 1205*y**3 - 484*y - 1892</answer>


Question:
Simplify this expression: (-19*x**2 - 85*x)*(24*x**3 + 87*x + 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -456*x**5 - 2040*x**4 - 1653*x**3 - 7661*x**2 - 1190*x


Question:
Simplify this expression: (9*z + 24)*(9*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: 81*z**3 + 450*z**2 + 624*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*z + 24)*(9*z**2 + 26*z)
Expanding the part (9*z + 24) using the distributive property, and we got: (9*z)*(9*z**2 + 26*z) + 24*(9*z**2 + 26*z)
<replace-#Step 1>#Step 2:
Current expression: (9*z)*(9*z**2 + 26*z) + 24*(9*z**2 + 26*z)</replace>
Simplifying the partial expression: 24*(9*z**2 + 26*z)
Expanding the part (9*z**2 + 26*z) using the distributive property, and we got: (26*z)*24 + (9*z**2)*24
Replacing 24*(9*z**2 + 26*z) with (26*z)*24 + (9*z**2)*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*z)*(9*z**2 + 26*z) + (26*z)*24 + (9*z**2)*24</replace>
Simplifying the partial expression: (9*z)*(9*z**2 + 26*z)
Expanding the part (9*z**2 + 26*z) using the distributive property, and we got: (9*z)*(26*z) + (9*z)*(9*z**2)
Replacing (9*z)*(9*z**2 + 26*z) with (9*z)*(26*z) + (9*z)*(9*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*z)*(26*z) + (9*z)*(9*z**2) + (26*z)*24 + (9*z**2)*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*z**2)*24 = 216*z**2
  (9*z**2)*(9*z) = 81*z**3
  (26*z)*24 = 624*z
  (26*z)*(9*z) = 234*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 81*z**3 + 216*z**2 + 234*z**2 + 624*z</replace>
Combining like terms, got 81*z**3 + 450*z**2 + 624*z
<replace-#Step 5>#Step 6:
Current expression: 81*z**3 + 450*z**2 + 624*z</replace>
No more calculations needed.
<answer>81*z**3 + 450*z**2 + 624*z</answer>


Question:
Calculate the following: (-10*x**2 + 48*x - 22)*(2*x**2 + 31*x + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -20*x**4 - 214*x**3 + 1114*x**2 + 902*x - 726


Question:
Simplify this expression: 583*z**3 - 159*z**2 + 2067*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: 583*z**3 - 159*z**2 + 2067*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: 583*z**3 - 159*z**2 + 2067*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 583*z**3 - 159*z**2 + 2067*z</replace>
No more calculations needed.
<answer>583*z**3 - 159*z**2 + 2067*z</answer>


Question:
Simplify this expression: (6 - 44*x)*(50 - 45*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: 1980*x**2 - 2470*x + 300

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (6 - 44*x)*(50 - 45*x)
Expanding the part (6 - 44*x) using the distributive property, and we got: (-44*x)*(50 - 45*x) + 6*(50 - 45*x)
<replace-#Step 1>#Step 2:
Current expression: (-44*x)*(50 - 45*x) + 6*(50 - 45*x)</replace>
Simplifying the partial expression: 6*(50 - 45*x)
Expanding the part (50 - 45*x) using the distributive property, and we got: -45*x*6 + 50*6
Replacing 6*(50 - 45*x) with -45*x*6 + 50*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*x*6 + (-44*x)*(50 - 45*x) + 300</replace>
Simplifying the partial expression: (-44*x)*(50 - 45*x)
Expanding the part (50 - 45*x) using the distributive property, and we got: (-45*x)*(-44*x) + 50*(-44*x)
Replacing (-44*x)*(50 - 45*x) with (-45*x)*(-44*x) + 50*(-44*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*x)*(-44*x) - 45*x*6 + 50*(-44)*x + 300</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*x)*6 = -270*x
  (-45*x)*(-44*x) = 1980*x**2
  50*-44*x = -2200*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1980*x**2 - 2200*x - 270*x + 300</replace>
Combining like terms, got 1980*x**2 - 2470*x + 300
<replace-#Step 5>#Step 6:
Current expression: 1980*x**2 - 2470*x + 300</replace>
No more calculations needed.
<answer>1980*x**2 - 2470*x + 300</answer>


Question:
Calculate the following: -972*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: -972*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: -972*x
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: -972*x</replace>
No more calculations needed.
<answer>-972*x</answer>


Question:
Simplify this expression: (-24*x**2 + 47*x - 9)*(-24*x**3 + 25*x**2 - 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 576*x**5 - 1728*x**4 + 1391*x**3 + 207*x**2 - 846*x + 162


Question:
Calculate the following: (18*y**2 - 19)*(-7*y**2 - 47*y - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (18*y**2 - 19)*(-7*y**2 - 47*y - 40)
Expanding the part (18*y**2 - 19) using the distributive property, and we got: (18*y**2)*(-7*y**2 - 47*y - 40) - 19*(-7*y**2 - 47*y - 40)
<replace-#Step 1>#Step 2:
Current expression: (18*y**2)*(-7*y**2 - 47*y - 40) - 19*(-7*y**2 - 47*y - 40)</replace>
Simplifying the partial expression: -19*(-7*y**2 - 47*y - 40)
Expanding the part (-7*y**2 - 47*y - 40) using the distributive property, and we got: -47*y*(-19) - 7*y**2*(-19) - 40*(-19)
Replacing -19*(-7*y**2 - 47*y - 40) with -47*y*(-19) - 7*y**2*(-19) - 40*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -47*y*(-19) - 7*y**2*(-19) + (18*y**2)*(-7*y**2 - 47*y - 40) + 760</replace>
Simplifying the partial expression: (18*y**2)*(-7*y**2 - 47*y - 40)
Expanding the part (-7*y**2 - 47*y - 40) using the distributive property, and we got: (-47*y)*(18*y**2) - 720*y**2 + (-7*y**2)*(18*y**2)
Replacing (18*y**2)*(-7*y**2 - 47*y - 40) with (-47*y)*(18*y**2) - 720*y**2 + (-7*y**2)*(18*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*y)*(18*y**2) - 47*y*(-19) - 40*18*y**2 + (-7*y**2)*(18*y**2) - 7*y**2*(-19) + 760</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y)*-19 = 893*y
  (-47*y)*(18*y**2) = -846*y**3
  (-7*y**2)*-19 = 133*y**2
  (-7*y**2)*(18*y**2) = -126*y**4
  -40*18*y**2 = -720*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -126*y**4 - 846*y**3 - 720*y**2 + 133*y**2 + 893*y + 760</replace>
Combining like terms, got -126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760
<replace-#Step 5>#Step 6:
Current expression: -126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760</replace>
No more calculations needed.
<answer>-126*y**4 - 846*y**3 - 587*y**2 + 893*y + 760</answer>


Question:
Calculate the following: 81*y**2*(-25*y**3 + 20*y + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2025*y**5 + 1620*y**3 + 2754*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: 81*y**2*(-25*y**3 + 20*y + 34)
Expanding the part (-25*y**3 + 20*y + 34) using the distributive property, and we got: 34*(81*y**2) + (20*y)*(81*y**2) + (81*y**2)*(-25*y**3)
<replace-#Step 1>#Step 2:
Current expression: 34*(81*y**2) + (20*y)*(81*y**2) + (81*y**2)*(-25*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  34*(81*y**2) = 2754*y**2
  (-25*y**3)*(81*y**2) = -2025*y**5
  (20*y)*(81*y**2) = 1620*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2025*y**5 + 1620*y**3 + 2754*y**2</replace>
No more calculations needed.
<answer>-2025*y**5 + 1620*y**3 + 2754*y**2</answer>


Question:
Simplify this expression: -77*z**3*(-19*z**3 - 11*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1463*z**6 + 847*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: -77*z**3*(-19*z**3 - 11*z**2)
Expanding the part (-19*z**3 - 11*z**2) using the distributive property, and we got: (-11*z**2)*(-77*z**3) + (-77*z**3)*(-19*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*z**2)*(-77*z**3) + (-77*z**3)*(-19*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*z**3)*(-77*z**3) = 1463*z**6
  (-11*z**2)*(-77*z**3) = 847*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1463*z**6 + 847*z**5</replace>
No more calculations needed.
<answer>1463*z**6 + 847*z**5</answer>


Question:
Simplify this expression: (16*x**2 + 15*x)*(-3*x**3 - 9*x + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (16*x**2 + 15*x)*(-3*x**3 - 9*x + 33)
Expanding the part (16*x**2 + 15*x) using the distributive property, and we got: (15*x)*(-3*x**3 - 9*x + 33) + (16*x**2)*(-3*x**3 - 9*x + 33)
<replace-#Step 1>#Step 2:
Current expression: (15*x)*(-3*x**3 - 9*x + 33) + (16*x**2)*(-3*x**3 - 9*x + 33)</replace>
Simplifying the partial expression: (15*x)*(-3*x**3 - 9*x + 33)
Expanding the part (-3*x**3 - 9*x + 33) using the distributive property, and we got: (-9*x)*(15*x) + 33*(15*x) + (15*x)*(-3*x**3)
Replacing (15*x)*(-3*x**3 - 9*x + 33) with (-9*x)*(15*x) + 33*(15*x) + (15*x)*(-3*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*x)*(15*x) + 33*15*x + (15*x)*(-3*x**3) + (16*x**2)*(-3*x**3 - 9*x + 33)</replace>
Simplifying the partial expression: (16*x**2)*(-3*x**3 - 9*x + 33)
Expanding the part (-3*x**3 - 9*x + 33) using the distributive property, and we got: (-9*x)*(16*x**2) + 33*(16*x**2) + (16*x**2)*(-3*x**3)
Replacing (16*x**2)*(-3*x**3 - 9*x + 33) with (-9*x)*(16*x**2) + 33*(16*x**2) + (16*x**2)*(-3*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*x)*(15*x) + (-9*x)*(16*x**2) + 33*16*x**2 + 33*15*x + (15*x)*(-3*x**3) + (16*x**2)*(-3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*x)*(15*x) = -135*x**2
  (-9*x)*(16*x**2) = -144*x**3
  (-3*x**3)*(15*x) = -45*x**4
  (-3*x**3)*(16*x**2) = -48*x**5
  33*15*x = 495*x
  33*16*x**2 = 528*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -48*x**5 - 45*x**4 - 144*x**3 - 135*x**2 + 528*x**2 + 495*x</replace>
Combining like terms, got -48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x
<replace-#Step 5>#Step 6:
Current expression: -48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x</replace>
No more calculations needed.
<answer>-48*x**5 - 45*x**4 - 144*x**3 + 393*x**2 + 495*x</answer>


Question:
Simplify this expression: (-46*y**3 - 26)*(-34*y**3 + 9*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1564*y**6 - 414*y**5 + 884*y**3 - 234*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: (-46*y**3 - 26)*(-34*y**3 + 9*y**2)
Expanding the part (-46*y**3 - 26) using the distributive property, and we got: (-46*y**3)*(-34*y**3 + 9*y**2) - 26*(-34*y**3 + 9*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-46*y**3)*(-34*y**3 + 9*y**2) - 26*(-34*y**3 + 9*y**2)</replace>
Simplifying the partial expression: -26*(-34*y**3 + 9*y**2)
Expanding the part (-34*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-26) - 34*y**3*(-26)
Replacing -26*(-34*y**3 + 9*y**2) with (9*y**2)*(-26) - 34*y**3*(-26) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y**2)*(-26) + (-46*y**3)*(-34*y**3 + 9*y**2) - 34*y**3*(-26)</replace>
Simplifying the partial expression: (-46*y**3)*(-34*y**3 + 9*y**2)
Expanding the part (-34*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-46*y**3) + (-46*y**3)*(-34*y**3)
Replacing (-46*y**3)*(-34*y**3 + 9*y**2) with (9*y**2)*(-46*y**3) + (-46*y**3)*(-34*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*y**2)*(-46*y**3) + (9*y**2)*(-26) + (-46*y**3)*(-34*y**3) - 34*y**3*(-26)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*y**3)*-26 = 884*y**3
  (-34*y**3)*(-46*y**3) = 1564*y**6
  (9*y**2)*-26 = -234*y**2
  (9*y**2)*(-46*y**3) = -414*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2</replace>
No more calculations needed.
<answer>1564*y**6 - 414*y**5 + 884*y**3 - 234*y**2</answer>


Question:
Simplify this expression: (-48*y**3 - 35*y**2)*(27*y**3 - 49*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1296*y**6 + 1407*y**5 + 1715*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: (-48*y**3 - 35*y**2)*(27*y**3 - 49*y**2)
Expanding the part (27*y**3 - 49*y**2) using the distributive property, and we got: (-49*y**2)*(-48*y**3 - 35*y**2) + (27*y**3)*(-48*y**3 - 35*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-49*y**2)*(-48*y**3 - 35*y**2) + (27*y**3)*(-48*y**3 - 35*y**2)</replace>
Simplifying the partial expression: (-49*y**2)*(-48*y**3 - 35*y**2)
Expanding the part (-48*y**3 - 35*y**2) using the distributive property, and we got: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3)
Replacing (-49*y**2)*(-48*y**3 - 35*y**2) with (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) + (27*y**3)*(-48*y**3 - 35*y**2)</replace>
Simplifying the partial expression: (27*y**3)*(-48*y**3 - 35*y**2)
Expanding the part (-48*y**3 - 35*y**2) using the distributive property, and we got: (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3)
Replacing (27*y**3)*(-48*y**3 - 35*y**2) with (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*y**2)*(-35*y**2) + (-49*y**2)*(-48*y**3) + (-35*y**2)*(27*y**3) + (-48*y**3)*(27*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*y**3)*(-49*y**2) = 2352*y**5
  (-48*y**3)*(27*y**3) = -1296*y**6
  (-35*y**2)*(-49*y**2) = 1715*y**4
  (-35*y**2)*(27*y**3) = -945*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1296*y**6 - 945*y**5 + 2352*y**5 + 1715*y**4</replace>
Combining like terms, got -1296*y**6 + 1407*y**5 + 1715*y**4
<replace-#Step 5>#Step 6:
Current expression: -1296*y**6 + 1407*y**5 + 1715*y**4</replace>
No more calculations needed.
<answer>-1296*y**6 + 1407*y**5 + 1715*y**4</answer>


Question:
Simplify this expression: 3*x*(35*x**3 + 37*x**2 - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 105*x**4 + 111*x**3 - 63*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 3*x*(35*x**3 + 37*x**2 - 21)
Expanding the part (35*x**3 + 37*x**2 - 21) using the distributive property, and we got: -63*x + (3*x)*(37*x**2) + (3*x)*(35*x**3)
<replace-#Step 1>#Step 2:
Current expression: -63*x + (3*x)*(37*x**2) + (3*x)*(35*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -21*(3*x) = -63*x
  (35*x**3)*(3*x) = 105*x**4
  (37*x**2)*(3*x) = 111*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 105*x**4 + 111*x**3 - 63*x</replace>
No more calculations needed.
<answer>105*x**4 + 111*x**3 - 63*x</answer>


Question:
Calculate the following: (-38*z**2 - 116*z)*(-2*z**3 - 45*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: 76*z**5 + 1942*z**4 + 5220*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**2 - 116*z)*(-2*z**3 - 45*z**2)
Expanding the part (-38*z**2 - 116*z) using the distributive property, and we got: (-116*z)*(-2*z**3 - 45*z**2) + (-38*z**2)*(-2*z**3 - 45*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-116*z)*(-2*z**3 - 45*z**2) + (-38*z**2)*(-2*z**3 - 45*z**2)</replace>
Simplifying the partial expression: (-116*z)*(-2*z**3 - 45*z**2)
Expanding the part (-2*z**3 - 45*z**2) using the distributive property, and we got: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3)
Replacing (-116*z)*(-2*z**3 - 45*z**2) with (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) + (-38*z**2)*(-2*z**3 - 45*z**2)</replace>
Simplifying the partial expression: (-38*z**2)*(-2*z**3 - 45*z**2)
Expanding the part (-2*z**3 - 45*z**2) using the distributive property, and we got: (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3)
Replacing (-38*z**2)*(-2*z**3 - 45*z**2) with (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-116*z)*(-45*z**2) + (-116*z)*(-2*z**3) + (-45*z**2)*(-38*z**2) + (-38*z**2)*(-2*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*z**2)*(-116*z) = 5220*z**3
  (-45*z**2)*(-38*z**2) = 1710*z**4
  (-2*z**3)*(-116*z) = 232*z**4
  (-2*z**3)*(-38*z**2) = 76*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 76*z**5 + 232*z**4 + 1710*z**4 + 5220*z**3</replace>
Combining like terms, got 76*z**5 + 1942*z**4 + 5220*z**3
<replace-#Step 5>#Step 6:
Current expression: 76*z**5 + 1942*z**4 + 5220*z**3</replace>
No more calculations needed.
<answer>76*z**5 + 1942*z**4 + 5220*z**3</answer>


Question:
Simplify this expression: (9*z**2 + 24)*(-28*z**3 - 23*z**2 + 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*z**2 + 24)*(-28*z**3 - 23*z**2 + 36)
Expanding the part (9*z**2 + 24) using the distributive property, and we got: (9*z**2)*(-28*z**3 - 23*z**2 + 36) + 24*(-28*z**3 - 23*z**2 + 36)
<replace-#Step 1>#Step 2:
Current expression: (9*z**2)*(-28*z**3 - 23*z**2 + 36) + 24*(-28*z**3 - 23*z**2 + 36)</replace>
Simplifying the partial expression: 24*(-28*z**3 - 23*z**2 + 36)
Expanding the part (-28*z**3 - 23*z**2 + 36) using the distributive property, and we got: -23*z**2*24 - 28*z**3*24 + 36*24
Replacing 24*(-28*z**3 - 23*z**2 + 36) with -23*z**2*24 - 28*z**3*24 + 36*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*z**2*24 + (9*z**2)*(-28*z**3 - 23*z**2 + 36) - 28*z**3*24 + 864</replace>
Simplifying the partial expression: (9*z**2)*(-28*z**3 - 23*z**2 + 36)
Expanding the part (-28*z**3 - 23*z**2 + 36) using the distributive property, and we got: 36*(9*z**2) + (-23*z**2)*(9*z**2) + (9*z**2)*(-28*z**3)
Replacing (9*z**2)*(-28*z**3 - 23*z**2 + 36) with 36*(9*z**2) + (-23*z**2)*(9*z**2) + (9*z**2)*(-28*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 36*9*z**2 + (-23*z**2)*(9*z**2) - 23*z**2*24 + (9*z**2)*(-28*z**3) - 28*z**3*24 + 864</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*z**3)*24 = -672*z**3
  (-28*z**3)*(9*z**2) = -252*z**5
  (-23*z**2)*24 = -552*z**2
  (-23*z**2)*(9*z**2) = -207*z**4
  36*9*z**2 = 324*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -252*z**5 - 207*z**4 - 672*z**3 - 552*z**2 + 324*z**2 + 864</replace>
Combining like terms, got -252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864
<replace-#Step 5>#Step 6:
Current expression: -252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864</replace>
No more calculations needed.
<answer>-252*z**5 - 207*z**4 - 672*z**3 - 228*z**2 + 864</answer>


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

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


Question:
Simplify this expression: (50*z**2 + 9)*(-46*z**3 + 12*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: -2300*z**5 + 600*z**4 - 414*z**3 + 108*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: (50*z**2 + 9)*(-46*z**3 + 12*z**2)
Expanding the part (50*z**2 + 9) using the distributive property, and we got: (50*z**2)*(-46*z**3 + 12*z**2) + 9*(-46*z**3 + 12*z**2)
<replace-#Step 1>#Step 2:
Current expression: (50*z**2)*(-46*z**3 + 12*z**2) + 9*(-46*z**3 + 12*z**2)</replace>
Simplifying the partial expression: 9*(-46*z**3 + 12*z**2)
Expanding the part (-46*z**3 + 12*z**2) using the distributive property, and we got: (12*z**2)*9 - 46*z**3*9
Replacing 9*(-46*z**3 + 12*z**2) with (12*z**2)*9 - 46*z**3*9 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*z**2)*9 + (50*z**2)*(-46*z**3 + 12*z**2) - 46*z**3*9</replace>
Simplifying the partial expression: (50*z**2)*(-46*z**3 + 12*z**2)
Expanding the part (-46*z**3 + 12*z**2) using the distributive property, and we got: (12*z**2)*(50*z**2) + (50*z**2)*(-46*z**3)
Replacing (50*z**2)*(-46*z**3 + 12*z**2) with (12*z**2)*(50*z**2) + (50*z**2)*(-46*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (12*z**2)*(50*z**2) + (12*z**2)*9 + (50*z**2)*(-46*z**3) - 46*z**3*9</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*z**3)*9 = -414*z**3
  (-46*z**3)*(50*z**2) = -2300*z**5
  (12*z**2)*9 = 108*z**2
  (12*z**2)*(50*z**2) = 600*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2</replace>
No more calculations needed.
<answer>-2300*z**5 + 600*z**4 - 414*z**3 + 108*z**2</answer>


Question:
Calculate the following: 69*x*(104*x**3 + 19*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: 7176*x**4 + 1311*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: 69*x*(104*x**3 + 19*x**2)
Expanding the part (104*x**3 + 19*x**2) using the distributive property, and we got: (69*x)*(19*x**2) + (69*x)*(104*x**3)
<replace-#Step 1>#Step 2:
Current expression: (69*x)*(19*x**2) + (69*x)*(104*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**2)*(69*x) = 1311*x**3
  (104*x**3)*(69*x) = 7176*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 7176*x**4 + 1311*x**3</replace>
No more calculations needed.
<answer>7176*x**4 + 1311*x**3</answer>


Question:
Calculate the following: (7 - 47*y**3)*(-27*y**3 + 20*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: 1269*y**6 - 940*y**4 - 189*y**3 + 140*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: (7 - 47*y**3)*(-27*y**3 + 20*y)
Expanding the part (7 - 47*y**3) using the distributive property, and we got: (-47*y**3)*(-27*y**3 + 20*y) + 7*(-27*y**3 + 20*y)
<replace-#Step 1>#Step 2:
Current expression: (-47*y**3)*(-27*y**3 + 20*y) + 7*(-27*y**3 + 20*y)</replace>
Simplifying the partial expression: 7*(-27*y**3 + 20*y)
Expanding the part (-27*y**3 + 20*y) using the distributive property, and we got: (20*y)*7 - 27*y**3*7
Replacing 7*(-27*y**3 + 20*y) with (20*y)*7 - 27*y**3*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (20*y)*7 + (-47*y**3)*(-27*y**3 + 20*y) - 27*y**3*7</replace>
Simplifying the partial expression: (-47*y**3)*(-27*y**3 + 20*y)
Expanding the part (-27*y**3 + 20*y) using the distributive property, and we got: (20*y)*(-47*y**3) + (-47*y**3)*(-27*y**3)
Replacing (-47*y**3)*(-27*y**3 + 20*y) with (20*y)*(-47*y**3) + (-47*y**3)*(-27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (20*y)*(-47*y**3) + (20*y)*7 + (-47*y**3)*(-27*y**3) - 27*y**3*7</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**3)*7 = -189*y**3
  (-27*y**3)*(-47*y**3) = 1269*y**6
  (20*y)*7 = 140*y
  (20*y)*(-47*y**3) = -940*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1269*y**6 - 940*y**4 - 189*y**3 + 140*y</replace>
No more calculations needed.
<answer>1269*y**6 - 940*y**4 - 189*y**3 + 140*y</answer>


Question:
Calculate the following: (36*y**2 - 30*y)*(-4*y**3 - 38*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -144*y**5 - 1248*y**4 + 1140*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (36*y**2 - 30*y)*(-4*y**3 - 38*y**2)
Expanding the part (-4*y**3 - 38*y**2) using the distributive property, and we got: (-38*y**2)*(36*y**2 - 30*y) + (-4*y**3)*(36*y**2 - 30*y)
<replace-#Step 1>#Step 2:
Current expression: (-38*y**2)*(36*y**2 - 30*y) + (-4*y**3)*(36*y**2 - 30*y)</replace>
Simplifying the partial expression: (-38*y**2)*(36*y**2 - 30*y)
Expanding the part (36*y**2 - 30*y) using the distributive property, and we got: (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2)
Replacing (-38*y**2)*(36*y**2 - 30*y) with (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-30*y)*(-38*y**2) + (-38*y**2)*(36*y**2) + (-4*y**3)*(36*y**2 - 30*y)</replace>
Simplifying the partial expression: (-4*y**3)*(36*y**2 - 30*y)
Expanding the part (36*y**2 - 30*y) using the distributive property, and we got: (-30*y)*(-4*y**3) + (36*y**2)*(-4*y**3)
Replacing (-4*y**3)*(36*y**2 - 30*y) with (-30*y)*(-4*y**3) + (36*y**2)*(-4*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*y)*(-38*y**2) + (-30*y)*(-4*y**3) + (-38*y**2)*(36*y**2) + (36*y**2)*(-4*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y)*(-38*y**2) = 1140*y**3
  (-30*y)*(-4*y**3) = 120*y**4
  (36*y**2)*(-38*y**2) = -1368*y**4
  (36*y**2)*(-4*y**3) = -144*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -144*y**5 - 1368*y**4 + 120*y**4 + 1140*y**3</replace>
Combining like terms, got -144*y**5 - 1248*y**4 + 1140*y**3
<replace-#Step 5>#Step 6:
Current expression: -144*y**5 - 1248*y**4 + 1140*y**3</replace>
No more calculations needed.
<answer>-144*y**5 - 1248*y**4 + 1140*y**3</answer>


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

Answer: -18*y**3 + 38*y**2 + 276*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: (46 - 9*y)*(2*y**2 + 6*y)
Expanding the part (46 - 9*y) using the distributive property, and we got: (-9*y)*(2*y**2 + 6*y) + 46*(2*y**2 + 6*y)
<replace-#Step 1>#Step 2:
Current expression: (-9*y)*(2*y**2 + 6*y) + 46*(2*y**2 + 6*y)</replace>
Simplifying the partial expression: 46*(2*y**2 + 6*y)
Expanding the part (2*y**2 + 6*y) using the distributive property, and we got: (6*y)*46 + (2*y**2)*46
Replacing 46*(2*y**2 + 6*y) with (6*y)*46 + (2*y**2)*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*y)*(2*y**2 + 6*y) + (6*y)*46 + (2*y**2)*46</replace>
Simplifying the partial expression: (-9*y)*(2*y**2 + 6*y)
Expanding the part (2*y**2 + 6*y) using the distributive property, and we got: (-9*y)*(6*y) + (-9*y)*(2*y**2)
Replacing (-9*y)*(2*y**2 + 6*y) with (-9*y)*(6*y) + (-9*y)*(2*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*y)*(6*y) + (-9*y)*(2*y**2) + (6*y)*46 + (2*y**2)*46</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*y**2)*46 = 92*y**2
  (2*y**2)*(-9*y) = -18*y**3
  (6*y)*46 = 276*y
  (6*y)*(-9*y) = -54*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -18*y**3 - 54*y**2 + 92*y**2 + 276*y</replace>
Combining like terms, got -18*y**3 + 38*y**2 + 276*y
<replace-#Step 5>#Step 6:
Current expression: -18*y**3 + 38*y**2 + 276*y</replace>
No more calculations needed.
<answer>-18*y**3 + 38*y**2 + 276*y</answer>


Question:
Simplify this expression: (-10*y - 3)*(20*y**3 + 19*y**2 + 78)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*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**4 - 250*y**3 - 57*y**2 - 780*y - 234

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-10*y - 3)*(20*y**3 + 19*y**2 + 78)
Expanding the part (-10*y - 3) using the distributive property, and we got: (-10*y)*(20*y**3 + 19*y**2 + 78) - 3*(20*y**3 + 19*y**2 + 78)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(20*y**3 + 19*y**2 + 78) - 3*(20*y**3 + 19*y**2 + 78)</replace>
Simplifying the partial expression: -3*(20*y**3 + 19*y**2 + 78)
Expanding the part (20*y**3 + 19*y**2 + 78) using the distributive property, and we got: (19*y**2)*(-3) + (20*y**3)*(-3) + 78*(-3)
Replacing -3*(20*y**3 + 19*y**2 + 78) with (19*y**2)*(-3) + (20*y**3)*(-3) + 78*(-3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*y)*(20*y**3 + 19*y**2 + 78) + (19*y**2)*(-3) + (20*y**3)*(-3) - 234</replace>
Simplifying the partial expression: (-10*y)*(20*y**3 + 19*y**2 + 78)
Expanding the part (20*y**3 + 19*y**2 + 78) using the distributive property, and we got: (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10*y)
Replacing (-10*y)*(20*y**3 + 19*y**2 + 78) with (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*y)*(19*y**2) + (-10*y)*(20*y**3) + 78*(-10)*y + (19*y**2)*(-3) + (20*y**3)*(-3) - 234</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (19*y**2)*-3 = -57*y**2
  (19*y**2)*(-10*y) = -190*y**3
  (20*y**3)*-3 = -60*y**3
  (20*y**3)*(-10*y) = -200*y**4
  78*-10*y = -780*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -200*y**4 - 190*y**3 - 60*y**3 - 57*y**2 - 780*y - 234</replace>
Combining like terms, got -200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234
<replace-#Step 5>#Step 6:
Current expression: -200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234</replace>
No more calculations needed.
<answer>-200*y**4 - 250*y**3 - 57*y**2 - 780*y - 234</answer>


Question:
Calculate the following: (-26*x**3 - 8*x + 42)*(10*x**3 - 54*x**2 + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -260*x**6 + 1404*x**5 - 80*x**4 + 46*x**3 - 2268*x**2 - 248*x + 1302


Question:
Calculate the following: (26 - 26*y)*(y**3 - 33*y + 2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (26 - 26*y)*(y**3 - 33*y + 2)
Expanding the part (26 - 26*y) using the distributive property, and we got: (-26*y)*(y**3 - 33*y + 2) + 26*(y**3 - 33*y + 2)
<replace-#Step 1>#Step 2:
Current expression: (-26*y)*(y**3 - 33*y + 2) + 26*(y**3 - 33*y + 2)</replace>
Simplifying the partial expression: 26*(y**3 - 33*y + 2)
Expanding the part (y**3 - 33*y + 2) using the distributive property, and we got: -33*y*26 + y**3*26 + 2*26
Replacing 26*(y**3 - 33*y + 2) with -33*y*26 + y**3*26 + 2*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*y*26 + (-26*y)*(y**3 - 33*y + 2) + y**3*26 + 52</replace>
Simplifying the partial expression: (-26*y)*(y**3 - 33*y + 2)
Expanding the part (y**3 - 33*y + 2) using the distributive property, and we got: (-33*y)*(-26*y) + (-26*y)*y**3 + 2*(-26*y)
Replacing (-26*y)*(y**3 - 33*y + 2) with (-33*y)*(-26*y) + (-26*y)*y**3 + 2*(-26*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*y)*(-26*y) - 33*y*26 + (-26*y)*y**3 + y**3*26 + 2*(-26)*y + 52</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**3*26 = 26*y**3
  y**3*(-26*y) = -26*y**4
  (-33*y)*26 = -858*y
  (-33*y)*(-26*y) = 858*y**2
  2*-26*y = -52*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -26*y**4 + 26*y**3 + 858*y**2 - 858*y - 52*y + 52</replace>
Combining like terms, got -26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52
<replace-#Step 5>#Step 6:
Current expression: -26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52</replace>
No more calculations needed.
<answer>-26*y**4 + 26*y**3 + 858*y**2 - 910*y + 52</answer>


Question:
Simplify this expression: 19*z**2*(-37*z**3 + 25*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: -703*z**5 + 475*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 19*z**2*(-37*z**3 + 25*z**2)
Expanding the part (-37*z**3 + 25*z**2) using the distributive property, and we got: (19*z**2)*(25*z**2) + (19*z**2)*(-37*z**3)
<replace-#Step 1>#Step 2:
Current expression: (19*z**2)*(25*z**2) + (19*z**2)*(-37*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z**3)*(19*z**2) = -703*z**5
  (25*z**2)*(19*z**2) = 475*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -703*z**5 + 475*z**4</replace>
No more calculations needed.
<answer>-703*z**5 + 475*z**4</answer>


Question:
Calculate the following: (22*z**3 - 25)*(-36*z**3 + 27*z**2 + 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: -792*z**6 + 594*z**5 + 858*z**4 + 900*z**3 - 675*z**2 - 975*z


Question:
Calculate the following: (-36*z**3 + 12*z)*(2*z**3 + 6*z + 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: -72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-36*z**3 + 12*z)*(2*z**3 + 6*z + 11)
Expanding the part (-36*z**3 + 12*z) using the distributive property, and we got: (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3 + 6*z + 11)
<replace-#Step 1>#Step 2:
Current expression: (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3 + 6*z + 11)</replace>
Simplifying the partial expression: (-36*z**3)*(2*z**3 + 6*z + 11)
Expanding the part (2*z**3 + 6*z + 11) using the distributive property, and we got: 11*(-36*z**3) + (6*z)*(-36*z**3) + (-36*z**3)*(2*z**3)
Replacing (-36*z**3)*(2*z**3 + 6*z + 11) with 11*(-36*z**3) + (6*z)*(-36*z**3) + (-36*z**3)*(2*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 11*(-36)*z**3 + (6*z)*(-36*z**3) + (12*z)*(2*z**3 + 6*z + 11) + (-36*z**3)*(2*z**3)</replace>
Simplifying the partial expression: (12*z)*(2*z**3 + 6*z + 11)
Expanding the part (2*z**3 + 6*z + 11) using the distributive property, and we got: 11*(12*z) + (6*z)*(12*z) + (12*z)*(2*z**3)
Replacing (12*z)*(2*z**3 + 6*z + 11) with 11*(12*z) + (6*z)*(12*z) + (12*z)*(2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 11*(-36)*z**3 + 11*12*z + (6*z)*(12*z) + (6*z)*(-36*z**3) + (12*z)*(2*z**3) + (-36*z**3)*(2*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*z**3)*(-36*z**3) = -72*z**6
  (2*z**3)*(12*z) = 24*z**4
  (6*z)*(-36*z**3) = -216*z**4
  (6*z)*(12*z) = 72*z**2
  11*-36*z**3 = -396*z**3
  11*12*z = 132*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -72*z**6 - 216*z**4 + 24*z**4 - 396*z**3 + 72*z**2 + 132*z</replace>
Combining like terms, got -72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z
<replace-#Step 5>#Step 6:
Current expression: -72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z</replace>
No more calculations needed.
<answer>-72*z**6 - 192*z**4 - 396*z**3 + 72*z**2 + 132*z</answer>


Question:
Calculate the following: (2*z**3 - 6*z)*(14*z**2 - 54*z - 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: 28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*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: (2*z**3 - 6*z)*(14*z**2 - 54*z - 31)
Expanding the part (2*z**3 - 6*z) using the distributive property, and we got: (-6*z)*(14*z**2 - 54*z - 31) + (2*z**3)*(14*z**2 - 54*z - 31)
<replace-#Step 1>#Step 2:
Current expression: (-6*z)*(14*z**2 - 54*z - 31) + (2*z**3)*(14*z**2 - 54*z - 31)</replace>
Simplifying the partial expression: (-6*z)*(14*z**2 - 54*z - 31)
Expanding the part (14*z**2 - 54*z - 31) using the distributive property, and we got: (-54*z)*(-6*z) + (-6*z)*(14*z**2) - (-1)*186*z
Replacing (-6*z)*(14*z**2 - 54*z - 31) with (-54*z)*(-6*z) + (-6*z)*(14*z**2) - (-1)*186*z in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-54*z)*(-6*z) + (-6*z)*(14*z**2) - 31*(-6)*z + (2*z**3)*(14*z**2 - 54*z - 31)</replace>
Simplifying the partial expression: (2*z**3)*(14*z**2 - 54*z - 31)
Expanding the part (14*z**2 - 54*z - 31) using the distributive property, and we got: (-54*z)*(2*z**3) - 62*z**3 + (14*z**2)*(2*z**3)
Replacing (2*z**3)*(14*z**2 - 54*z - 31) with (-54*z)*(2*z**3) - 62*z**3 + (14*z**2)*(2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-54*z)*(-6*z) + (-54*z)*(2*z**3) + (-6*z)*(14*z**2) - 31*2*z**3 - 31*(-6)*z + (14*z**2)*(2*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-54*z)*(-6*z) = 324*z**2
  (-54*z)*(2*z**3) = -108*z**4
  (14*z**2)*(-6*z) = -84*z**3
  (14*z**2)*(2*z**3) = 28*z**5
  -31*-6*z = 186*z
  -31*2*z**3 = -62*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 28*z**5 - 108*z**4 - 84*z**3 - 62*z**3 + 324*z**2 + 186*z</replace>
Combining like terms, got 28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z
<replace-#Step 5>#Step 6:
Current expression: 28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z</replace>
No more calculations needed.
<answer>28*z**5 - 108*z**4 - 146*z**3 + 324*z**2 + 186*z</answer>


Question:
Calculate the following: (-15*y**2 - 29)*(-29*y**3 - 50*y + 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*y**2 - 29)*(-29*y**3 - 50*y + 41)
Expanding the part (-15*y**2 - 29) using the distributive property, and we got: (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*(-29*y**3 - 50*y + 41)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*(-29*y**3 - 50*y + 41)</replace>
Simplifying the partial expression: -29*(-29*y**3 - 50*y + 41)
Expanding the part (-29*y**3 - 50*y + 41) using the distributive property, and we got: -50*y*(-29) - 29*y**3*(-29) + 41*(-29)
Replacing -29*(-29*y**3 - 50*y + 41) with -50*y*(-29) - 29*y**3*(-29) + 41*(-29) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -50*y*(-29) + (-15*y**2)*(-29*y**3 - 50*y + 41) - 29*y**3*(-29) - 1189</replace>
Simplifying the partial expression: (-15*y**2)*(-29*y**3 - 50*y + 41)
Expanding the part (-29*y**3 - 50*y + 41) using the distributive property, and we got: (-50*y)*(-15*y**2) + 41*(-15*y**2) + (-15*y**2)*(-29*y**3)
Replacing (-15*y**2)*(-29*y**3 - 50*y + 41) with (-50*y)*(-15*y**2) + 41*(-15*y**2) + (-15*y**2)*(-29*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*y)*(-15*y**2) - 50*y*(-29) + 41*(-15)*y**2 + (-15*y**2)*(-29*y**3) - 29*y**3*(-29) - 1189</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*y)*-29 = 1450*y
  (-50*y)*(-15*y**2) = 750*y**3
  (-29*y**3)*-29 = 841*y**3
  (-29*y**3)*(-15*y**2) = 435*y**5
  41*-15*y**2 = -615*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 435*y**5 + 750*y**3 + 841*y**3 - 615*y**2 + 1450*y - 1189</replace>
Combining like terms, got 435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189
<replace-#Step 5>#Step 6:
Current expression: 435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189</replace>
No more calculations needed.
<answer>435*y**5 + 1591*y**3 - 615*y**2 + 1450*y - 1189</answer>


Question:
Calculate the following: -51*y**3*(39 - 49*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2499*y**5 - 1989*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -51*y**3*(39 - 49*y**2)
Expanding the part (39 - 49*y**2) using the distributive property, and we got: 39*(-51*y**3) + (-49*y**2)*(-51*y**3)
<replace-#Step 1>#Step 2:
Current expression: 39*(-51*y**3) + (-49*y**2)*(-51*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  39*(-51*y**3) = -1989*y**3
  (-49*y**2)*(-51*y**3) = 2499*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2499*y**5 - 1989*y**3</replace>
No more calculations needed.
<answer>2499*y**5 - 1989*y**3</answer>


Question:
Calculate the following: (42*z - 23)*(14*z**2 + 51)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 588*z**3 - 322*z**2 + 2142*z - 1173

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42*z - 23)*(14*z**2 + 51)
Expanding the part (42*z - 23) using the distributive property, and we got: (42*z)*(14*z**2 + 51) - 23*(14*z**2 + 51)
<replace-#Step 1>#Step 2:
Current expression: (42*z)*(14*z**2 + 51) - 23*(14*z**2 + 51)</replace>
Simplifying the partial expression: -23*(14*z**2 + 51)
Expanding the part (14*z**2 + 51) using the distributive property, and we got: (14*z**2)*(-23) + 51*(-23)
Replacing -23*(14*z**2 + 51) with (14*z**2)*(-23) + 51*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z)*(14*z**2 + 51) + (14*z**2)*(-23) - 1173</replace>
Simplifying the partial expression: (42*z)*(14*z**2 + 51)
Expanding the part (14*z**2 + 51) using the distributive property, and we got: 51*(42*z) + (42*z)*(14*z**2)
Replacing (42*z)*(14*z**2 + 51) with 51*(42*z) + (42*z)*(14*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 51*42*z + (42*z)*(14*z**2) + (14*z**2)*(-23) - 1173</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*z**2)*-23 = -322*z**2
  (14*z**2)*(42*z) = 588*z**3
  51*42*z = 2142*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 588*z**3 - 322*z**2 + 2142*z - 1173</replace>
No more calculations needed.
<answer>588*z**3 - 322*z**2 + 2142*z - 1173</answer>


Question:
Simplify this expression: (15*x**2 - 48)*(-24*x**3 + 21*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: -360*x**5 + 315*x**4 + 1152*x**3 - 1008*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: (15*x**2 - 48)*(-24*x**3 + 21*x**2)
Expanding the part (15*x**2 - 48) using the distributive property, and we got: (15*x**2)*(-24*x**3 + 21*x**2) - 48*(-24*x**3 + 21*x**2)
<replace-#Step 1>#Step 2:
Current expression: (15*x**2)*(-24*x**3 + 21*x**2) - 48*(-24*x**3 + 21*x**2)</replace>
Simplifying the partial expression: -48*(-24*x**3 + 21*x**2)
Expanding the part (-24*x**3 + 21*x**2) using the distributive property, and we got: (21*x**2)*(-48) - 24*x**3*(-48)
Replacing -48*(-24*x**3 + 21*x**2) with (21*x**2)*(-48) - 24*x**3*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (15*x**2)*(-24*x**3 + 21*x**2) + (21*x**2)*(-48) - 24*x**3*(-48)</replace>
Simplifying the partial expression: (15*x**2)*(-24*x**3 + 21*x**2)
Expanding the part (-24*x**3 + 21*x**2) using the distributive property, and we got: (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3)
Replacing (15*x**2)*(-24*x**3 + 21*x**2) with (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (15*x**2)*(21*x**2) + (15*x**2)*(-24*x**3) + (21*x**2)*(-48) - 24*x**3*(-48)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*x**3)*-48 = 1152*x**3
  (-24*x**3)*(15*x**2) = -360*x**5
  (21*x**2)*-48 = -1008*x**2
  (21*x**2)*(15*x**2) = 315*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2</replace>
No more calculations needed.
<answer>-360*x**5 + 315*x**4 + 1152*x**3 - 1008*x**2</answer>


Question:
Calculate the following: (-24*y**2 - 40*y)*(44*y**3 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1056*y**5 - 1760*y**4 + 744*y**2 + 1240*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: (-24*y**2 - 40*y)*(44*y**3 - 31)
Expanding the part (44*y**3 - 31) using the distributive property, and we got: (44*y**3)*(-24*y**2 - 40*y) - 31*(-24*y**2 - 40*y)
<replace-#Step 1>#Step 2:
Current expression: (44*y**3)*(-24*y**2 - 40*y) - 31*(-24*y**2 - 40*y)</replace>
Simplifying the partial expression: -31*(-24*y**2 - 40*y)
Expanding the part (-24*y**2 - 40*y) using the distributive property, and we got: -40*y*(-31) - 24*y**2*(-31)
Replacing -31*(-24*y**2 - 40*y) with -40*y*(-31) - 24*y**2*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -40*y*(-31) - 24*y**2*(-31) + (44*y**3)*(-24*y**2 - 40*y)</replace>
Simplifying the partial expression: (44*y**3)*(-24*y**2 - 40*y)
Expanding the part (-24*y**2 - 40*y) using the distributive property, and we got: (-40*y)*(44*y**3) + (-24*y**2)*(44*y**3)
Replacing (44*y**3)*(-24*y**2 - 40*y) with (-40*y)*(44*y**3) + (-24*y**2)*(44*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*y)*(44*y**3) - 40*y*(-31) + (-24*y**2)*(44*y**3) - 24*y**2*(-31)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y)*-31 = 1240*y
  (-40*y)*(44*y**3) = -1760*y**4
  (-24*y**2)*-31 = 744*y**2
  (-24*y**2)*(44*y**3) = -1056*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y</replace>
No more calculations needed.
<answer>-1056*y**5 - 1760*y**4 + 744*y**2 + 1240*y</answer>


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

Answer: -720*x**6 - 816*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -24*x**3*(30*x**3 + 34*x)
Expanding the part (30*x**3 + 34*x) using the distributive property, and we got: (34*x)*(-24*x**3) + (-24*x**3)*(30*x**3)
<replace-#Step 1>#Step 2:
Current expression: (34*x)*(-24*x**3) + (-24*x**3)*(30*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*x**3)*(-24*x**3) = -720*x**6
  (34*x)*(-24*x**3) = -816*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -720*x**6 - 816*x**4</replace>
No more calculations needed.
<answer>-720*x**6 - 816*x**4</answer>


Question:
Calculate the following: (-z**3 - 19)*(35*z**2 - 24*z + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-z**3 - 19)*(35*z**2 - 24*z + 7)
Expanding the part (-z**3 - 19) using the distributive property, and we got: (-z**3)*(35*z**2 - 24*z + 7) - 19*(35*z**2 - 24*z + 7)
<replace-#Step 1>#Step 2:
Current expression: (-z**3)*(35*z**2 - 24*z + 7) - 19*(35*z**2 - 24*z + 7)</replace>
Simplifying the partial expression: -19*(35*z**2 - 24*z + 7)
Expanding the part (35*z**2 - 24*z + 7) using the distributive property, and we got: -24*z*(-19) + (35*z**2)*(-19) + 7*(-19)
Replacing -19*(35*z**2 - 24*z + 7) with -24*z*(-19) + (35*z**2)*(-19) + 7*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -24*z*(-19) + (35*z**2)*(-19) + (-z**3)*(35*z**2 - 24*z + 7) - 133</replace>
Simplifying the partial expression: (-z**3)*(35*z**2 - 24*z + 7)
Expanding the part (35*z**2 - 24*z + 7) using the distributive property, and we got: (-24*z)*(-z**3) + 7*(-z**3) + (35*z**2)*(-z**3)
Replacing (-z**3)*(35*z**2 - 24*z + 7) with (-24*z)*(-z**3) + 7*(-z**3) + (35*z**2)*(-z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-24*z)*(-z**3) - 24*z*(-19) + 7*(-1)*z**3 + (35*z**2)*(-z**3) + (35*z**2)*(-19) - 133</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-24*z)*-19 = 456*z
  (-24*z)*(-z**3) = 24*z**4
  (35*z**2)*-19 = -665*z**2
  (35*z**2)*(-z**3) = -35*z**5
  7*-1*z**3 = -7*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133</replace>
No more calculations needed.
<answer>-35*z**5 + 24*z**4 - 7*z**3 - 665*z**2 + 456*z - 133</answer>


Question:
Simplify this expression: (3*y**2 - 44)*(70*y**3 - 2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 210*y**5 - 3080*y**3 - 6*y**2 + 88

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**2 - 44)*(70*y**3 - 2)
Expanding the part (3*y**2 - 44) using the distributive property, and we got: (3*y**2)*(70*y**3 - 2) - 44*(70*y**3 - 2)
<replace-#Step 1>#Step 2:
Current expression: (3*y**2)*(70*y**3 - 2) - 44*(70*y**3 - 2)</replace>
Simplifying the partial expression: -44*(70*y**3 - 2)
Expanding the part (70*y**3 - 2) using the distributive property, and we got: (70*y**3)*(-44) - 2*(-44)
Replacing -44*(70*y**3 - 2) with (70*y**3)*(-44) - 2*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*y**2)*(70*y**3 - 2) + (70*y**3)*(-44) + 88</replace>
Simplifying the partial expression: (3*y**2)*(70*y**3 - 2)
Expanding the part (70*y**3 - 2) using the distributive property, and we got: -6*y**2 + (3*y**2)*(70*y**3)
Replacing (3*y**2)*(70*y**3 - 2) with -6*y**2 + (3*y**2)*(70*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -2*3*y**2 + (3*y**2)*(70*y**3) + (70*y**3)*(-44) + 88</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (70*y**3)*-44 = -3080*y**3
  (70*y**3)*(3*y**2) = 210*y**5
  -2*3*y**2 = -6*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 210*y**5 - 3080*y**3 - 6*y**2 + 88</replace>
No more calculations needed.
<answer>210*y**5 - 3080*y**3 - 6*y**2 + 88</answer>


Question:
Calculate the following: (31*z**2 - 10*z)*(-13*z**3 + 5*z**2 + 55*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: -403*z**5 + 285*z**4 + 1655*z**3 - 550*z**2


Question:
Simplify this expression: (62 - 3*x**2)*(20*x**3 - 34*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: -60*x**5 + 102*x**4 + 1240*x**3 - 2108*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: (62 - 3*x**2)*(20*x**3 - 34*x**2)
Expanding the part (62 - 3*x**2) using the distributive property, and we got: (-3*x**2)*(20*x**3 - 34*x**2) + 62*(20*x**3 - 34*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-3*x**2)*(20*x**3 - 34*x**2) + 62*(20*x**3 - 34*x**2)</replace>
Simplifying the partial expression: 62*(20*x**3 - 34*x**2)
Expanding the part (20*x**3 - 34*x**2) using the distributive property, and we got: -34*x**2*62 + (20*x**3)*62
Replacing 62*(20*x**3 - 34*x**2) with -34*x**2*62 + (20*x**3)*62 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -34*x**2*62 + (-3*x**2)*(20*x**3 - 34*x**2) + (20*x**3)*62</replace>
Simplifying the partial expression: (-3*x**2)*(20*x**3 - 34*x**2)
Expanding the part (20*x**3 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(-3*x**2) + (-3*x**2)*(20*x**3)
Replacing (-3*x**2)*(20*x**3 - 34*x**2) with (-34*x**2)*(-3*x**2) + (-3*x**2)*(20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*x**2)*(-3*x**2) - 34*x**2*62 + (-3*x**2)*(20*x**3) + (20*x**3)*62</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**2)*62 = -2108*x**2
  (-34*x**2)*(-3*x**2) = 102*x**4
  (20*x**3)*62 = 1240*x**3
  (20*x**3)*(-3*x**2) = -60*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2</replace>
No more calculations needed.
<answer>-60*x**5 + 102*x**4 + 1240*x**3 - 2108*x**2</answer>


Question:
Simplify this expression: 735*x**2 - 945*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: 735*x**2 - 945*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: 735*x**2 - 945*x
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: 735*x**2 - 945*x</replace>
No more calculations needed.
<answer>735*x**2 - 945*x</answer>


Question:
Simplify this expression: -5*z**3*(19*z**3 - 50*z**2 + 47*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: -95*z**6 + 250*z**5 - 235*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -5*z**3*(19*z**3 - 50*z**2 + 47*z)
Expanding the part (19*z**3 - 50*z**2 + 47*z) using the distributive property, and we got: (47*z)*(-5*z**3) + (-50*z**2)*(-5*z**3) + (-5*z**3)*(19*z**3)
<replace-#Step 1>#Step 2:
Current expression: (47*z)*(-5*z**3) + (-50*z**2)*(-5*z**3) + (-5*z**3)*(19*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*z**2)*(-5*z**3) = 250*z**5
  (19*z**3)*(-5*z**3) = -95*z**6
  (47*z)*(-5*z**3) = -235*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -95*z**6 + 250*z**5 - 235*z**4</replace>
No more calculations needed.
<answer>-95*z**6 + 250*z**5 - 235*z**4</answer>