Question:
Calculate the following: (9*z**3 - 48*z)*(39*z**3 - 52*z**2 - 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 351*z**6 - 468*z**5 - 1872*z**4 + 2442*z**3 + 288*z


Question:
Calculate the following: (37*x**2 + 8*x + 49)*(-82*x**3 + 4*x - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3034*x**5 - 656*x**4 - 3870*x**3 - 893*x**2 - 4*x - 1225


Question:
Calculate the following: (25*y**2 + 11*y)*(15*y**3 - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 375*y**5 + 165*y**4 - 625*y**2 - 275*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (25*y**2 + 11*y)*(15*y**3 - 25)
Expanding the part (15*y**3 - 25) using the distributive property, and we got: (15*y**3)*(25*y**2 + 11*y) - 25*(25*y**2 + 11*y)
<replace-#Step 1>#Step 2:
Current expression: (15*y**3)*(25*y**2 + 11*y) - 25*(25*y**2 + 11*y)</replace>
Simplifying the partial expression: -25*(25*y**2 + 11*y)
Expanding the part (25*y**2 + 11*y) using the distributive property, and we got: (11*y)*(-25) + (25*y**2)*(-25)
Replacing -25*(25*y**2 + 11*y) with (11*y)*(-25) + (25*y**2)*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*y)*(-25) + (25*y**2)*(-25) + (15*y**3)*(25*y**2 + 11*y)</replace>
Simplifying the partial expression: (15*y**3)*(25*y**2 + 11*y)
Expanding the part (25*y**2 + 11*y) using the distributive property, and we got: (11*y)*(15*y**3) + (25*y**2)*(15*y**3)
Replacing (15*y**3)*(25*y**2 + 11*y) with (11*y)*(15*y**3) + (25*y**2)*(15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*y)*(15*y**3) + (11*y)*(-25) + (25*y**2)*(15*y**3) + (25*y**2)*(-25)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*y)*-25 = -275*y
  (11*y)*(15*y**3) = 165*y**4
  (25*y**2)*-25 = -625*y**2
  (25*y**2)*(15*y**3) = 375*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 375*y**5 + 165*y**4 - 625*y**2 - 275*y</replace>
No more calculations needed.
<answer>375*y**5 + 165*y**4 - 625*y**2 - 275*y</answer>


Question:
Calculate the following: (-19*y**3 + 8*y)*(48*y**3 - 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: -912*y**6 + 384*y**4 + 1007*y**3 - 424*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: (-19*y**3 + 8*y)*(48*y**3 - 53)
Expanding the part (48*y**3 - 53) using the distributive property, and we got: (48*y**3)*(-19*y**3 + 8*y) - 53*(-19*y**3 + 8*y)
<replace-#Step 1>#Step 2:
Current expression: (48*y**3)*(-19*y**3 + 8*y) - 53*(-19*y**3 + 8*y)</replace>
Simplifying the partial expression: -53*(-19*y**3 + 8*y)
Expanding the part (-19*y**3 + 8*y) using the distributive property, and we got: (8*y)*(-53) - 19*y**3*(-53)
Replacing -53*(-19*y**3 + 8*y) with (8*y)*(-53) - 19*y**3*(-53) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*y)*(-53) - 19*y**3*(-53) + (48*y**3)*(-19*y**3 + 8*y)</replace>
Simplifying the partial expression: (48*y**3)*(-19*y**3 + 8*y)
Expanding the part (-19*y**3 + 8*y) using the distributive property, and we got: (8*y)*(48*y**3) + (-19*y**3)*(48*y**3)
Replacing (48*y**3)*(-19*y**3 + 8*y) with (8*y)*(48*y**3) + (-19*y**3)*(48*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*y)*(48*y**3) + (8*y)*(-53) + (-19*y**3)*(48*y**3) - 19*y**3*(-53)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**3)*-53 = 1007*y**3
  (-19*y**3)*(48*y**3) = -912*y**6
  (8*y)*-53 = -424*y
  (8*y)*(48*y**3) = 384*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -912*y**6 + 384*y**4 + 1007*y**3 - 424*y</replace>
No more calculations needed.
<answer>-912*y**6 + 384*y**4 + 1007*y**3 - 424*y</answer>


Question:
Calculate the following: (38 - 10*x)*(9*x**2 - 5*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -90*x**3 + 392*x**2 - 190*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: (38 - 10*x)*(9*x**2 - 5*x)
Expanding the part (38 - 10*x) using the distributive property, and we got: (-10*x)*(9*x**2 - 5*x) + 38*(9*x**2 - 5*x)
<replace-#Step 1>#Step 2:
Current expression: (-10*x)*(9*x**2 - 5*x) + 38*(9*x**2 - 5*x)</replace>
Simplifying the partial expression: 38*(9*x**2 - 5*x)
Expanding the part (9*x**2 - 5*x) using the distributive property, and we got: -5*x*38 + (9*x**2)*38
Replacing 38*(9*x**2 - 5*x) with -5*x*38 + (9*x**2)*38 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*x)*(9*x**2 - 5*x) - 5*x*38 + (9*x**2)*38</replace>
Simplifying the partial expression: (-10*x)*(9*x**2 - 5*x)
Expanding the part (9*x**2 - 5*x) using the distributive property, and we got: (-10*x)*(-5*x) + (-10*x)*(9*x**2)
Replacing (-10*x)*(9*x**2 - 5*x) with (-10*x)*(-5*x) + (-10*x)*(9*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*x)*(-5*x) + (-10*x)*(9*x**2) - 5*x*38 + (9*x**2)*38</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-5*x)*38 = -190*x
  (-5*x)*(-10*x) = 50*x**2
  (9*x**2)*38 = 342*x**2
  (9*x**2)*(-10*x) = -90*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -90*x**3 + 50*x**2 + 342*x**2 - 190*x</replace>
Combining like terms, got -90*x**3 + 392*x**2 - 190*x
<replace-#Step 5>#Step 6:
Current expression: -90*x**3 + 392*x**2 - 190*x</replace>
No more calculations needed.
<answer>-90*x**3 + 392*x**2 - 190*x</answer>


Question:
Calculate the following: 22*y**2*(31*y**3 + 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: 682*y**5 + 22*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: 22*y**2*(31*y**3 + y)
Expanding the part (31*y**3 + y) using the distributive property, and we got: y*(22*y**2) + (22*y**2)*(31*y**3)
<replace-#Step 1>#Step 2:
Current expression: y*(22*y**2) + (22*y**2)*(31*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*(22*y**2) = 22*y**3
  (31*y**3)*(22*y**2) = 682*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 682*y**5 + 22*y**3</replace>
No more calculations needed.
<answer>682*y**5 + 22*y**3</answer>


Question:
Simplify this expression: (26 - 43*z**3)*(36*z + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1548*z**4 - 1419*z**3 + 936*z + 858

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 - 43*z**3)*(36*z + 33)
Expanding the part (26 - 43*z**3) using the distributive property, and we got: (-43*z**3)*(36*z + 33) + 26*(36*z + 33)
<replace-#Step 1>#Step 2:
Current expression: (-43*z**3)*(36*z + 33) + 26*(36*z + 33)</replace>
Simplifying the partial expression: 26*(36*z + 33)
Expanding the part (36*z + 33) using the distributive property, and we got: (36*z)*26 + 33*26
Replacing 26*(36*z + 33) with (36*z)*26 + 33*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*z)*26 + (-43*z**3)*(36*z + 33) + 858</replace>
Simplifying the partial expression: (-43*z**3)*(36*z + 33)
Expanding the part (36*z + 33) using the distributive property, and we got: 33*(-43*z**3) + (36*z)*(-43*z**3)
Replacing (-43*z**3)*(36*z + 33) with 33*(-43*z**3) + (36*z)*(-43*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*(-43)*z**3 + (36*z)*(-43*z**3) + (36*z)*26 + 858</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (36*z)*26 = 936*z
  (36*z)*(-43*z**3) = -1548*z**4
  33*-43*z**3 = -1419*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1548*z**4 - 1419*z**3 + 936*z + 858</replace>
No more calculations needed.
<answer>-1548*z**4 - 1419*z**3 + 936*z + 858</answer>


Question:
Calculate the following: (-41*x**2 + 33*x)*(39*x**2 - 35*x + 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1599*x**4 + 2722*x**3 - 1278*x**2 + 99*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: (-41*x**2 + 33*x)*(39*x**2 - 35*x + 3)
Expanding the part (-41*x**2 + 33*x) using the distributive property, and we got: (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2 - 35*x + 3)
<replace-#Step 1>#Step 2:
Current expression: (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2 - 35*x + 3)</replace>
Simplifying the partial expression: (-41*x**2)*(39*x**2 - 35*x + 3)
Expanding the part (39*x**2 - 35*x + 3) using the distributive property, and we got: (-35*x)*(-41*x**2) + 3*(-41*x**2) + (-41*x**2)*(39*x**2)
Replacing (-41*x**2)*(39*x**2 - 35*x + 3) with (-35*x)*(-41*x**2) + 3*(-41*x**2) + (-41*x**2)*(39*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*x)*(-41*x**2) + 3*(-41)*x**2 + (33*x)*(39*x**2 - 35*x + 3) + (-41*x**2)*(39*x**2)</replace>
Simplifying the partial expression: (33*x)*(39*x**2 - 35*x + 3)
Expanding the part (39*x**2 - 35*x + 3) using the distributive property, and we got: (-35*x)*(33*x) + 3*(33*x) + (33*x)*(39*x**2)
Replacing (33*x)*(39*x**2 - 35*x + 3) with (-35*x)*(33*x) + 3*(33*x) + (33*x)*(39*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*x)*(33*x) + (-35*x)*(-41*x**2) + 3*(-41)*x**2 + 3*33*x + (33*x)*(39*x**2) + (-41*x**2)*(39*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x)*(-41*x**2) = 1435*x**3
  (-35*x)*(33*x) = -1155*x**2
  (39*x**2)*(-41*x**2) = -1599*x**4
  (39*x**2)*(33*x) = 1287*x**3
  3*-41*x**2 = -123*x**2
  3*33*x = 99*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1599*x**4 + 1287*x**3 + 1435*x**3 - 1155*x**2 - 123*x**2 + 99*x</replace>
Combining like terms, got -1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x
<replace-#Step 5>#Step 6:
Current expression: -1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x</replace>
No more calculations needed.
<answer>-1599*x**4 + 2722*x**3 - 1278*x**2 + 99*x</answer>


Question:
Simplify this expression: -13*y*(62 - 50*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: 650*y**2 - 806*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: -13*y*(62 - 50*y)
Expanding the part (62 - 50*y) using the distributive property, and we got: (-50*y)*(-13*y) + 62*(-13*y)
<replace-#Step 1>#Step 2:
Current expression: (-50*y)*(-13*y) + 62*(-13*y)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  62*(-13*y) = -806*y
  (-50*y)*(-13*y) = 650*y**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 650*y**2 - 806*y</replace>
No more calculations needed.
<answer>650*y**2 - 806*y</answer>


Question:
Simplify this expression: (26*x**3 + 15*x**2)*(24*x**3 + 32*x**2 + 26*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: 624*x**6 + 1192*x**5 + 1156*x**4 + 390*x**3


Question:
Simplify this expression: (9*y**2 + 36)*(-41*y**3 - 25*y**2 - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180

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**2 + 36)*(-41*y**3 - 25*y**2 - 5)
Expanding the part (9*y**2 + 36) using the distributive property, and we got: (9*y**2)*(-41*y**3 - 25*y**2 - 5) + 36*(-41*y**3 - 25*y**2 - 5)
<replace-#Step 1>#Step 2:
Current expression: (9*y**2)*(-41*y**3 - 25*y**2 - 5) + 36*(-41*y**3 - 25*y**2 - 5)</replace>
Simplifying the partial expression: 36*(-41*y**3 - 25*y**2 - 5)
Expanding the part (-41*y**3 - 25*y**2 - 5) using the distributive property, and we got: -25*y**2*36 - 41*y**3*36 - 5*36
Replacing 36*(-41*y**3 - 25*y**2 - 5) with -25*y**2*36 - 41*y**3*36 - 5*36 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -25*y**2*36 + (9*y**2)*(-41*y**3 - 25*y**2 - 5) - 41*y**3*36 - 180</replace>
Simplifying the partial expression: (9*y**2)*(-41*y**3 - 25*y**2 - 5)
Expanding the part (-41*y**3 - 25*y**2 - 5) using the distributive property, and we got: -45*y**2 + (-25*y**2)*(9*y**2) + (9*y**2)*(-41*y**3)
Replacing (9*y**2)*(-41*y**3 - 25*y**2 - 5) with -45*y**2 + (-25*y**2)*(9*y**2) + (9*y**2)*(-41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -5*9*y**2 + (-25*y**2)*(9*y**2) - 25*y**2*36 + (9*y**2)*(-41*y**3) - 41*y**3*36 - 180</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**3)*36 = -1476*y**3
  (-41*y**3)*(9*y**2) = -369*y**5
  (-25*y**2)*36 = -900*y**2
  (-25*y**2)*(9*y**2) = -225*y**4
  -5*9*y**2 = -45*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -369*y**5 - 225*y**4 - 1476*y**3 - 900*y**2 - 45*y**2 - 180</replace>
Combining like terms, got -369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180
<replace-#Step 5>#Step 6:
Current expression: -369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180</replace>
No more calculations needed.
<answer>-369*y**5 - 225*y**4 - 1476*y**3 - 945*y**2 - 180</answer>


Question:
Calculate the following: (-17*z**3 + 11*z)*(47*z**3 + 33*z**2 + 34*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -799*z**6 - 561*z**5 - 61*z**4 + 363*z**3 + 374*z**2


Question:
Calculate the following: (10*x**3 - 14)*(76*x**2 + 29*x - 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: 760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252

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*x**3 - 14)*(76*x**2 + 29*x - 18)
Expanding the part (10*x**3 - 14) using the distributive property, and we got: (10*x**3)*(76*x**2 + 29*x - 18) - 14*(76*x**2 + 29*x - 18)
<replace-#Step 1>#Step 2:
Current expression: (10*x**3)*(76*x**2 + 29*x - 18) - 14*(76*x**2 + 29*x - 18)</replace>
Simplifying the partial expression: -14*(76*x**2 + 29*x - 18)
Expanding the part (76*x**2 + 29*x - 18) using the distributive property, and we got: (29*x)*(-14) + (76*x**2)*(-14) - 18*(-14)
Replacing -14*(76*x**2 + 29*x - 18) with (29*x)*(-14) + (76*x**2)*(-14) - 18*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*x)*(-14) + (76*x**2)*(-14) + (10*x**3)*(76*x**2 + 29*x - 18) + 252</replace>
Simplifying the partial expression: (10*x**3)*(76*x**2 + 29*x - 18)
Expanding the part (76*x**2 + 29*x - 18) using the distributive property, and we got: -180*x**3 + (29*x)*(10*x**3) + (76*x**2)*(10*x**3)
Replacing (10*x**3)*(76*x**2 + 29*x - 18) with -180*x**3 + (29*x)*(10*x**3) + (76*x**2)*(10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -18*10*x**3 + (29*x)*(10*x**3) + (29*x)*(-14) + (76*x**2)*(10*x**3) + (76*x**2)*(-14) + 252</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*x)*-14 = -406*x
  (29*x)*(10*x**3) = 290*x**4
  (76*x**2)*-14 = -1064*x**2
  (76*x**2)*(10*x**3) = 760*x**5
  -18*10*x**3 = -180*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252</replace>
No more calculations needed.
<answer>760*x**5 + 290*x**4 - 180*x**3 - 1064*x**2 - 406*x + 252</answer>


Question:
Simplify this expression: (48*x**2 - 48)*(22*x**3 + 28*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1056*x**5 + 288*x**3 - 1344*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: (48*x**2 - 48)*(22*x**3 + 28*x)
Expanding the part (48*x**2 - 48) using the distributive property, and we got: (48*x**2)*(22*x**3 + 28*x) - 48*(22*x**3 + 28*x)
<replace-#Step 1>#Step 2:
Current expression: (48*x**2)*(22*x**3 + 28*x) - 48*(22*x**3 + 28*x)</replace>
Simplifying the partial expression: -48*(22*x**3 + 28*x)
Expanding the part (22*x**3 + 28*x) using the distributive property, and we got: (28*x)*(-48) + (22*x**3)*(-48)
Replacing -48*(22*x**3 + 28*x) with (28*x)*(-48) + (22*x**3)*(-48) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*x)*(-48) + (48*x**2)*(22*x**3 + 28*x) + (22*x**3)*(-48)</replace>
Simplifying the partial expression: (48*x**2)*(22*x**3 + 28*x)
Expanding the part (22*x**3 + 28*x) using the distributive property, and we got: (28*x)*(48*x**2) + (48*x**2)*(22*x**3)
Replacing (48*x**2)*(22*x**3 + 28*x) with (28*x)*(48*x**2) + (48*x**2)*(22*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*x)*(48*x**2) + (28*x)*(-48) + (48*x**2)*(22*x**3) + (22*x**3)*(-48)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (22*x**3)*-48 = -1056*x**3
  (22*x**3)*(48*x**2) = 1056*x**5
  (28*x)*-48 = -1344*x
  (28*x)*(48*x**2) = 1344*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1056*x**5 - 1056*x**3 + 1344*x**3 - 1344*x</replace>
Combining like terms, got 1056*x**5 + 288*x**3 - 1344*x
<replace-#Step 5>#Step 6:
Current expression: 1056*x**5 + 288*x**3 - 1344*x</replace>
No more calculations needed.
<answer>1056*x**5 + 288*x**3 - 1344*x</answer>


Question:
Simplify this expression: 4480*z**3 - 4704*z + 3024
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 4480*z**3 - 4704*z + 3024

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: 4480*z**3 - 4704*z + 3024
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: 4480*z**3 - 4704*z + 3024</replace>
No more calculations needed.
<answer>4480*z**3 - 4704*z + 3024</answer>


Question:
Simplify this expression: (42 - 8*x**3)*(-49*x**3 - 39*x + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42 - 8*x**3)*(-49*x**3 - 39*x + 48)
Expanding the part (42 - 8*x**3) using the distributive property, and we got: (-8*x**3)*(-49*x**3 - 39*x + 48) + 42*(-49*x**3 - 39*x + 48)
<replace-#Step 1>#Step 2:
Current expression: (-8*x**3)*(-49*x**3 - 39*x + 48) + 42*(-49*x**3 - 39*x + 48)</replace>
Simplifying the partial expression: 42*(-49*x**3 - 39*x + 48)
Expanding the part (-49*x**3 - 39*x + 48) using the distributive property, and we got: -39*x*42 - 49*x**3*42 + 48*42
Replacing 42*(-49*x**3 - 39*x + 48) with -39*x*42 - 49*x**3*42 + 48*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -39*x*42 - 49*x**3*42 + (-8*x**3)*(-49*x**3 - 39*x + 48) + 2016</replace>
Simplifying the partial expression: (-8*x**3)*(-49*x**3 - 39*x + 48)
Expanding the part (-49*x**3 - 39*x + 48) using the distributive property, and we got: (-39*x)*(-8*x**3) + 48*(-8*x**3) + (-49*x**3)*(-8*x**3)
Replacing (-8*x**3)*(-49*x**3 - 39*x + 48) with (-39*x)*(-8*x**3) + 48*(-8*x**3) + (-49*x**3)*(-8*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-39*x)*(-8*x**3) - 39*x*42 + 48*(-8)*x**3 + (-49*x**3)*(-8*x**3) - 49*x**3*42 + 2016</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**3)*42 = -2058*x**3
  (-49*x**3)*(-8*x**3) = 392*x**6
  (-39*x)*42 = -1638*x
  (-39*x)*(-8*x**3) = 312*x**4
  48*-8*x**3 = -384*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 392*x**6 + 312*x**4 - 2058*x**3 - 384*x**3 - 1638*x + 2016</replace>
Combining like terms, got 392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016
<replace-#Step 5>#Step 6:
Current expression: 392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016</replace>
No more calculations needed.
<answer>392*x**6 + 312*x**4 - 2442*x**3 - 1638*x + 2016</answer>


Question:
Calculate the following: (-29*z**2 - 48)*(-7*z**3 + 17*z**2 + 27*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: 203*z**5 - 493*z**4 - 447*z**3 - 816*z**2 - 1296*z


Question:
Simplify this expression: (38*x**2 + 10*x)*(-x**3 + 35*x**2 - 10*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: -38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (38*x**2 + 10*x)*(-x**3 + 35*x**2 - 10*x)
Expanding the part (38*x**2 + 10*x) using the distributive property, and we got: (10*x)*(-x**3 + 35*x**2 - 10*x) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)
<replace-#Step 1>#Step 2:
Current expression: (10*x)*(-x**3 + 35*x**2 - 10*x) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)</replace>
Simplifying the partial expression: (10*x)*(-x**3 + 35*x**2 - 10*x)
Expanding the part (-x**3 + 35*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3)
Replacing (10*x)*(-x**3 + 35*x**2 - 10*x) with (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*x)*(10*x) + (10*x)*(35*x**2) + (10*x)*(-x**3) + (38*x**2)*(-x**3 + 35*x**2 - 10*x)</replace>
Simplifying the partial expression: (38*x**2)*(-x**3 + 35*x**2 - 10*x)
Expanding the part (-x**3 + 35*x**2 - 10*x) using the distributive property, and we got: (-10*x)*(38*x**2) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3)
Replacing (38*x**2)*(-x**3 + 35*x**2 - 10*x) with (-10*x)*(38*x**2) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*x)*(10*x) + (-10*x)*(38*x**2) + (10*x)*(35*x**2) + (10*x)*(-x**3) + (35*x**2)*(38*x**2) + (38*x**2)*(-x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**3)*(10*x) = -10*x**4
  (-x**3)*(38*x**2) = -38*x**5
  (-10*x)*(10*x) = -100*x**2
  (-10*x)*(38*x**2) = -380*x**3
  (35*x**2)*(10*x) = 350*x**3
  (35*x**2)*(38*x**2) = 1330*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -38*x**5 - 10*x**4 + 1330*x**4 - 380*x**3 + 350*x**3 - 100*x**2</replace>
Combining like terms, got -38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2
<replace-#Step 5>#Step 6:
Current expression: -38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2</replace>
No more calculations needed.
<answer>-38*x**5 + 1320*x**4 - 30*x**3 - 100*x**2</answer>


Question:
Simplify this expression: (-41*y**3 - 47)*(3*y**3 + 31*y**2 - 10*y - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -123*y**6 - 1271*y**5 + 410*y**4 + 351*y**3 - 1457*y**2 + 470*y + 564


Question:
Simplify this expression: 11*y**3*(-68*y**3 - 14*y - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -748*y**6 - 154*y**4 - 242*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: 11*y**3*(-68*y**3 - 14*y - 22)
Expanding the part (-68*y**3 - 14*y - 22) using the distributive property, and we got: (-14*y)*(11*y**3) - 242*y**3 + (-68*y**3)*(11*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-14*y)*(11*y**3) - 242*y**3 + (-68*y**3)*(11*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -22*(11*y**3) = -242*y**3
  (-68*y**3)*(11*y**3) = -748*y**6
  (-14*y)*(11*y**3) = -154*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -748*y**6 - 154*y**4 - 242*y**3</replace>
No more calculations needed.
<answer>-748*y**6 - 154*y**4 - 242*y**3</answer>


Question:
Simplify this expression: (-16*z**2 - 43*z)*(11*z**3 + 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: -176*z**5 - 473*z**4 - 656*z**2 - 1763*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: (-16*z**2 - 43*z)*(11*z**3 + 41)
Expanding the part (11*z**3 + 41) using the distributive property, and we got: (11*z**3)*(-16*z**2 - 43*z) + 41*(-16*z**2 - 43*z)
<replace-#Step 1>#Step 2:
Current expression: (11*z**3)*(-16*z**2 - 43*z) + 41*(-16*z**2 - 43*z)</replace>
Simplifying the partial expression: 41*(-16*z**2 - 43*z)
Expanding the part (-16*z**2 - 43*z) using the distributive property, and we got: -43*z*41 - 16*z**2*41
Replacing 41*(-16*z**2 - 43*z) with -43*z*41 - 16*z**2*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -43*z*41 - 16*z**2*41 + (11*z**3)*(-16*z**2 - 43*z)</replace>
Simplifying the partial expression: (11*z**3)*(-16*z**2 - 43*z)
Expanding the part (-16*z**2 - 43*z) using the distributive property, and we got: (-43*z)*(11*z**3) + (-16*z**2)*(11*z**3)
Replacing (11*z**3)*(-16*z**2 - 43*z) with (-43*z)*(11*z**3) + (-16*z**2)*(11*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*z)*(11*z**3) - 43*z*41 + (-16*z**2)*(11*z**3) - 16*z**2*41</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*z)*41 = -1763*z
  (-43*z)*(11*z**3) = -473*z**4
  (-16*z**2)*41 = -656*z**2
  (-16*z**2)*(11*z**3) = -176*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -176*z**5 - 473*z**4 - 656*z**2 - 1763*z</replace>
No more calculations needed.
<answer>-176*z**5 - 473*z**4 - 656*z**2 - 1763*z</answer>


Question:
Calculate the following: (-25*y**3 + 17*y**2 - 13*y)*(19*y**3 - 9*y - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -475*y**6 + 323*y**5 - 22*y**4 + 822*y**3 - 546*y**2 + 507*y


Question:
Simplify this expression: (-44*y**3 + 40*y**2 - 32)*(-y**3 + 6*y**2 + 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 44*y**6 - 304*y**5 + 240*y**4 - 1244*y**3 + 968*y**2 - 928


Question:
Simplify this expression: 6*y**2*(56*y**2 - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 336*y**4 - 198*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: 6*y**2*(56*y**2 - 33)
Expanding the part (56*y**2 - 33) using the distributive property, and we got: -198*y**2 + (6*y**2)*(56*y**2)
<replace-#Step 1>#Step 2:
Current expression: -198*y**2 + (6*y**2)*(56*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -33*(6*y**2) = -198*y**2
  (56*y**2)*(6*y**2) = 336*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 336*y**4 - 198*y**2</replace>
No more calculations needed.
<answer>336*y**4 - 198*y**2</answer>


Question:
Calculate the following: (46*x - 47)*(-16*x**3 + 36*x - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504

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*x - 47)*(-16*x**3 + 36*x - 32)
Expanding the part (46*x - 47) using the distributive property, and we got: (46*x)*(-16*x**3 + 36*x - 32) - 47*(-16*x**3 + 36*x - 32)
<replace-#Step 1>#Step 2:
Current expression: (46*x)*(-16*x**3 + 36*x - 32) - 47*(-16*x**3 + 36*x - 32)</replace>
Simplifying the partial expression: -47*(-16*x**3 + 36*x - 32)
Expanding the part (-16*x**3 + 36*x - 32) using the distributive property, and we got: (36*x)*(-47) - 16*x**3*(-47) - 32*(-47)
Replacing -47*(-16*x**3 + 36*x - 32) with (36*x)*(-47) - 16*x**3*(-47) - 32*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*x)*(-47) + (46*x)*(-16*x**3 + 36*x - 32) - 16*x**3*(-47) + 1504</replace>
Simplifying the partial expression: (46*x)*(-16*x**3 + 36*x - 32)
Expanding the part (-16*x**3 + 36*x - 32) using the distributive property, and we got: -1472*x + (36*x)*(46*x) + (46*x)*(-16*x**3)
Replacing (46*x)*(-16*x**3 + 36*x - 32) with -1472*x + (36*x)*(46*x) + (46*x)*(-16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -32*46*x + (36*x)*(46*x) + (36*x)*(-47) + (46*x)*(-16*x**3) - 16*x**3*(-47) + 1504</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*x**3)*-47 = 752*x**3
  (-16*x**3)*(46*x) = -736*x**4
  (36*x)*-47 = -1692*x
  (36*x)*(46*x) = 1656*x**2
  -32*46*x = -1472*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -736*x**4 + 752*x**3 + 1656*x**2 - 1692*x - 1472*x + 1504</replace>
Combining like terms, got -736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504
<replace-#Step 5>#Step 6:
Current expression: -736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504</replace>
No more calculations needed.
<answer>-736*x**4 + 752*x**3 + 1656*x**2 - 3164*x + 1504</answer>


Question:
Simplify this expression: (18 - 69*x**3)*(-7*x**3 - 12*x**2 - 26*x - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 483*x**6 + 828*x**5 + 1794*x**4 + 1875*x**3 - 216*x**2 - 468*x - 522


Question:
Simplify this expression: (-72*z**3 - 47*z**2 - 39)*(48*z**3 - 16*z**2 - 83*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: -3456*z**6 - 1104*z**5 + 6728*z**4 + 2029*z**3 + 624*z**2 + 3237*z


Question:
Simplify this expression: (-26*z**3 + 16*z**2)*(11*z**3 - 21*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: -286*z**6 + 722*z**5 - 336*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: (-26*z**3 + 16*z**2)*(11*z**3 - 21*z**2)
Expanding the part (-26*z**3 + 16*z**2) using the distributive property, and we got: (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3 - 21*z**2)
<replace-#Step 1>#Step 2:
Current expression: (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3 - 21*z**2)</replace>
Simplifying the partial expression: (-26*z**3)*(11*z**3 - 21*z**2)
Expanding the part (11*z**3 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(-26*z**3) + (-26*z**3)*(11*z**3)
Replacing (-26*z**3)*(11*z**3 - 21*z**2) with (-21*z**2)*(-26*z**3) + (-26*z**3)*(11*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*z**2)*(-26*z**3) + (16*z**2)*(11*z**3 - 21*z**2) + (-26*z**3)*(11*z**3)</replace>
Simplifying the partial expression: (16*z**2)*(11*z**3 - 21*z**2)
Expanding the part (11*z**3 - 21*z**2) using the distributive property, and we got: (-21*z**2)*(16*z**2) + (16*z**2)*(11*z**3)
Replacing (16*z**2)*(11*z**3 - 21*z**2) with (-21*z**2)*(16*z**2) + (16*z**2)*(11*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*z**2)*(16*z**2) + (-21*z**2)*(-26*z**3) + (16*z**2)*(11*z**3) + (-26*z**3)*(11*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*z**2)*(-26*z**3) = 546*z**5
  (-21*z**2)*(16*z**2) = -336*z**4
  (11*z**3)*(-26*z**3) = -286*z**6
  (11*z**3)*(16*z**2) = 176*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -286*z**6 + 176*z**5 + 546*z**5 - 336*z**4</replace>
Combining like terms, got -286*z**6 + 722*z**5 - 336*z**4
<replace-#Step 5>#Step 6:
Current expression: -286*z**6 + 722*z**5 - 336*z**4</replace>
No more calculations needed.
<answer>-286*z**6 + 722*z**5 - 336*z**4</answer>


Question:
Calculate the following: (51 - 57*x**3)*(25*x**3 + 5*x**2 - 6*x - 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1425*x**6 - 285*x**5 + 342*x**4 + 2358*x**3 + 255*x**2 - 306*x - 969


Question:
Calculate the following: (46*y**3 - 10)*(-39*y**3 + 24*y**2 + 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1794*y**6 + 1104*y**5 + 1080*y**3 - 240*y**2 - 150


Question:
Calculate the following: (46 - 90*x**2)*(15*x**3 + 41*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: -1350*x**5 - 3000*x**3 + 1886*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: (46 - 90*x**2)*(15*x**3 + 41*x)
Expanding the part (46 - 90*x**2) using the distributive property, and we got: (-90*x**2)*(15*x**3 + 41*x) + 46*(15*x**3 + 41*x)
<replace-#Step 1>#Step 2:
Current expression: (-90*x**2)*(15*x**3 + 41*x) + 46*(15*x**3 + 41*x)</replace>
Simplifying the partial expression: 46*(15*x**3 + 41*x)
Expanding the part (15*x**3 + 41*x) using the distributive property, and we got: (41*x)*46 + (15*x**3)*46
Replacing 46*(15*x**3 + 41*x) with (41*x)*46 + (15*x**3)*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (41*x)*46 + (-90*x**2)*(15*x**3 + 41*x) + (15*x**3)*46</replace>
Simplifying the partial expression: (-90*x**2)*(15*x**3 + 41*x)
Expanding the part (15*x**3 + 41*x) using the distributive property, and we got: (41*x)*(-90*x**2) + (-90*x**2)*(15*x**3)
Replacing (-90*x**2)*(15*x**3 + 41*x) with (41*x)*(-90*x**2) + (-90*x**2)*(15*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (41*x)*(-90*x**2) + (41*x)*46 + (-90*x**2)*(15*x**3) + (15*x**3)*46</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*x**3)*46 = 690*x**3
  (15*x**3)*(-90*x**2) = -1350*x**5
  (41*x)*46 = 1886*x
  (41*x)*(-90*x**2) = -3690*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1350*x**5 - 3690*x**3 + 690*x**3 + 1886*x</replace>
Combining like terms, got -1350*x**5 - 3000*x**3 + 1886*x
<replace-#Step 5>#Step 6:
Current expression: -1350*x**5 - 3000*x**3 + 1886*x</replace>
No more calculations needed.
<answer>-1350*x**5 - 3000*x**3 + 1886*x</answer>


Question:
Simplify this expression: (-32*y**2 + 27*y)*(-38*y**3 - 2*y - 65)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*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: (-32*y**2 + 27*y)*(-38*y**3 - 2*y - 65)
Expanding the part (-32*y**2 + 27*y) using the distributive property, and we got: (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3 - 2*y - 65)
<replace-#Step 1>#Step 2:
Current expression: (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3 - 2*y - 65)</replace>
Simplifying the partial expression: (-32*y**2)*(-38*y**3 - 2*y - 65)
Expanding the part (-38*y**3 - 2*y - 65) using the distributive property, and we got: (-2*y)*(-32*y**2) - (-1)*2080*y**2 + (-32*y**2)*(-38*y**3)
Replacing (-32*y**2)*(-38*y**3 - 2*y - 65) with (-2*y)*(-32*y**2) - (-1)*2080*y**2 + (-32*y**2)*(-38*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*y)*(-32*y**2) - 65*(-32)*y**2 + (27*y)*(-38*y**3 - 2*y - 65) + (-32*y**2)*(-38*y**3)</replace>
Simplifying the partial expression: (27*y)*(-38*y**3 - 2*y - 65)
Expanding the part (-38*y**3 - 2*y - 65) using the distributive property, and we got: (-2*y)*(27*y) - 1755*y + (27*y)*(-38*y**3)
Replacing (27*y)*(-38*y**3 - 2*y - 65) with (-2*y)*(27*y) - 1755*y + (27*y)*(-38*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(27*y) + (-2*y)*(-32*y**2) - 65*(-32)*y**2 - 65*27*y + (27*y)*(-38*y**3) + (-32*y**2)*(-38*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*y**3)*(-32*y**2) = 1216*y**5
  (-38*y**3)*(27*y) = -1026*y**4
  (-2*y)*(-32*y**2) = 64*y**3
  (-2*y)*(27*y) = -54*y**2
  -65*-32*y**2 = 2080*y**2
  -65*27*y = -1755*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1216*y**5 - 1026*y**4 + 64*y**3 - 54*y**2 + 2080*y**2 - 1755*y</replace>
Combining like terms, got 1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y
<replace-#Step 5>#Step 6:
Current expression: 1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y</replace>
No more calculations needed.
<answer>1216*y**5 - 1026*y**4 + 64*y**3 + 2026*y**2 - 1755*y</answer>


Question:
Calculate the following: -52*z*(18*z**3 - 15*z**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: -936*z**4 + 780*z**3 - 156*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: -52*z*(18*z**3 - 15*z**2 + 3)
Expanding the part (18*z**3 - 15*z**2 + 3) using the distributive property, and we got: (-52*z)*(-15*z**2) + (-52*z)*(18*z**3) + 3*(-52*z)
<replace-#Step 1>#Step 2:
Current expression: (-52*z)*(-15*z**2) + (-52*z)*(18*z**3) + 3*(-52*z)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  3*(-52*z) = -156*z
  (-15*z**2)*(-52*z) = 780*z**3
  (18*z**3)*(-52*z) = -936*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -936*z**4 + 780*z**3 - 156*z</replace>
No more calculations needed.
<answer>-936*z**4 + 780*z**3 - 156*z</answer>


Question:
Calculate the following: (3*y**2 + y)*(18*y**2 + 11*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: 54*y**4 + 51*y**3 + 11*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (3*y**2 + y)*(18*y**2 + 11*y)
Expanding the part (3*y**2 + y) using the distributive property, and we got: y*(18*y**2 + 11*y) + (3*y**2)*(18*y**2 + 11*y)
<replace-#Step 1>#Step 2:
Current expression: y*(18*y**2 + 11*y) + (3*y**2)*(18*y**2 + 11*y)</replace>
Simplifying the partial expression: y*(18*y**2 + 11*y)
Expanding the part (18*y**2 + 11*y) using the distributive property, and we got: y*(11*y) + y*(18*y**2)
Replacing y*(18*y**2 + 11*y) with y*(11*y) + y*(18*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*(11*y) + y*(18*y**2) + (3*y**2)*(18*y**2 + 11*y)</replace>
Simplifying the partial expression: (3*y**2)*(18*y**2 + 11*y)
Expanding the part (18*y**2 + 11*y) using the distributive property, and we got: (11*y)*(3*y**2) + (3*y**2)*(18*y**2)
Replacing (3*y**2)*(18*y**2 + 11*y) with (11*y)*(3*y**2) + (3*y**2)*(18*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: y*(11*y) + y*(18*y**2) + (11*y)*(3*y**2) + (3*y**2)*(18*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*y)*y = 11*y**2
  (11*y)*(3*y**2) = 33*y**3
  (18*y**2)*y = 18*y**3
  (18*y**2)*(3*y**2) = 54*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 54*y**4 + 18*y**3 + 33*y**3 + 11*y**2</replace>
Combining like terms, got 54*y**4 + 51*y**3 + 11*y**2
<replace-#Step 5>#Step 6:
Current expression: 54*y**4 + 51*y**3 + 11*y**2</replace>
No more calculations needed.
<answer>54*y**4 + 51*y**3 + 11*y**2</answer>


Question:
Calculate the following: (-29*y**2 - 29*y)*(-35*y**3 + 27*y**2 - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1015*y**5 + 232*y**4 - 783*y**3 + 580*y**2 + 580*y


Question:
Calculate the following: (16 - 8*y)*(41*y**3 - 15*y**2 - 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: -328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640

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 - 8*y)*(41*y**3 - 15*y**2 - 40)
Expanding the part (16 - 8*y) using the distributive property, and we got: (-8*y)*(41*y**3 - 15*y**2 - 40) + 16*(41*y**3 - 15*y**2 - 40)
<replace-#Step 1>#Step 2:
Current expression: (-8*y)*(41*y**3 - 15*y**2 - 40) + 16*(41*y**3 - 15*y**2 - 40)</replace>
Simplifying the partial expression: 16*(41*y**3 - 15*y**2 - 40)
Expanding the part (41*y**3 - 15*y**2 - 40) using the distributive property, and we got: -15*y**2*16 + (41*y**3)*16 - 40*16
Replacing 16*(41*y**3 - 15*y**2 - 40) with -15*y**2*16 + (41*y**3)*16 - 40*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-8*y)*(41*y**3 - 15*y**2 - 40) - 15*y**2*16 + (41*y**3)*16 - 640</replace>
Simplifying the partial expression: (-8*y)*(41*y**3 - 15*y**2 - 40)
Expanding the part (41*y**3 - 15*y**2 - 40) using the distributive property, and we got: (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - (-1)*320*y
Replacing (-8*y)*(41*y**3 - 15*y**2 - 40) with (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - (-1)*320*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*y)*(-15*y**2) + (-8*y)*(41*y**3) - 40*(-8)*y - 15*y**2*16 + (41*y**3)*16 - 640</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*y**2)*16 = -240*y**2
  (-15*y**2)*(-8*y) = 120*y**3
  (41*y**3)*16 = 656*y**3
  (41*y**3)*(-8*y) = -328*y**4
  -40*-8*y = 320*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -328*y**4 + 120*y**3 + 656*y**3 - 240*y**2 + 320*y - 640</replace>
Combining like terms, got -328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640
<replace-#Step 5>#Step 6:
Current expression: -328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640</replace>
No more calculations needed.
<answer>-328*y**4 + 776*y**3 - 240*y**2 + 320*y - 640</answer>


Question:
Simplify this expression: (43*x**2 + 29)*(22*x**3 + 25*x - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (43*x**2 + 29)*(22*x**3 + 25*x - 16)
Expanding the part (43*x**2 + 29) using the distributive property, and we got: (43*x**2)*(22*x**3 + 25*x - 16) + 29*(22*x**3 + 25*x - 16)
<replace-#Step 1>#Step 2:
Current expression: (43*x**2)*(22*x**3 + 25*x - 16) + 29*(22*x**3 + 25*x - 16)</replace>
Simplifying the partial expression: 29*(22*x**3 + 25*x - 16)
Expanding the part (22*x**3 + 25*x - 16) using the distributive property, and we got: (25*x)*29 + (22*x**3)*29 - 16*29
Replacing 29*(22*x**3 + 25*x - 16) with (25*x)*29 + (22*x**3)*29 - 16*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (25*x)*29 + (43*x**2)*(22*x**3 + 25*x - 16) + (22*x**3)*29 - 464</replace>
Simplifying the partial expression: (43*x**2)*(22*x**3 + 25*x - 16)
Expanding the part (22*x**3 + 25*x - 16) using the distributive property, and we got: -688*x**2 + (25*x)*(43*x**2) + (43*x**2)*(22*x**3)
Replacing (43*x**2)*(22*x**3 + 25*x - 16) with -688*x**2 + (25*x)*(43*x**2) + (43*x**2)*(22*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -16*43*x**2 + (25*x)*(43*x**2) + (25*x)*29 + (43*x**2)*(22*x**3) + (22*x**3)*29 - 464</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (22*x**3)*29 = 638*x**3
  (22*x**3)*(43*x**2) = 946*x**5
  (25*x)*29 = 725*x
  (25*x)*(43*x**2) = 1075*x**3
  -16*43*x**2 = -688*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 946*x**5 + 638*x**3 + 1075*x**3 - 688*x**2 + 725*x - 464</replace>
Combining like terms, got 946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464
<replace-#Step 5>#Step 6:
Current expression: 946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464</replace>
No more calculations needed.
<answer>946*x**5 + 1713*x**3 - 688*x**2 + 725*x - 464</answer>


Question:
Calculate the following: (-56*x**3 - x**2)*(-47*x**3 - 23*x - 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2632*x**6 + 47*x**5 + 1288*x**4 + 2207*x**3 + 39*x**2


Question:
Simplify this expression: (40 - 34*y**3)*(-40*y**3 - 45*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: 1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*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: (40 - 34*y**3)*(-40*y**3 - 45*y**2)
Expanding the part (40 - 34*y**3) using the distributive property, and we got: (-34*y**3)*(-40*y**3 - 45*y**2) + 40*(-40*y**3 - 45*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-34*y**3)*(-40*y**3 - 45*y**2) + 40*(-40*y**3 - 45*y**2)</replace>
Simplifying the partial expression: 40*(-40*y**3 - 45*y**2)
Expanding the part (-40*y**3 - 45*y**2) using the distributive property, and we got: -45*y**2*40 - 40*y**3*40
Replacing 40*(-40*y**3 - 45*y**2) with -45*y**2*40 - 40*y**3*40 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*y**2*40 - 40*y**3*40 + (-34*y**3)*(-40*y**3 - 45*y**2)</replace>
Simplifying the partial expression: (-34*y**3)*(-40*y**3 - 45*y**2)
Expanding the part (-40*y**3 - 45*y**2) using the distributive property, and we got: (-45*y**2)*(-34*y**3) + (-40*y**3)*(-34*y**3)
Replacing (-34*y**3)*(-40*y**3 - 45*y**2) with (-45*y**2)*(-34*y**3) + (-40*y**3)*(-34*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*y**2)*(-34*y**3) - 45*y**2*40 + (-40*y**3)*(-34*y**3) - 40*y**3*40</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*y**2)*40 = -1800*y**2
  (-45*y**2)*(-34*y**3) = 1530*y**5
  (-40*y**3)*40 = -1600*y**3
  (-40*y**3)*(-34*y**3) = 1360*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2</replace>
No more calculations needed.
<answer>1360*y**6 + 1530*y**5 - 1600*y**3 - 1800*y**2</answer>


Question:
Simplify this expression: (44 - 33*z)*(44*z**3 - 36*z**2 - 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: -1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 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: (44 - 33*z)*(44*z**3 - 36*z**2 - 2)
Expanding the part (44 - 33*z) using the distributive property, and we got: (-33*z)*(44*z**3 - 36*z**2 - 2) + 44*(44*z**3 - 36*z**2 - 2)
<replace-#Step 1>#Step 2:
Current expression: (-33*z)*(44*z**3 - 36*z**2 - 2) + 44*(44*z**3 - 36*z**2 - 2)</replace>
Simplifying the partial expression: 44*(44*z**3 - 36*z**2 - 2)
Expanding the part (44*z**3 - 36*z**2 - 2) using the distributive property, and we got: -36*z**2*44 + (44*z**3)*44 - 2*44
Replacing 44*(44*z**3 - 36*z**2 - 2) with -36*z**2*44 + (44*z**3)*44 - 2*44 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-33*z)*(44*z**3 - 36*z**2 - 2) - 36*z**2*44 + (44*z**3)*44 - 88</replace>
Simplifying the partial expression: (-33*z)*(44*z**3 - 36*z**2 - 2)
Expanding the part (44*z**3 - 36*z**2 - 2) using the distributive property, and we got: (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - (-1)*66*z
Replacing (-33*z)*(44*z**3 - 36*z**2 - 2) with (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - (-1)*66*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*z)*(-36*z**2) + (-33*z)*(44*z**3) - 2*(-33)*z - 36*z**2*44 + (44*z**3)*44 - 88</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*z**2)*44 = -1584*z**2
  (-36*z**2)*(-33*z) = 1188*z**3
  (44*z**3)*44 = 1936*z**3
  (44*z**3)*(-33*z) = -1452*z**4
  -2*-33*z = 66*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1452*z**4 + 1188*z**3 + 1936*z**3 - 1584*z**2 + 66*z - 88</replace>
Combining like terms, got -1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88
<replace-#Step 5>#Step 6:
Current expression: -1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88</replace>
No more calculations needed.
<answer>-1452*z**4 + 3124*z**3 - 1584*z**2 + 66*z - 88</answer>


Question:
Simplify this expression: (-8*x**3 + 21*x**2)*(-3*x**3 - 44*x**2 + 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 24*x**6 + 289*x**5 - 924*x**4 - 96*x**3 + 252*x**2


Question:
Simplify this expression: (-9*y**2 - 42)*(-6*y**3 + 13*y**2 + 23*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: 54*y**5 - 117*y**4 + 45*y**3 - 546*y**2 - 966*y


Question:
Simplify this expression: 93*z*(32*z**3 + 43*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2976*z**4 + 3999*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: 93*z*(32*z**3 + 43*z)
Expanding the part (32*z**3 + 43*z) using the distributive property, and we got: (43*z)*(93*z) + (93*z)*(32*z**3)
<replace-#Step 1>#Step 2:
Current expression: (43*z)*(93*z) + (93*z)*(32*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*z**3)*(93*z) = 2976*z**4
  (43*z)*(93*z) = 3999*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2976*z**4 + 3999*z**2</replace>
No more calculations needed.
<answer>2976*z**4 + 3999*z**2</answer>


Question:
Calculate the following: (54*x**3 + 8*x)*(44*x**3 + 50*x**2 - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*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: (54*x**3 + 8*x)*(44*x**3 + 50*x**2 - 13)
Expanding the part (54*x**3 + 8*x) using the distributive property, and we got: (8*x)*(44*x**3 + 50*x**2 - 13) + (54*x**3)*(44*x**3 + 50*x**2 - 13)
<replace-#Step 1>#Step 2:
Current expression: (8*x)*(44*x**3 + 50*x**2 - 13) + (54*x**3)*(44*x**3 + 50*x**2 - 13)</replace>
Simplifying the partial expression: (8*x)*(44*x**3 + 50*x**2 - 13)
Expanding the part (44*x**3 + 50*x**2 - 13) using the distributive property, and we got: -104*x + (8*x)*(50*x**2) + (8*x)*(44*x**3)
Replacing (8*x)*(44*x**3 + 50*x**2 - 13) with -104*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -13*8*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) + (54*x**3)*(44*x**3 + 50*x**2 - 13)</replace>
Simplifying the partial expression: (54*x**3)*(44*x**3 + 50*x**2 - 13)
Expanding the part (44*x**3 + 50*x**2 - 13) using the distributive property, and we got: -702*x**3 + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3)
Replacing (54*x**3)*(44*x**3 + 50*x**2 - 13) with -702*x**3 + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*54*x**3 - 13*8*x + (8*x)*(50*x**2) + (8*x)*(44*x**3) + (50*x**2)*(54*x**3) + (44*x**3)*(54*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (44*x**3)*(8*x) = 352*x**4
  (44*x**3)*(54*x**3) = 2376*x**6
  (50*x**2)*(8*x) = 400*x**3
  (50*x**2)*(54*x**3) = 2700*x**5
  -13*8*x = -104*x
  -13*54*x**3 = -702*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2376*x**6 + 2700*x**5 + 352*x**4 - 702*x**3 + 400*x**3 - 104*x</replace>
Combining like terms, got 2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x
<replace-#Step 5>#Step 6:
Current expression: 2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x</replace>
No more calculations needed.
<answer>2376*x**6 + 2700*x**5 + 352*x**4 - 302*x**3 - 104*x</answer>


Question:
Simplify this expression: (30*x - 53)*(48*x**2 + 59*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: 1440*x**3 - 774*x**2 - 3127*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: (30*x - 53)*(48*x**2 + 59*x)
Expanding the part (30*x - 53) using the distributive property, and we got: (30*x)*(48*x**2 + 59*x) - 53*(48*x**2 + 59*x)
<replace-#Step 1>#Step 2:
Current expression: (30*x)*(48*x**2 + 59*x) - 53*(48*x**2 + 59*x)</replace>
Simplifying the partial expression: -53*(48*x**2 + 59*x)
Expanding the part (48*x**2 + 59*x) using the distributive property, and we got: (59*x)*(-53) + (48*x**2)*(-53)
Replacing -53*(48*x**2 + 59*x) with (59*x)*(-53) + (48*x**2)*(-53) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (30*x)*(48*x**2 + 59*x) + (59*x)*(-53) + (48*x**2)*(-53)</replace>
Simplifying the partial expression: (30*x)*(48*x**2 + 59*x)
Expanding the part (48*x**2 + 59*x) using the distributive property, and we got: (30*x)*(59*x) + (30*x)*(48*x**2)
Replacing (30*x)*(48*x**2 + 59*x) with (30*x)*(59*x) + (30*x)*(48*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (30*x)*(59*x) + (30*x)*(48*x**2) + (59*x)*(-53) + (48*x**2)*(-53)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*x**2)*-53 = -2544*x**2
  (48*x**2)*(30*x) = 1440*x**3
  (59*x)*-53 = -3127*x
  (59*x)*(30*x) = 1770*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1440*x**3 - 2544*x**2 + 1770*x**2 - 3127*x</replace>
Combining like terms, got 1440*x**3 - 774*x**2 - 3127*x
<replace-#Step 5>#Step 6:
Current expression: 1440*x**3 - 774*x**2 - 3127*x</replace>
No more calculations needed.
<answer>1440*x**3 - 774*x**2 - 3127*x</answer>


Question:
Calculate the following: (-32*x**2 - 5*x)*(41*x**2 + 25*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: -1312*x**4 - 1005*x**3 - 125*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-32*x**2 - 5*x)*(41*x**2 + 25*x)
Expanding the part (-32*x**2 - 5*x) using the distributive property, and we got: (-5*x)*(41*x**2 + 25*x) + (-32*x**2)*(41*x**2 + 25*x)
<replace-#Step 1>#Step 2:
Current expression: (-5*x)*(41*x**2 + 25*x) + (-32*x**2)*(41*x**2 + 25*x)</replace>
Simplifying the partial expression: (-32*x**2)*(41*x**2 + 25*x)
Expanding the part (41*x**2 + 25*x) using the distributive property, and we got: (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)
Replacing (-32*x**2)*(41*x**2 + 25*x) with (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-5*x)*(41*x**2 + 25*x) + (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)</replace>
Simplifying the partial expression: (-5*x)*(41*x**2 + 25*x)
Expanding the part (41*x**2 + 25*x) using the distributive property, and we got: (-5*x)*(25*x) + (-5*x)*(41*x**2)
Replacing (-5*x)*(41*x**2 + 25*x) with (-5*x)*(25*x) + (-5*x)*(41*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*x)*(25*x) + (-5*x)*(41*x**2) + (25*x)*(-32*x**2) + (-32*x**2)*(41*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*x)*(-32*x**2) = -800*x**3
  (25*x)*(-5*x) = -125*x**2
  (41*x**2)*(-32*x**2) = -1312*x**4
  (41*x**2)*(-5*x) = -205*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1312*x**4 - 800*x**3 - 205*x**3 - 125*x**2</replace>
Combining like terms, got -1312*x**4 - 1005*x**3 - 125*x**2
<replace-#Step 5>#Step 6:
Current expression: -1312*x**4 - 1005*x**3 - 125*x**2</replace>
No more calculations needed.
<answer>-1312*x**4 - 1005*x**3 - 125*x**2</answer>


Question:
Calculate the following: (45 - 29*y**2)*(57*y**3 - 44*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: -1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*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: (45 - 29*y**2)*(57*y**3 - 44*y**2)
Expanding the part (45 - 29*y**2) using the distributive property, and we got: (-29*y**2)*(57*y**3 - 44*y**2) + 45*(57*y**3 - 44*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-29*y**2)*(57*y**3 - 44*y**2) + 45*(57*y**3 - 44*y**2)</replace>
Simplifying the partial expression: 45*(57*y**3 - 44*y**2)
Expanding the part (57*y**3 - 44*y**2) using the distributive property, and we got: -44*y**2*45 + (57*y**3)*45
Replacing 45*(57*y**3 - 44*y**2) with -44*y**2*45 + (57*y**3)*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -44*y**2*45 + (-29*y**2)*(57*y**3 - 44*y**2) + (57*y**3)*45</replace>
Simplifying the partial expression: (-29*y**2)*(57*y**3 - 44*y**2)
Expanding the part (57*y**3 - 44*y**2) using the distributive property, and we got: (-44*y**2)*(-29*y**2) + (-29*y**2)*(57*y**3)
Replacing (-29*y**2)*(57*y**3 - 44*y**2) with (-44*y**2)*(-29*y**2) + (-29*y**2)*(57*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-44*y**2)*(-29*y**2) - 44*y**2*45 + (-29*y**2)*(57*y**3) + (57*y**3)*45</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*y**2)*45 = -1980*y**2
  (-44*y**2)*(-29*y**2) = 1276*y**4
  (57*y**3)*45 = 2565*y**3
  (57*y**3)*(-29*y**2) = -1653*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2</replace>
No more calculations needed.
<answer>-1653*y**5 + 1276*y**4 + 2565*y**3 - 1980*y**2</answer>


Question:
Simplify this expression: (27*x**2 - 23*x)*(11*x**3 - 45*x**2 + 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 297*x**5 - 1468*x**4 + 1035*x**3 + 405*x**2 - 345*x


Question:
Simplify this expression: (2 - 44*x**3)*(23*x**3 + 23*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: -1012*x**6 - 1012*x**5 + 46*x**3 + 46*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: (2 - 44*x**3)*(23*x**3 + 23*x**2)
Expanding the part (2 - 44*x**3) using the distributive property, and we got: (-44*x**3)*(23*x**3 + 23*x**2) + 2*(23*x**3 + 23*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-44*x**3)*(23*x**3 + 23*x**2) + 2*(23*x**3 + 23*x**2)</replace>
Simplifying the partial expression: 2*(23*x**3 + 23*x**2)
Expanding the part (23*x**3 + 23*x**2) using the distributive property, and we got: (23*x**2)*2 + (23*x**3)*2
Replacing 2*(23*x**3 + 23*x**2) with (23*x**2)*2 + (23*x**3)*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*x**2)*2 + (-44*x**3)*(23*x**3 + 23*x**2) + (23*x**3)*2</replace>
Simplifying the partial expression: (-44*x**3)*(23*x**3 + 23*x**2)
Expanding the part (23*x**3 + 23*x**2) using the distributive property, and we got: (23*x**2)*(-44*x**3) + (-44*x**3)*(23*x**3)
Replacing (-44*x**3)*(23*x**3 + 23*x**2) with (23*x**2)*(-44*x**3) + (-44*x**3)*(23*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (23*x**2)*(-44*x**3) + (23*x**2)*2 + (-44*x**3)*(23*x**3) + (23*x**3)*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*x**2)*2 = 46*x**2
  (23*x**2)*(-44*x**3) = -1012*x**5
  (23*x**3)*2 = 46*x**3
  (23*x**3)*(-44*x**3) = -1012*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2</replace>
No more calculations needed.
<answer>-1012*x**6 - 1012*x**5 + 46*x**3 + 46*x**2</answer>


Question:
Calculate the following: (-54*x**3 - 61)*(6*x**3 + 25*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: -324*x**6 - 1350*x**4 - 366*x**3 - 1525*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: (-54*x**3 - 61)*(6*x**3 + 25*x)
Expanding the part (-54*x**3 - 61) using the distributive property, and we got: (-54*x**3)*(6*x**3 + 25*x) - 61*(6*x**3 + 25*x)
<replace-#Step 1>#Step 2:
Current expression: (-54*x**3)*(6*x**3 + 25*x) - 61*(6*x**3 + 25*x)</replace>
Simplifying the partial expression: -61*(6*x**3 + 25*x)
Expanding the part (6*x**3 + 25*x) using the distributive property, and we got: (25*x)*(-61) + (6*x**3)*(-61)
Replacing -61*(6*x**3 + 25*x) with (25*x)*(-61) + (6*x**3)*(-61) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (25*x)*(-61) + (-54*x**3)*(6*x**3 + 25*x) + (6*x**3)*(-61)</replace>
Simplifying the partial expression: (-54*x**3)*(6*x**3 + 25*x)
Expanding the part (6*x**3 + 25*x) using the distributive property, and we got: (25*x)*(-54*x**3) + (-54*x**3)*(6*x**3)
Replacing (-54*x**3)*(6*x**3 + 25*x) with (25*x)*(-54*x**3) + (-54*x**3)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*x)*(-54*x**3) + (25*x)*(-61) + (-54*x**3)*(6*x**3) + (6*x**3)*(-61)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**3)*-61 = -366*x**3
  (6*x**3)*(-54*x**3) = -324*x**6
  (25*x)*-61 = -1525*x
  (25*x)*(-54*x**3) = -1350*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -324*x**6 - 1350*x**4 - 366*x**3 - 1525*x</replace>
No more calculations needed.
<answer>-324*x**6 - 1350*x**4 - 366*x**3 - 1525*x</answer>


Question:
Simplify this expression: 3430*y**3 - 350*y + 2310
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3430*y**3 - 350*y + 2310

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: 3430*y**3 - 350*y + 2310
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: 3430*y**3 - 350*y + 2310</replace>
No more calculations needed.
<answer>3430*y**3 - 350*y + 2310</answer>


Question:
Calculate the following: (26*y**3 - 6*y)*(45*y**3 + 24*y**2 + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1170*y**6 + 624*y**5 - 270*y**4 + 948*y**3 - 252*y


Question:
Calculate the following: (-2*z**2 - 18*z)*(-2*z**2 + 56*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: 4*z**4 - 76*z**3 - 1008*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: (-2*z**2 - 18*z)*(-2*z**2 + 56*z)
Expanding the part (-2*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(-2*z**2 + 56*z) + (-2*z**2)*(-2*z**2 + 56*z)
<replace-#Step 1>#Step 2:
Current expression: (-18*z)*(-2*z**2 + 56*z) + (-2*z**2)*(-2*z**2 + 56*z)</replace>
Simplifying the partial expression: (-18*z)*(-2*z**2 + 56*z)
Expanding the part (-2*z**2 + 56*z) using the distributive property, and we got: (-18*z)*(56*z) + (-18*z)*(-2*z**2)
Replacing (-18*z)*(-2*z**2 + 56*z) with (-18*z)*(56*z) + (-18*z)*(-2*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*z)*(56*z) + (-18*z)*(-2*z**2) + (-2*z**2)*(-2*z**2 + 56*z)</replace>
Simplifying the partial expression: (-2*z**2)*(-2*z**2 + 56*z)
Expanding the part (-2*z**2 + 56*z) using the distributive property, and we got: (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2)
Replacing (-2*z**2)*(-2*z**2 + 56*z) with (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*z)*(56*z) + (-18*z)*(-2*z**2) + (56*z)*(-2*z**2) + (-2*z**2)*(-2*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*z**2)*(-18*z) = 36*z**3
  (-2*z**2)*(-2*z**2) = 4*z**4
  (56*z)*(-18*z) = -1008*z**2
  (56*z)*(-2*z**2) = -112*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 4*z**4 - 112*z**3 + 36*z**3 - 1008*z**2</replace>
Combining like terms, got 4*z**4 - 76*z**3 - 1008*z**2
<replace-#Step 5>#Step 6:
Current expression: 4*z**4 - 76*z**3 - 1008*z**2</replace>
No more calculations needed.
<answer>4*z**4 - 76*z**3 - 1008*z**2</answer>


Question:
Simplify this expression: (52*z**3 + 2)*(12*z**2 - 32*z + 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (52*z**3 + 2)*(12*z**2 - 32*z + 39)
Expanding the part (52*z**3 + 2) using the distributive property, and we got: (52*z**3)*(12*z**2 - 32*z + 39) + 2*(12*z**2 - 32*z + 39)
<replace-#Step 1>#Step 2:
Current expression: (52*z**3)*(12*z**2 - 32*z + 39) + 2*(12*z**2 - 32*z + 39)</replace>
Simplifying the partial expression: 2*(12*z**2 - 32*z + 39)
Expanding the part (12*z**2 - 32*z + 39) using the distributive property, and we got: -32*z*2 + (12*z**2)*2 + 39*2
Replacing 2*(12*z**2 - 32*z + 39) with -32*z*2 + (12*z**2)*2 + 39*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -32*z*2 + (12*z**2)*2 + (52*z**3)*(12*z**2 - 32*z + 39) + 78</replace>
Simplifying the partial expression: (52*z**3)*(12*z**2 - 32*z + 39)
Expanding the part (12*z**2 - 32*z + 39) using the distributive property, and we got: (-32*z)*(52*z**3) + 39*(52*z**3) + (12*z**2)*(52*z**3)
Replacing (52*z**3)*(12*z**2 - 32*z + 39) with (-32*z)*(52*z**3) + 39*(52*z**3) + (12*z**2)*(52*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*z)*(52*z**3) - 32*z*2 + 39*52*z**3 + (12*z**2)*(52*z**3) + (12*z**2)*2 + 78</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*z)*2 = -64*z
  (-32*z)*(52*z**3) = -1664*z**4
  (12*z**2)*2 = 24*z**2
  (12*z**2)*(52*z**3) = 624*z**5
  39*52*z**3 = 2028*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78</replace>
No more calculations needed.
<answer>624*z**5 - 1664*z**4 + 2028*z**3 + 24*z**2 - 64*z + 78</answer>


Question:
Calculate the following: (-30*y**2 - 23*y)*(y**3 - 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*y**5 - 23*y**4 + 840*y**2 + 644*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: (-30*y**2 - 23*y)*(y**3 - 28)
Expanding the part (y**3 - 28) using the distributive property, and we got: y**3*(-30*y**2 - 23*y) - 28*(-30*y**2 - 23*y)
<replace-#Step 1>#Step 2:
Current expression: y**3*(-30*y**2 - 23*y) - 28*(-30*y**2 - 23*y)</replace>
Simplifying the partial expression: -28*(-30*y**2 - 23*y)
Expanding the part (-30*y**2 - 23*y) using the distributive property, and we got: -23*y*(-28) - 30*y**2*(-28)
Replacing -28*(-30*y**2 - 23*y) with -23*y*(-28) - 30*y**2*(-28) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*y*(-28) + y**3*(-30*y**2 - 23*y) - 30*y**2*(-28)</replace>
Simplifying the partial expression: y**3*(-30*y**2 - 23*y)
Expanding the part (-30*y**2 - 23*y) using the distributive property, and we got: (-23*y)*y**3 + (-30*y**2)*y**3
Replacing y**3*(-30*y**2 - 23*y) with (-23*y)*y**3 + (-30*y**2)*y**3 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*y)*y**3 - 23*y*(-28) + (-30*y**2)*y**3 - 30*y**2*(-28)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y**2)*-28 = 840*y**2
  (-30*y**2)*y**3 = -30*y**5
  (-23*y)*-28 = 644*y
  (-23*y)*y**3 = -23*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -30*y**5 - 23*y**4 + 840*y**2 + 644*y</replace>
No more calculations needed.
<answer>-30*y**5 - 23*y**4 + 840*y**2 + 644*y</answer>


Question:
Simplify this expression: (-18*x**2 + 7*x)*(29*x**3 + 12*x**2 - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -522*x**5 - 13*x**4 + 84*x**3 + 252*x**2 - 98*x


Question:
Simplify this expression: (46*y**3 - 13*y**2)*(50*y**3 - 42*y**2 - 99*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: 2300*y**6 - 2582*y**5 - 4008*y**4 + 1287*y**3


Question:
Calculate the following: (-9*y**3 - 39)*(34*y**3 + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -306*y**6 - 1398*y**3 - 312

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 - 39)*(34*y**3 + 8)
Expanding the part (-9*y**3 - 39) using the distributive property, and we got: (-9*y**3)*(34*y**3 + 8) - 39*(34*y**3 + 8)
<replace-#Step 1>#Step 2:
Current expression: (-9*y**3)*(34*y**3 + 8) - 39*(34*y**3 + 8)</replace>
Simplifying the partial expression: -39*(34*y**3 + 8)
Expanding the part (34*y**3 + 8) using the distributive property, and we got: (34*y**3)*(-39) + 8*(-39)
Replacing -39*(34*y**3 + 8) with (34*y**3)*(-39) + 8*(-39) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*y**3)*(34*y**3 + 8) + (34*y**3)*(-39) - 312</replace>
Simplifying the partial expression: (-9*y**3)*(34*y**3 + 8)
Expanding the part (34*y**3 + 8) using the distributive property, and we got: 8*(-9*y**3) + (-9*y**3)*(34*y**3)
Replacing (-9*y**3)*(34*y**3 + 8) with 8*(-9*y**3) + (-9*y**3)*(34*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 8*(-9)*y**3 + (-9*y**3)*(34*y**3) + (34*y**3)*(-39) - 312</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*y**3)*-39 = -1326*y**3
  (34*y**3)*(-9*y**3) = -306*y**6
  8*-9*y**3 = -72*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -306*y**6 - 1326*y**3 - 72*y**3 - 312</replace>
Combining like terms, got -306*y**6 - 1398*y**3 - 312
<replace-#Step 5>#Step 6:
Current expression: -306*y**6 - 1398*y**3 - 312</replace>
No more calculations needed.
<answer>-306*y**6 - 1398*y**3 - 312</answer>


Question:
Simplify this expression: (17*x - 22)*(-47*x**2 - 8*x + 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -799*x**3 + 898*x**2 + 1026*x - 1100

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*x - 22)*(-47*x**2 - 8*x + 50)
Expanding the part (17*x - 22) using the distributive property, and we got: (17*x)*(-47*x**2 - 8*x + 50) - 22*(-47*x**2 - 8*x + 50)
<replace-#Step 1>#Step 2:
Current expression: (17*x)*(-47*x**2 - 8*x + 50) - 22*(-47*x**2 - 8*x + 50)</replace>
Simplifying the partial expression: -22*(-47*x**2 - 8*x + 50)
Expanding the part (-47*x**2 - 8*x + 50) using the distributive property, and we got: -8*x*(-22) - 47*x**2*(-22) + 50*(-22)
Replacing -22*(-47*x**2 - 8*x + 50) with -8*x*(-22) - 47*x**2*(-22) + 50*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -8*x*(-22) + (17*x)*(-47*x**2 - 8*x + 50) - 47*x**2*(-22) - 1100</replace>
Simplifying the partial expression: (17*x)*(-47*x**2 - 8*x + 50)
Expanding the part (-47*x**2 - 8*x + 50) using the distributive property, and we got: (-8*x)*(17*x) + 50*(17*x) + (17*x)*(-47*x**2)
Replacing (17*x)*(-47*x**2 - 8*x + 50) with (-8*x)*(17*x) + 50*(17*x) + (17*x)*(-47*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-8*x)*(17*x) - 8*x*(-22) + 50*17*x + (17*x)*(-47*x**2) - 47*x**2*(-22) - 1100</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*x**2)*-22 = 1034*x**2
  (-47*x**2)*(17*x) = -799*x**3
  (-8*x)*-22 = 176*x
  (-8*x)*(17*x) = -136*x**2
  50*17*x = 850*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -799*x**3 - 136*x**2 + 1034*x**2 + 176*x + 850*x - 1100</replace>
Combining like terms, got -799*x**3 + 898*x**2 + 1026*x - 1100
<replace-#Step 5>#Step 6:
Current expression: -799*x**3 + 898*x**2 + 1026*x - 1100</replace>
No more calculations needed.
<answer>-799*x**3 + 898*x**2 + 1026*x - 1100</answer>


Question:
Calculate the following: (-29*z - 17)*(-4*z**2 + 14*z + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 116*z**3 - 338*z**2 - 1195*z - 561

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-29*z - 17)*(-4*z**2 + 14*z + 33)
Expanding the part (-29*z - 17) using the distributive property, and we got: (-29*z)*(-4*z**2 + 14*z + 33) - 17*(-4*z**2 + 14*z + 33)
<replace-#Step 1>#Step 2:
Current expression: (-29*z)*(-4*z**2 + 14*z + 33) - 17*(-4*z**2 + 14*z + 33)</replace>
Simplifying the partial expression: -17*(-4*z**2 + 14*z + 33)
Expanding the part (-4*z**2 + 14*z + 33) using the distributive property, and we got: (14*z)*(-17) - 4*z**2*(-17) + 33*(-17)
Replacing -17*(-4*z**2 + 14*z + 33) with (14*z)*(-17) - 4*z**2*(-17) + 33*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-29*z)*(-4*z**2 + 14*z + 33) + (14*z)*(-17) - 4*z**2*(-17) - 561</replace>
Simplifying the partial expression: (-29*z)*(-4*z**2 + 14*z + 33)
Expanding the part (-4*z**2 + 14*z + 33) using the distributive property, and we got: (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29*z)
Replacing (-29*z)*(-4*z**2 + 14*z + 33) with (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-29*z)*(14*z) + (-29*z)*(-4*z**2) + 33*(-29)*z + (14*z)*(-17) - 4*z**2*(-17) - 561</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*z**2)*-17 = 68*z**2
  (-4*z**2)*(-29*z) = 116*z**3
  (14*z)*-17 = -238*z
  (14*z)*(-29*z) = -406*z**2
  33*-29*z = -957*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 116*z**3 - 406*z**2 + 68*z**2 - 957*z - 238*z - 561</replace>
Combining like terms, got 116*z**3 - 338*z**2 - 1195*z - 561
<replace-#Step 5>#Step 6:
Current expression: 116*z**3 - 338*z**2 - 1195*z - 561</replace>
No more calculations needed.
<answer>116*z**3 - 338*z**2 - 1195*z - 561</answer>