Question:
Simplify this expression: -y*(-19*y**3 + 78*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: 19*y**4 - 78*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: -y*(-19*y**3 + 78*y**2)
Expanding the part (-19*y**3 + 78*y**2) using the distributive property, and we got: (-y)*(78*y**2) + (-y)*(-19*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-y)*(78*y**2) + (-y)*(-19*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**3)*(-y) = 19*y**4
  (78*y**2)*(-y) = -78*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 19*y**4 - 78*y**3</replace>
No more calculations needed.
<answer>19*y**4 - 78*y**3</answer>


Question:
Simplify this expression: -1026*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: -1026*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: -1026*x**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -1026*x**2</replace>
No more calculations needed.
<answer>-1026*x**2</answer>


Question:
Calculate the following: (26 - 87*y**2)*(-32*y**3 - 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: 2784*y**5 - 832*y**3 + 1653*y**2 - 494

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 - 87*y**2)*(-32*y**3 - 19)
Expanding the part (-32*y**3 - 19) using the distributive property, and we got: (-32*y**3)*(26 - 87*y**2) - 19*(26 - 87*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-32*y**3)*(26 - 87*y**2) - 19*(26 - 87*y**2)</replace>
Simplifying the partial expression: -19*(26 - 87*y**2)
Expanding the part (26 - 87*y**2) using the distributive property, and we got: -87*y**2*(-19) + 26*(-19)
Replacing -19*(26 - 87*y**2) with -87*y**2*(-19) + 26*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -87*y**2*(-19) + (-32*y**3)*(26 - 87*y**2) - 494</replace>
Simplifying the partial expression: (-32*y**3)*(26 - 87*y**2)
Expanding the part (26 - 87*y**2) using the distributive property, and we got: 26*(-32*y**3) + (-87*y**2)*(-32*y**3)
Replacing (-32*y**3)*(26 - 87*y**2) with 26*(-32*y**3) + (-87*y**2)*(-32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 26*(-32)*y**3 + (-87*y**2)*(-32*y**3) - 87*y**2*(-19) - 494</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-87*y**2)*-19 = 1653*y**2
  (-87*y**2)*(-32*y**3) = 2784*y**5
  26*-32*y**3 = -832*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2784*y**5 - 832*y**3 + 1653*y**2 - 494</replace>
No more calculations needed.
<answer>2784*y**5 - 832*y**3 + 1653*y**2 - 494</answer>


Question:
Calculate the following: (-29*x**3 - 2*x**2 - 5)*(6*x**3 + 3*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: -174*x**6 - 12*x**5 - 87*x**4 + 515*x**3 + 38*x**2 - 15*x + 95


Question:
Simplify this expression: (6 - 53*x**3)*(-12*x**3 + 16*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: 636*x**6 - 848*x**5 - 72*x**3 + 96*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: (6 - 53*x**3)*(-12*x**3 + 16*x**2)
Expanding the part (6 - 53*x**3) using the distributive property, and we got: (-53*x**3)*(-12*x**3 + 16*x**2) + 6*(-12*x**3 + 16*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-53*x**3)*(-12*x**3 + 16*x**2) + 6*(-12*x**3 + 16*x**2)</replace>
Simplifying the partial expression: 6*(-12*x**3 + 16*x**2)
Expanding the part (-12*x**3 + 16*x**2) using the distributive property, and we got: (16*x**2)*6 - 12*x**3*6
Replacing 6*(-12*x**3 + 16*x**2) with (16*x**2)*6 - 12*x**3*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*x**2)*6 + (-53*x**3)*(-12*x**3 + 16*x**2) - 12*x**3*6</replace>
Simplifying the partial expression: (-53*x**3)*(-12*x**3 + 16*x**2)
Expanding the part (-12*x**3 + 16*x**2) using the distributive property, and we got: (16*x**2)*(-53*x**3) + (-53*x**3)*(-12*x**3)
Replacing (-53*x**3)*(-12*x**3 + 16*x**2) with (16*x**2)*(-53*x**3) + (-53*x**3)*(-12*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (16*x**2)*(-53*x**3) + (16*x**2)*6 + (-53*x**3)*(-12*x**3) - 12*x**3*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**3)*6 = -72*x**3
  (-12*x**3)*(-53*x**3) = 636*x**6
  (16*x**2)*6 = 96*x**2
  (16*x**2)*(-53*x**3) = -848*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 636*x**6 - 848*x**5 - 72*x**3 + 96*x**2</replace>
No more calculations needed.
<answer>636*x**6 - 848*x**5 - 72*x**3 + 96*x**2</answer>


Question:
Calculate the following: (50*z + 11)*(-8*z**3 + 33*z - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (50*z + 11)*(-8*z**3 + 33*z - 36)
Expanding the part (50*z + 11) using the distributive property, and we got: (50*z)*(-8*z**3 + 33*z - 36) + 11*(-8*z**3 + 33*z - 36)
<replace-#Step 1>#Step 2:
Current expression: (50*z)*(-8*z**3 + 33*z - 36) + 11*(-8*z**3 + 33*z - 36)</replace>
Simplifying the partial expression: 11*(-8*z**3 + 33*z - 36)
Expanding the part (-8*z**3 + 33*z - 36) using the distributive property, and we got: (33*z)*11 - 8*z**3*11 - 36*11
Replacing 11*(-8*z**3 + 33*z - 36) with (33*z)*11 - 8*z**3*11 - 36*11 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*z)*11 + (50*z)*(-8*z**3 + 33*z - 36) - 8*z**3*11 - 396</replace>
Simplifying the partial expression: (50*z)*(-8*z**3 + 33*z - 36)
Expanding the part (-8*z**3 + 33*z - 36) using the distributive property, and we got: -1800*z + (33*z)*(50*z) + (50*z)*(-8*z**3)
Replacing (50*z)*(-8*z**3 + 33*z - 36) with -1800*z + (33*z)*(50*z) + (50*z)*(-8*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -36*50*z + (33*z)*(50*z) + (33*z)*11 + (50*z)*(-8*z**3) - 8*z**3*11 - 396</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*z**3)*11 = -88*z**3
  (-8*z**3)*(50*z) = -400*z**4
  (33*z)*11 = 363*z
  (33*z)*(50*z) = 1650*z**2
  -36*50*z = -1800*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -400*z**4 - 88*z**3 + 1650*z**2 - 1800*z + 363*z - 396</replace>
Combining like terms, got -400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396
<replace-#Step 5>#Step 6:
Current expression: -400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396</replace>
No more calculations needed.
<answer>-400*z**4 - 88*z**3 + 1650*z**2 - 1437*z - 396</answer>


Question:
Simplify this expression: (22*z**2 + 39)*(-38*z**3 + 41*z**2 + 30*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: -836*z**5 + 902*z**4 - 822*z**3 + 1599*z**2 + 1170*z


Question:
Simplify this expression: (43*z**3 + 14)*(-50*z**3 + 10*z**2 + 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518

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*z**3 + 14)*(-50*z**3 + 10*z**2 + 37)
Expanding the part (43*z**3 + 14) using the distributive property, and we got: (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 14*(-50*z**3 + 10*z**2 + 37)
<replace-#Step 1>#Step 2:
Current expression: (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 14*(-50*z**3 + 10*z**2 + 37)</replace>
Simplifying the partial expression: 14*(-50*z**3 + 10*z**2 + 37)
Expanding the part (-50*z**3 + 10*z**2 + 37) using the distributive property, and we got: (10*z**2)*14 - 50*z**3*14 + 37*14
Replacing 14*(-50*z**3 + 10*z**2 + 37) with (10*z**2)*14 - 50*z**3*14 + 37*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*z**2)*14 - 50*z**3*14 + (43*z**3)*(-50*z**3 + 10*z**2 + 37) + 518</replace>
Simplifying the partial expression: (43*z**3)*(-50*z**3 + 10*z**2 + 37)
Expanding the part (-50*z**3 + 10*z**2 + 37) using the distributive property, and we got: 37*(43*z**3) + (10*z**2)*(43*z**3) + (-50*z**3)*(43*z**3)
Replacing (43*z**3)*(-50*z**3 + 10*z**2 + 37) with 37*(43*z**3) + (10*z**2)*(43*z**3) + (-50*z**3)*(43*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 37*43*z**3 + (10*z**2)*(43*z**3) + (10*z**2)*14 + (-50*z**3)*(43*z**3) - 50*z**3*14 + 518</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*z**3)*14 = -700*z**3
  (-50*z**3)*(43*z**3) = -2150*z**6
  (10*z**2)*14 = 140*z**2
  (10*z**2)*(43*z**3) = 430*z**5
  37*43*z**3 = 1591*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2150*z**6 + 430*z**5 - 700*z**3 + 1591*z**3 + 140*z**2 + 518</replace>
Combining like terms, got -2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518
<replace-#Step 5>#Step 6:
Current expression: -2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518</replace>
No more calculations needed.
<answer>-2150*z**6 + 430*z**5 + 891*z**3 + 140*z**2 + 518</answer>


Question:
Calculate the following: (-z - 40)*(-15*z**2 - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 15*z**3 + 600*z**2 + 16*z + 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: (-z - 40)*(-15*z**2 - 16)
Expanding the part (-z - 40) using the distributive property, and we got: (-z)*(-15*z**2 - 16) - 40*(-15*z**2 - 16)
<replace-#Step 1>#Step 2:
Current expression: (-z)*(-15*z**2 - 16) - 40*(-15*z**2 - 16)</replace>
Simplifying the partial expression: -40*(-15*z**2 - 16)
Expanding the part (-15*z**2 - 16) using the distributive property, and we got: -15*z**2*(-40) - 16*(-40)
Replacing -40*(-15*z**2 - 16) with -15*z**2*(-40) - 16*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-z)*(-15*z**2 - 16) - 15*z**2*(-40) + 640</replace>
Simplifying the partial expression: (-z)*(-15*z**2 - 16)
Expanding the part (-15*z**2 - 16) using the distributive property, and we got: (-z)*(-15*z**2) - (-1)*16*z
Replacing (-z)*(-15*z**2 - 16) with (-z)*(-15*z**2) - (-1)*16*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-z)*(-15*z**2) - 16*(-1)*z - 15*z**2*(-40) + 640</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*z**2)*-40 = 600*z**2
  (-15*z**2)*(-z) = 15*z**3
  -16*-1*z = 16*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 15*z**3 + 600*z**2 + 16*z + 640</replace>
No more calculations needed.
<answer>15*z**3 + 600*z**2 + 16*z + 640</answer>


Question:
Calculate the following: (-7*y**3 - 29*y)*(-9*y**3 - 21*y**2 - 34*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: 63*y**6 + 147*y**5 + 499*y**4 + 609*y**3 + 986*y**2


Question:
Simplify this expression: (41 - 31*x)*(-30*x**3 + 47*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: 930*x**4 - 2687*x**3 + 1927*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (41 - 31*x)*(-30*x**3 + 47*x**2)
Expanding the part (41 - 31*x) using the distributive property, and we got: (-31*x)*(-30*x**3 + 47*x**2) + 41*(-30*x**3 + 47*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-31*x)*(-30*x**3 + 47*x**2) + 41*(-30*x**3 + 47*x**2)</replace>
Simplifying the partial expression: 41*(-30*x**3 + 47*x**2)
Expanding the part (-30*x**3 + 47*x**2) using the distributive property, and we got: (47*x**2)*41 - 30*x**3*41
Replacing 41*(-30*x**3 + 47*x**2) with (47*x**2)*41 - 30*x**3*41 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-31*x)*(-30*x**3 + 47*x**2) + (47*x**2)*41 - 30*x**3*41</replace>
Simplifying the partial expression: (-31*x)*(-30*x**3 + 47*x**2)
Expanding the part (-30*x**3 + 47*x**2) using the distributive property, and we got: (-31*x)*(47*x**2) + (-31*x)*(-30*x**3)
Replacing (-31*x)*(-30*x**3 + 47*x**2) with (-31*x)*(47*x**2) + (-31*x)*(-30*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-31*x)*(47*x**2) + (-31*x)*(-30*x**3) + (47*x**2)*41 - 30*x**3*41</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*x**3)*41 = -1230*x**3
  (-30*x**3)*(-31*x) = 930*x**4
  (47*x**2)*41 = 1927*x**2
  (47*x**2)*(-31*x) = -1457*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 930*x**4 - 1457*x**3 - 1230*x**3 + 1927*x**2</replace>
Combining like terms, got 930*x**4 - 2687*x**3 + 1927*x**2
<replace-#Step 5>#Step 6:
Current expression: 930*x**4 - 2687*x**3 + 1927*x**2</replace>
No more calculations needed.
<answer>930*x**4 - 2687*x**3 + 1927*x**2</answer>


Question:
Calculate the following: (-13*y**3 + 38*y**2 - 49*y)*(3*y**3 - 21*y - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -39*y**6 + 114*y**5 + 126*y**4 - 733*y**3 + 839*y**2 + 245*y


Question:
Calculate the following: (-35*z**3 - 50*z)*(-45*z**3 + 25*z**2 + 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1575*z**6 - 875*z**5 + 2250*z**4 - 2475*z**3 - 1750*z


Question:
Calculate the following: -32*z*(-27*z**3 + 44*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: 864*z**4 - 1408*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -32*z*(-27*z**3 + 44*z**2)
Expanding the part (-27*z**3 + 44*z**2) using the distributive property, and we got: (-32*z)*(44*z**2) + (-32*z)*(-27*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-32*z)*(44*z**2) + (-32*z)*(-27*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*z**3)*(-32*z) = 864*z**4
  (44*z**2)*(-32*z) = -1408*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 864*z**4 - 1408*z**3</replace>
No more calculations needed.
<answer>864*z**4 - 1408*z**3</answer>


Question:
Calculate the following: (56*z**3 - 2)*(19*z**3 - 2*z - 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: 1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100

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: (56*z**3 - 2)*(19*z**3 - 2*z - 50)
Expanding the part (56*z**3 - 2) using the distributive property, and we got: (56*z**3)*(19*z**3 - 2*z - 50) - 2*(19*z**3 - 2*z - 50)
<replace-#Step 1>#Step 2:
Current expression: (56*z**3)*(19*z**3 - 2*z - 50) - 2*(19*z**3 - 2*z - 50)</replace>
Simplifying the partial expression: -2*(19*z**3 - 2*z - 50)
Expanding the part (19*z**3 - 2*z - 50) using the distributive property, and we got: -2*z*(-2) + (19*z**3)*(-2) - 50*(-2)
Replacing -2*(19*z**3 - 2*z - 50) with -2*z*(-2) + (19*z**3)*(-2) - 50*(-2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2*z*(-2) + (19*z**3)*(-2) + (56*z**3)*(19*z**3 - 2*z - 50) + 100</replace>
Simplifying the partial expression: (56*z**3)*(19*z**3 - 2*z - 50)
Expanding the part (19*z**3 - 2*z - 50) using the distributive property, and we got: (-2*z)*(56*z**3) - 2800*z**3 + (19*z**3)*(56*z**3)
Replacing (56*z**3)*(19*z**3 - 2*z - 50) with (-2*z)*(56*z**3) - 2800*z**3 + (19*z**3)*(56*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(56*z**3) - 2*z*(-2) - 50*56*z**3 + (19*z**3)*(56*z**3) + (19*z**3)*(-2) + 100</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-2*z)*-2 = 4*z
  (-2*z)*(56*z**3) = -112*z**4
  (19*z**3)*-2 = -38*z**3
  (19*z**3)*(56*z**3) = 1064*z**6
  -50*56*z**3 = -2800*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1064*z**6 - 112*z**4 - 2800*z**3 - 38*z**3 + 4*z + 100</replace>
Combining like terms, got 1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100
<replace-#Step 5>#Step 6:
Current expression: 1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100</replace>
No more calculations needed.
<answer>1064*z**6 - 112*z**4 - 2838*z**3 + 4*z + 100</answer>


Question:
Calculate the following: -47*z**3*(25*z**3 + 52*z + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1175*z**6 - 2444*z**4 - 2209*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -47*z**3*(25*z**3 + 52*z + 47)
Expanding the part (25*z**3 + 52*z + 47) using the distributive property, and we got: 47*(-47*z**3) + (52*z)*(-47*z**3) + (-47*z**3)*(25*z**3)
<replace-#Step 1>#Step 2:
Current expression: 47*(-47*z**3) + (52*z)*(-47*z**3) + (-47*z**3)*(25*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  47*(-47*z**3) = -2209*z**3
  (25*z**3)*(-47*z**3) = -1175*z**6
  (52*z)*(-47*z**3) = -2444*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1175*z**6 - 2444*z**4 - 2209*z**3</replace>
No more calculations needed.
<answer>-1175*z**6 - 2444*z**4 - 2209*z**3</answer>


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

Answer: 522*z**5 + 630*z**4 - 1015*z**3 - 1225*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: (-29*z**2 - 35*z)*(-18*z**3 + 35*z)
Expanding the part (-29*z**2 - 35*z) using the distributive property, and we got: (-35*z)*(-18*z**3 + 35*z) + (-29*z**2)*(-18*z**3 + 35*z)
<replace-#Step 1>#Step 2:
Current expression: (-35*z)*(-18*z**3 + 35*z) + (-29*z**2)*(-18*z**3 + 35*z)</replace>
Simplifying the partial expression: (-35*z)*(-18*z**3 + 35*z)
Expanding the part (-18*z**3 + 35*z) using the distributive property, and we got: (-35*z)*(35*z) + (-35*z)*(-18*z**3)
Replacing (-35*z)*(-18*z**3 + 35*z) with (-35*z)*(35*z) + (-35*z)*(-18*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-35*z)*(35*z) + (-35*z)*(-18*z**3) + (-29*z**2)*(-18*z**3 + 35*z)</replace>
Simplifying the partial expression: (-29*z**2)*(-18*z**3 + 35*z)
Expanding the part (-18*z**3 + 35*z) using the distributive property, and we got: (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3)
Replacing (-29*z**2)*(-18*z**3 + 35*z) with (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*z)*(35*z) + (-35*z)*(-18*z**3) + (35*z)*(-29*z**2) + (-29*z**2)*(-18*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*z**3)*(-35*z) = 630*z**4
  (-18*z**3)*(-29*z**2) = 522*z**5
  (35*z)*(-35*z) = -1225*z**2
  (35*z)*(-29*z**2) = -1015*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2</replace>
No more calculations needed.
<answer>522*z**5 + 630*z**4 - 1015*z**3 - 1225*z**2</answer>


Question:
Calculate the following: (-5*y**3 - 2*y)*(65*y**3 + 34*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: -325*y**6 - 300*y**4 - 68*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-5*y**3 - 2*y)*(65*y**3 + 34*y)
Expanding the part (-5*y**3 - 2*y) using the distributive property, and we got: (-2*y)*(65*y**3 + 34*y) + (-5*y**3)*(65*y**3 + 34*y)
<replace-#Step 1>#Step 2:
Current expression: (-2*y)*(65*y**3 + 34*y) + (-5*y**3)*(65*y**3 + 34*y)</replace>
Simplifying the partial expression: (-5*y**3)*(65*y**3 + 34*y)
Expanding the part (65*y**3 + 34*y) using the distributive property, and we got: (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)
Replacing (-5*y**3)*(65*y**3 + 34*y) with (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*y)*(65*y**3 + 34*y) + (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)</replace>
Simplifying the partial expression: (-2*y)*(65*y**3 + 34*y)
Expanding the part (65*y**3 + 34*y) using the distributive property, and we got: (-2*y)*(34*y) + (-2*y)*(65*y**3)
Replacing (-2*y)*(65*y**3 + 34*y) with (-2*y)*(34*y) + (-2*y)*(65*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*y)*(34*y) + (-2*y)*(65*y**3) + (34*y)*(-5*y**3) + (-5*y**3)*(65*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*y)*(-5*y**3) = -170*y**4
  (34*y)*(-2*y) = -68*y**2
  (65*y**3)*(-5*y**3) = -325*y**6
  (65*y**3)*(-2*y) = -130*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -325*y**6 - 170*y**4 - 130*y**4 - 68*y**2</replace>
Combining like terms, got -325*y**6 - 300*y**4 - 68*y**2
<replace-#Step 5>#Step 6:
Current expression: -325*y**6 - 300*y**4 - 68*y**2</replace>
No more calculations needed.
<answer>-325*y**6 - 300*y**4 - 68*y**2</answer>


Question:
Simplify this expression: (31 - 7*z**3)*(-13*z**3 - 11*z**2 + 18)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (31 - 7*z**3)*(-13*z**3 - 11*z**2 + 18)
Expanding the part (31 - 7*z**3) using the distributive property, and we got: (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 31*(-13*z**3 - 11*z**2 + 18)
<replace-#Step 1>#Step 2:
Current expression: (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 31*(-13*z**3 - 11*z**2 + 18)</replace>
Simplifying the partial expression: 31*(-13*z**3 - 11*z**2 + 18)
Expanding the part (-13*z**3 - 11*z**2 + 18) using the distributive property, and we got: -11*z**2*31 - 13*z**3*31 + 18*31
Replacing 31*(-13*z**3 - 11*z**2 + 18) with -11*z**2*31 - 13*z**3*31 + 18*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*z**2*31 - 13*z**3*31 + (-7*z**3)*(-13*z**3 - 11*z**2 + 18) + 558</replace>
Simplifying the partial expression: (-7*z**3)*(-13*z**3 - 11*z**2 + 18)
Expanding the part (-13*z**3 - 11*z**2 + 18) using the distributive property, and we got: 18*(-7*z**3) + (-11*z**2)*(-7*z**3) + (-13*z**3)*(-7*z**3)
Replacing (-7*z**3)*(-13*z**3 - 11*z**2 + 18) with 18*(-7*z**3) + (-11*z**2)*(-7*z**3) + (-13*z**3)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 18*(-7)*z**3 + (-11*z**2)*(-7*z**3) - 11*z**2*31 + (-13*z**3)*(-7*z**3) - 13*z**3*31 + 558</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z**3)*31 = -403*z**3
  (-13*z**3)*(-7*z**3) = 91*z**6
  (-11*z**2)*31 = -341*z**2
  (-11*z**2)*(-7*z**3) = 77*z**5
  18*-7*z**3 = -126*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 91*z**6 + 77*z**5 - 403*z**3 - 126*z**3 - 341*z**2 + 558</replace>
Combining like terms, got 91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558
<replace-#Step 5>#Step 6:
Current expression: 91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558</replace>
No more calculations needed.
<answer>91*z**6 + 77*z**5 - 529*z**3 - 341*z**2 + 558</answer>


Question:
Simplify this expression: 3*x**3*(24*x**3 - 29*x - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 72*x**6 - 87*x**4 - 48*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 3*x**3*(24*x**3 - 29*x - 16)
Expanding the part (24*x**3 - 29*x - 16) using the distributive property, and we got: (-29*x)*(3*x**3) - 48*x**3 + (3*x**3)*(24*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-29*x)*(3*x**3) - 48*x**3 + (3*x**3)*(24*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(3*x**3) = -48*x**3
  (-29*x)*(3*x**3) = -87*x**4
  (24*x**3)*(3*x**3) = 72*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 72*x**6 - 87*x**4 - 48*x**3</replace>
No more calculations needed.
<answer>72*x**6 - 87*x**4 - 48*x**3</answer>


Question:
Calculate the following: (43*y**3 + 4*y)*(2*y**3 + 31*y**2 + 13*y + 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 86*y**6 + 1333*y**5 + 567*y**4 + 1242*y**3 + 52*y**2 + 104*y


Question:
Simplify this expression: (-3*y**3 - 30*y**2 + 4*y)*(25*y**3 + 8*y - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -75*y**6 - 750*y**5 + 76*y**4 - 129*y**3 + 1142*y**2 - 148*y


Question:
Simplify this expression: (-33*z**3 - 6*z)*(-44*z**3 - 32*z**2 - 43*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1452*z**6 + 1056*z**5 + 1683*z**4 + 192*z**3 + 258*z**2


Question:
Simplify this expression: 3200*y - 4560
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3200*y - 4560

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: 3200*y - 4560
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: 3200*y - 4560</replace>
No more calculations needed.
<answer>3200*y - 4560</answer>


Question:
Calculate the following: (45*y + 45)*(-7*y**3 - 36*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: -315*y**4 - 1935*y**3 - 2115*y**2 - 495*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: (45*y + 45)*(-7*y**3 - 36*y**2 - 11*y)
Expanding the part (45*y + 45) using the distributive property, and we got: (45*y)*(-7*y**3 - 36*y**2 - 11*y) + 45*(-7*y**3 - 36*y**2 - 11*y)
<replace-#Step 1>#Step 2:
Current expression: (45*y)*(-7*y**3 - 36*y**2 - 11*y) + 45*(-7*y**3 - 36*y**2 - 11*y)</replace>
Simplifying the partial expression: 45*(-7*y**3 - 36*y**2 - 11*y)
Expanding the part (-7*y**3 - 36*y**2 - 11*y) using the distributive property, and we got: -11*y*45 - 36*y**2*45 - 7*y**3*45
Replacing 45*(-7*y**3 - 36*y**2 - 11*y) with -11*y*45 - 36*y**2*45 - 7*y**3*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*y*45 + (45*y)*(-7*y**3 - 36*y**2 - 11*y) - 36*y**2*45 - 7*y**3*45</replace>
Simplifying the partial expression: (45*y)*(-7*y**3 - 36*y**2 - 11*y)
Expanding the part (-7*y**3 - 36*y**2 - 11*y) using the distributive property, and we got: (-11*y)*(45*y) + (45*y)*(-36*y**2) + (45*y)*(-7*y**3)
Replacing (45*y)*(-7*y**3 - 36*y**2 - 11*y) with (-11*y)*(45*y) + (45*y)*(-36*y**2) + (45*y)*(-7*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*y)*(45*y) - 11*y*45 + (45*y)*(-36*y**2) + (45*y)*(-7*y**3) - 36*y**2*45 - 7*y**3*45</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*y**2)*45 = -1620*y**2
  (-36*y**2)*(45*y) = -1620*y**3
  (-11*y)*45 = -495*y
  (-11*y)*(45*y) = -495*y**2
  (-7*y**3)*45 = -315*y**3
  (-7*y**3)*(45*y) = -315*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -315*y**4 - 1620*y**3 - 315*y**3 - 1620*y**2 - 495*y**2 - 495*y</replace>
Combining like terms, got -315*y**4 - 1935*y**3 - 2115*y**2 - 495*y
<replace-#Step 5>#Step 6:
Current expression: -315*y**4 - 1935*y**3 - 2115*y**2 - 495*y</replace>
No more calculations needed.
<answer>-315*y**4 - 1935*y**3 - 2115*y**2 - 495*y</answer>


Question:
Simplify this expression: (-20*y**2 + 85*y)*(16*y**3 + 14*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -320*y**5 + 1360*y**4 - 280*y**3 + 1190*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: (-20*y**2 + 85*y)*(16*y**3 + 14*y)
Expanding the part (-20*y**2 + 85*y) using the distributive property, and we got: (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3 + 14*y)
<replace-#Step 1>#Step 2:
Current expression: (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3 + 14*y)</replace>
Simplifying the partial expression: (-20*y**2)*(16*y**3 + 14*y)
Expanding the part (16*y**3 + 14*y) using the distributive property, and we got: (14*y)*(-20*y**2) + (-20*y**2)*(16*y**3)
Replacing (-20*y**2)*(16*y**3 + 14*y) with (14*y)*(-20*y**2) + (-20*y**2)*(16*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*y)*(-20*y**2) + (85*y)*(16*y**3 + 14*y) + (-20*y**2)*(16*y**3)</replace>
Simplifying the partial expression: (85*y)*(16*y**3 + 14*y)
Expanding the part (16*y**3 + 14*y) using the distributive property, and we got: (14*y)*(85*y) + (85*y)*(16*y**3)
Replacing (85*y)*(16*y**3 + 14*y) with (14*y)*(85*y) + (85*y)*(16*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*y)*(85*y) + (14*y)*(-20*y**2) + (85*y)*(16*y**3) + (-20*y**2)*(16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*y)*(-20*y**2) = -280*y**3
  (14*y)*(85*y) = 1190*y**2
  (16*y**3)*(-20*y**2) = -320*y**5
  (16*y**3)*(85*y) = 1360*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2</replace>
No more calculations needed.
<answer>-320*y**5 + 1360*y**4 - 280*y**3 + 1190*y**2</answer>


Question:
Calculate the following: (13*x**3 + 7*x)*(43*x**3 + 17*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 559*x**6 + 221*x**5 + 301*x**4 + 119*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (13*x**3 + 7*x)*(43*x**3 + 17*x**2)
Expanding the part (13*x**3 + 7*x) using the distributive property, and we got: (7*x)*(43*x**3 + 17*x**2) + (13*x**3)*(43*x**3 + 17*x**2)
<replace-#Step 1>#Step 2:
Current expression: (7*x)*(43*x**3 + 17*x**2) + (13*x**3)*(43*x**3 + 17*x**2)</replace>
Simplifying the partial expression: (7*x)*(43*x**3 + 17*x**2)
Expanding the part (43*x**3 + 17*x**2) using the distributive property, and we got: (7*x)*(17*x**2) + (7*x)*(43*x**3)
Replacing (7*x)*(43*x**3 + 17*x**2) with (7*x)*(17*x**2) + (7*x)*(43*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*x)*(17*x**2) + (7*x)*(43*x**3) + (13*x**3)*(43*x**3 + 17*x**2)</replace>
Simplifying the partial expression: (13*x**3)*(43*x**3 + 17*x**2)
Expanding the part (43*x**3 + 17*x**2) using the distributive property, and we got: (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3)
Replacing (13*x**3)*(43*x**3 + 17*x**2) with (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*x)*(17*x**2) + (7*x)*(43*x**3) + (17*x**2)*(13*x**3) + (13*x**3)*(43*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*x**2)*(7*x) = 119*x**3
  (17*x**2)*(13*x**3) = 221*x**5
  (43*x**3)*(7*x) = 301*x**4
  (43*x**3)*(13*x**3) = 559*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 559*x**6 + 221*x**5 + 301*x**4 + 119*x**3</replace>
No more calculations needed.
<answer>559*x**6 + 221*x**5 + 301*x**4 + 119*x**3</answer>


Question:
Calculate the following: (14*z - 24)*(49*z**3 + 4*z**2 - 65*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: 686*z**4 - 1120*z**3 - 1006*z**2 + 1560*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: (14*z - 24)*(49*z**3 + 4*z**2 - 65*z)
Expanding the part (14*z - 24) using the distributive property, and we got: (14*z)*(49*z**3 + 4*z**2 - 65*z) - 24*(49*z**3 + 4*z**2 - 65*z)
<replace-#Step 1>#Step 2:
Current expression: (14*z)*(49*z**3 + 4*z**2 - 65*z) - 24*(49*z**3 + 4*z**2 - 65*z)</replace>
Simplifying the partial expression: -24*(49*z**3 + 4*z**2 - 65*z)
Expanding the part (49*z**3 + 4*z**2 - 65*z) using the distributive property, and we got: -65*z*(-24) + (4*z**2)*(-24) + (49*z**3)*(-24)
Replacing -24*(49*z**3 + 4*z**2 - 65*z) with -65*z*(-24) + (4*z**2)*(-24) + (49*z**3)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -65*z*(-24) + (14*z)*(49*z**3 + 4*z**2 - 65*z) + (4*z**2)*(-24) + (49*z**3)*(-24)</replace>
Simplifying the partial expression: (14*z)*(49*z**3 + 4*z**2 - 65*z)
Expanding the part (49*z**3 + 4*z**2 - 65*z) using the distributive property, and we got: (-65*z)*(14*z) + (14*z)*(4*z**2) + (14*z)*(49*z**3)
Replacing (14*z)*(49*z**3 + 4*z**2 - 65*z) with (-65*z)*(14*z) + (14*z)*(4*z**2) + (14*z)*(49*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-65*z)*(14*z) - 65*z*(-24) + (14*z)*(4*z**2) + (14*z)*(49*z**3) + (4*z**2)*(-24) + (49*z**3)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-65*z)*-24 = 1560*z
  (-65*z)*(14*z) = -910*z**2
  (4*z**2)*-24 = -96*z**2
  (4*z**2)*(14*z) = 56*z**3
  (49*z**3)*-24 = -1176*z**3
  (49*z**3)*(14*z) = 686*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 686*z**4 - 1176*z**3 + 56*z**3 - 910*z**2 - 96*z**2 + 1560*z</replace>
Combining like terms, got 686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z
<replace-#Step 5>#Step 6:
Current expression: 686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z</replace>
No more calculations needed.
<answer>686*z**4 - 1120*z**3 - 1006*z**2 + 1560*z</answer>


Question:
Calculate the following: 1911*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: 1911*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: 1911*y**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 1911*y**2</replace>
No more calculations needed.
<answer>1911*y**2</answer>


Question:
Simplify this expression: (-18*x**3 - 12*x)*(-3*x**3 - 17*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: 54*x**6 + 306*x**5 - 414*x**4 + 204*x**3 - 300*x**2


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

Answer: -252*y**6 - 828*y**4 - 648*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: (-18*y**3 - 36*y)*(14*y**3 + 18*y)
Expanding the part (-18*y**3 - 36*y) using the distributive property, and we got: (-36*y)*(14*y**3 + 18*y) + (-18*y**3)*(14*y**3 + 18*y)
<replace-#Step 1>#Step 2:
Current expression: (-36*y)*(14*y**3 + 18*y) + (-18*y**3)*(14*y**3 + 18*y)</replace>
Simplifying the partial expression: (-36*y)*(14*y**3 + 18*y)
Expanding the part (14*y**3 + 18*y) using the distributive property, and we got: (-36*y)*(18*y) + (-36*y)*(14*y**3)
Replacing (-36*y)*(14*y**3 + 18*y) with (-36*y)*(18*y) + (-36*y)*(14*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*y)*(18*y) + (-36*y)*(14*y**3) + (-18*y**3)*(14*y**3 + 18*y)</replace>
Simplifying the partial expression: (-18*y**3)*(14*y**3 + 18*y)
Expanding the part (14*y**3 + 18*y) using the distributive property, and we got: (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3)
Replacing (-18*y**3)*(14*y**3 + 18*y) with (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*y)*(18*y) + (-36*y)*(14*y**3) + (18*y)*(-18*y**3) + (-18*y**3)*(14*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*y**3)*(-36*y) = -504*y**4
  (14*y**3)*(-18*y**3) = -252*y**6
  (18*y)*(-36*y) = -648*y**2
  (18*y)*(-18*y**3) = -324*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -252*y**6 - 504*y**4 - 324*y**4 - 648*y**2</replace>
Combining like terms, got -252*y**6 - 828*y**4 - 648*y**2
<replace-#Step 5>#Step 6:
Current expression: -252*y**6 - 828*y**4 - 648*y**2</replace>
No more calculations needed.
<answer>-252*y**6 - 828*y**4 - 648*y**2</answer>


Question:
Calculate the following: (39*y**3 + 17)*(47*y**3 - 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: 1833*y**6 - 449*y**3 - 544

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*y**3 + 17)*(47*y**3 - 32)
Expanding the part (47*y**3 - 32) using the distributive property, and we got: (47*y**3)*(39*y**3 + 17) - 32*(39*y**3 + 17)
<replace-#Step 1>#Step 2:
Current expression: (47*y**3)*(39*y**3 + 17) - 32*(39*y**3 + 17)</replace>
Simplifying the partial expression: -32*(39*y**3 + 17)
Expanding the part (39*y**3 + 17) using the distributive property, and we got: (39*y**3)*(-32) + 17*(-32)
Replacing -32*(39*y**3 + 17) with (39*y**3)*(-32) + 17*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*y**3)*(-32) + (47*y**3)*(39*y**3 + 17) - 544</replace>
Simplifying the partial expression: (47*y**3)*(39*y**3 + 17)
Expanding the part (39*y**3 + 17) using the distributive property, and we got: 17*(47*y**3) + (39*y**3)*(47*y**3)
Replacing (47*y**3)*(39*y**3 + 17) with 17*(47*y**3) + (39*y**3)*(47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*47*y**3 + (39*y**3)*(47*y**3) + (39*y**3)*(-32) - 544</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (39*y**3)*-32 = -1248*y**3
  (39*y**3)*(47*y**3) = 1833*y**6
  17*47*y**3 = 799*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1833*y**6 - 1248*y**3 + 799*y**3 - 544</replace>
Combining like terms, got 1833*y**6 - 449*y**3 - 544
<replace-#Step 5>#Step 6:
Current expression: 1833*y**6 - 449*y**3 - 544</replace>
No more calculations needed.
<answer>1833*y**6 - 449*y**3 - 544</answer>


Question:
Calculate the following: (35*y**2 + 41*y)*(48*y**2 + 52*y - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1680*y**4 + 3788*y**3 + 1537*y**2 - 697*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: (35*y**2 + 41*y)*(48*y**2 + 52*y - 17)
Expanding the part (35*y**2 + 41*y) using the distributive property, and we got: (41*y)*(48*y**2 + 52*y - 17) + (35*y**2)*(48*y**2 + 52*y - 17)
<replace-#Step 1>#Step 2:
Current expression: (41*y)*(48*y**2 + 52*y - 17) + (35*y**2)*(48*y**2 + 52*y - 17)</replace>
Simplifying the partial expression: (35*y**2)*(48*y**2 + 52*y - 17)
Expanding the part (48*y**2 + 52*y - 17) using the distributive property, and we got: -595*y**2 + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)
Replacing (35*y**2)*(48*y**2 + 52*y - 17) with -595*y**2 + (52*y)*(35*y**2) + (35*y**2)*(48*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -17*35*y**2 + (41*y)*(48*y**2 + 52*y - 17) + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)</replace>
Simplifying the partial expression: (41*y)*(48*y**2 + 52*y - 17)
Expanding the part (48*y**2 + 52*y - 17) using the distributive property, and we got: -697*y + (41*y)*(52*y) + (41*y)*(48*y**2)
Replacing (41*y)*(48*y**2 + 52*y - 17) with -697*y + (41*y)*(52*y) + (41*y)*(48*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -17*35*y**2 - 17*41*y + (41*y)*(52*y) + (41*y)*(48*y**2) + (52*y)*(35*y**2) + (35*y**2)*(48*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (48*y**2)*(35*y**2) = 1680*y**4
  (48*y**2)*(41*y) = 1968*y**3
  (52*y)*(35*y**2) = 1820*y**3
  (52*y)*(41*y) = 2132*y**2
  -17*35*y**2 = -595*y**2
  -17*41*y = -697*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1680*y**4 + 1820*y**3 + 1968*y**3 - 595*y**2 + 2132*y**2 - 697*y</replace>
Combining like terms, got 1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y
<replace-#Step 5>#Step 6:
Current expression: 1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y</replace>
No more calculations needed.
<answer>1680*y**4 + 3788*y**3 + 1537*y**2 - 697*y</answer>


Question:
Simplify this expression: (12*x + 43)*(47*x**3 + 8*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: 564*x**4 + 2117*x**3 + 344*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: (12*x + 43)*(47*x**3 + 8*x**2)
Expanding the part (12*x + 43) using the distributive property, and we got: (12*x)*(47*x**3 + 8*x**2) + 43*(47*x**3 + 8*x**2)
<replace-#Step 1>#Step 2:
Current expression: (12*x)*(47*x**3 + 8*x**2) + 43*(47*x**3 + 8*x**2)</replace>
Simplifying the partial expression: 43*(47*x**3 + 8*x**2)
Expanding the part (47*x**3 + 8*x**2) using the distributive property, and we got: (8*x**2)*43 + (47*x**3)*43
Replacing 43*(47*x**3 + 8*x**2) with (8*x**2)*43 + (47*x**3)*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*x)*(47*x**3 + 8*x**2) + (8*x**2)*43 + (47*x**3)*43</replace>
Simplifying the partial expression: (12*x)*(47*x**3 + 8*x**2)
Expanding the part (47*x**3 + 8*x**2) using the distributive property, and we got: (12*x)*(8*x**2) + (12*x)*(47*x**3)
Replacing (12*x)*(47*x**3 + 8*x**2) with (12*x)*(8*x**2) + (12*x)*(47*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (12*x)*(8*x**2) + (12*x)*(47*x**3) + (8*x**2)*43 + (47*x**3)*43</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*x**2)*43 = 344*x**2
  (8*x**2)*(12*x) = 96*x**3
  (47*x**3)*43 = 2021*x**3
  (47*x**3)*(12*x) = 564*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 564*x**4 + 96*x**3 + 2021*x**3 + 344*x**2</replace>
Combining like terms, got 564*x**4 + 2117*x**3 + 344*x**2
<replace-#Step 5>#Step 6:
Current expression: 564*x**4 + 2117*x**3 + 344*x**2</replace>
No more calculations needed.
<answer>564*x**4 + 2117*x**3 + 344*x**2</answer>


Question:
Simplify this expression: (25*y - 41)*(39*y**3 + y**2 + 24*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: 975*y**4 - 1574*y**3 + 559*y**2 - 984*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 - 41)*(39*y**3 + y**2 + 24*y)
Expanding the part (25*y - 41) using the distributive property, and we got: (25*y)*(39*y**3 + y**2 + 24*y) - 41*(39*y**3 + y**2 + 24*y)
<replace-#Step 1>#Step 2:
Current expression: (25*y)*(39*y**3 + y**2 + 24*y) - 41*(39*y**3 + y**2 + 24*y)</replace>
Simplifying the partial expression: -41*(39*y**3 + y**2 + 24*y)
Expanding the part (39*y**3 + y**2 + 24*y) using the distributive property, and we got: y**2*(-41) + (24*y)*(-41) + (39*y**3)*(-41)
Replacing -41*(39*y**3 + y**2 + 24*y) with y**2*(-41) + (24*y)*(-41) + (39*y**3)*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y**2*(-41) + (24*y)*(-41) + (25*y)*(39*y**3 + y**2 + 24*y) + (39*y**3)*(-41)</replace>
Simplifying the partial expression: (25*y)*(39*y**3 + y**2 + 24*y)
Expanding the part (39*y**3 + y**2 + 24*y) using the distributive property, and we got: (25*y)*y**2 + (24*y)*(25*y) + (25*y)*(39*y**3)
Replacing (25*y)*(39*y**3 + y**2 + 24*y) with (25*y)*y**2 + (24*y)*(25*y) + (25*y)*(39*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (25*y)*y**2 + y**2*(-41) + (24*y)*(25*y) + (24*y)*(-41) + (25*y)*(39*y**3) + (39*y**3)*(-41)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y**2*-41 = -41*y**2
  y**2*(25*y) = 25*y**3
  (24*y)*-41 = -984*y
  (24*y)*(25*y) = 600*y**2
  (39*y**3)*-41 = -1599*y**3
  (39*y**3)*(25*y) = 975*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 975*y**4 - 1599*y**3 + 25*y**3 - 41*y**2 + 600*y**2 - 984*y</replace>
Combining like terms, got 975*y**4 - 1574*y**3 + 559*y**2 - 984*y
<replace-#Step 5>#Step 6:
Current expression: 975*y**4 - 1574*y**3 + 559*y**2 - 984*y</replace>
No more calculations needed.
<answer>975*y**4 - 1574*y**3 + 559*y**2 - 984*y</answer>


Question:
Calculate the following: (-45*z**2 + 47*z - 13)*(-49*z**3 - 24*z**2 - 16*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: 2205*z**5 - 1223*z**4 + 229*z**3 - 440*z**2 + 208*z


Question:
Calculate the following: (32*x**2 - 37)*(-41*x**3 + 17*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: -1312*x**5 + 544*x**4 + 1517*x**3 - 1109*x**2 + 555


Question:
Calculate the following: -33*z*(-16*z**2 - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 528*z**3 + 1188*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: -33*z*(-16*z**2 - 36)
Expanding the part (-16*z**2 - 36) using the distributive property, and we got: (-33*z)*(-16*z**2) - (-1)*1188*z
<replace-#Step 1>#Step 2:
Current expression: (-33*z)*(-16*z**2) - (-1)*1188*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -36*(-33*z) = 1188*z
  (-16*z**2)*(-33*z) = 528*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 528*z**3 + 1188*z</replace>
No more calculations needed.
<answer>528*z**3 + 1188*z</answer>


Question:
Simplify this expression: (-34*z**2 + 11*z)*(30*z**3 + 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: -1020*z**5 + 330*z**4 - 680*z**2 + 220*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: (-34*z**2 + 11*z)*(30*z**3 + 20)
Expanding the part (30*z**3 + 20) using the distributive property, and we got: (30*z**3)*(-34*z**2 + 11*z) + 20*(-34*z**2 + 11*z)
<replace-#Step 1>#Step 2:
Current expression: (30*z**3)*(-34*z**2 + 11*z) + 20*(-34*z**2 + 11*z)</replace>
Simplifying the partial expression: 20*(-34*z**2 + 11*z)
Expanding the part (-34*z**2 + 11*z) using the distributive property, and we got: (11*z)*20 - 34*z**2*20
Replacing 20*(-34*z**2 + 11*z) with (11*z)*20 - 34*z**2*20 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*z)*20 - 34*z**2*20 + (30*z**3)*(-34*z**2 + 11*z)</replace>
Simplifying the partial expression: (30*z**3)*(-34*z**2 + 11*z)
Expanding the part (-34*z**2 + 11*z) using the distributive property, and we got: (11*z)*(30*z**3) + (-34*z**2)*(30*z**3)
Replacing (30*z**3)*(-34*z**2 + 11*z) with (11*z)*(30*z**3) + (-34*z**2)*(30*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*z)*(30*z**3) + (11*z)*20 + (-34*z**2)*(30*z**3) - 34*z**2*20</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*z**2)*20 = -680*z**2
  (-34*z**2)*(30*z**3) = -1020*z**5
  (11*z)*20 = 220*z
  (11*z)*(30*z**3) = 330*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1020*z**5 + 330*z**4 - 680*z**2 + 220*z</replace>
No more calculations needed.
<answer>-1020*z**5 + 330*z**4 - 680*z**2 + 220*z</answer>


Question:
Simplify this expression: (29*z**3 - 23*z**2 - 34*z)*(37*z**3 + 48*z - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1073*z**6 - 851*z**5 + 134*z**4 - 1974*z**3 - 942*z**2 + 1020*z


Question:
Calculate the following: (17*x**3 + 26*x**2)*(-59*x**3 + 37*x + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1003*x**6 - 1534*x**5 + 629*x**4 + 1081*x**3 + 182*x**2


Question:
Simplify this expression: (30 - 36*y**2)*(13*y**2 - 20*y - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930

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 - 36*y**2)*(13*y**2 - 20*y - 31)
Expanding the part (30 - 36*y**2) using the distributive property, and we got: (-36*y**2)*(13*y**2 - 20*y - 31) + 30*(13*y**2 - 20*y - 31)
<replace-#Step 1>#Step 2:
Current expression: (-36*y**2)*(13*y**2 - 20*y - 31) + 30*(13*y**2 - 20*y - 31)</replace>
Simplifying the partial expression: 30*(13*y**2 - 20*y - 31)
Expanding the part (13*y**2 - 20*y - 31) using the distributive property, and we got: -20*y*30 + (13*y**2)*30 - 31*30
Replacing 30*(13*y**2 - 20*y - 31) with -20*y*30 + (13*y**2)*30 - 31*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*y*30 + (-36*y**2)*(13*y**2 - 20*y - 31) + (13*y**2)*30 - 930</replace>
Simplifying the partial expression: (-36*y**2)*(13*y**2 - 20*y - 31)
Expanding the part (13*y**2 - 20*y - 31) using the distributive property, and we got: (-20*y)*(-36*y**2) - (-1)*1116*y**2 + (-36*y**2)*(13*y**2)
Replacing (-36*y**2)*(13*y**2 - 20*y - 31) with (-20*y)*(-36*y**2) - (-1)*1116*y**2 + (-36*y**2)*(13*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*y)*(-36*y**2) - 20*y*30 - 31*(-36)*y**2 + (-36*y**2)*(13*y**2) + (13*y**2)*30 - 930</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*y)*30 = -600*y
  (-20*y)*(-36*y**2) = 720*y**3
  (13*y**2)*30 = 390*y**2
  (13*y**2)*(-36*y**2) = -468*y**4
  -31*-36*y**2 = 1116*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -468*y**4 + 720*y**3 + 390*y**2 + 1116*y**2 - 600*y - 930</replace>
Combining like terms, got -468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930
<replace-#Step 5>#Step 6:
Current expression: -468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930</replace>
No more calculations needed.
<answer>-468*y**4 + 720*y**3 + 1506*y**2 - 600*y - 930</answer>


Question:
Simplify this expression: 11*x**2*(52*x - 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: 572*x**3 - 451*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: 11*x**2*(52*x - 41)
Expanding the part (52*x - 41) using the distributive property, and we got: -451*x**2 + (52*x)*(11*x**2)
<replace-#Step 1>#Step 2:
Current expression: -451*x**2 + (52*x)*(11*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -41*(11*x**2) = -451*x**2
  (52*x)*(11*x**2) = 572*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 572*x**3 - 451*x**2</replace>
No more calculations needed.
<answer>572*x**3 - 451*x**2</answer>


Question:
Calculate the following: (33 - 49*z**2)*(-48*z**3 + 49*z**2 - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2352*z**5 - 2401*z**4 - 1584*z**3 + 2450*z**2 - 561


Question:
Simplify this expression: -1352*z**3 + 728*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: -1352*z**3 + 728*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: -1352*z**3 + 728*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -1352*z**3 + 728*z</replace>
No more calculations needed.
<answer>-1352*z**3 + 728*z</answer>


Question:
Calculate the following: (38*x**3 - 21*x**2)*(-11*x**2 - 5*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: -418*x**5 + 41*x**4 - 1795*x**3 + 1050*x**2


Question:
Simplify this expression: (-15*x**3 + 7*x**2 + 13*x)*(44*x**3 - 50*x - 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -660*x**6 + 308*x**5 + 1322*x**4 - 5*x**3 - 811*x**2 - 299*x


Question:
Simplify this expression: -301*z**3 + 4257*z**2 - 2107
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -301*z**3 + 4257*z**2 - 2107

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: -301*z**3 + 4257*z**2 - 2107
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: -301*z**3 + 4257*z**2 - 2107</replace>
No more calculations needed.
<answer>-301*z**3 + 4257*z**2 - 2107</answer>


Question:
Calculate the following: (5*y**2 - 36*y)*(26*y**2 - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 130*y**4 - 936*y**3 - 180*y**2 + 1296*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: (5*y**2 - 36*y)*(26*y**2 - 36)
Expanding the part (26*y**2 - 36) using the distributive property, and we got: (26*y**2)*(5*y**2 - 36*y) - 36*(5*y**2 - 36*y)
<replace-#Step 1>#Step 2:
Current expression: (26*y**2)*(5*y**2 - 36*y) - 36*(5*y**2 - 36*y)</replace>
Simplifying the partial expression: -36*(5*y**2 - 36*y)
Expanding the part (5*y**2 - 36*y) using the distributive property, and we got: -36*y*(-36) + (5*y**2)*(-36)
Replacing -36*(5*y**2 - 36*y) with -36*y*(-36) + (5*y**2)*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -36*y*(-36) + (5*y**2)*(-36) + (26*y**2)*(5*y**2 - 36*y)</replace>
Simplifying the partial expression: (26*y**2)*(5*y**2 - 36*y)
Expanding the part (5*y**2 - 36*y) using the distributive property, and we got: (-36*y)*(26*y**2) + (5*y**2)*(26*y**2)
Replacing (26*y**2)*(5*y**2 - 36*y) with (-36*y)*(26*y**2) + (5*y**2)*(26*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*y)*(26*y**2) - 36*y*(-36) + (5*y**2)*(26*y**2) + (5*y**2)*(-36)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*y)*-36 = 1296*y
  (-36*y)*(26*y**2) = -936*y**3
  (5*y**2)*-36 = -180*y**2
  (5*y**2)*(26*y**2) = 130*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 130*y**4 - 936*y**3 - 180*y**2 + 1296*y</replace>
No more calculations needed.
<answer>130*y**4 - 936*y**3 - 180*y**2 + 1296*y</answer>


Question:
Calculate the following: -33*y**2*(10*y**2 + 20*y + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -330*y**4 - 660*y**3 - 561*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: -33*y**2*(10*y**2 + 20*y + 17)
Expanding the part (10*y**2 + 20*y + 17) using the distributive property, and we got: 17*(-33*y**2) + (20*y)*(-33*y**2) + (-33*y**2)*(10*y**2)
<replace-#Step 1>#Step 2:
Current expression: 17*(-33*y**2) + (20*y)*(-33*y**2) + (-33*y**2)*(10*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  17*(-33*y**2) = -561*y**2
  (10*y**2)*(-33*y**2) = -330*y**4
  (20*y)*(-33*y**2) = -660*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -330*y**4 - 660*y**3 - 561*y**2</replace>
No more calculations needed.
<answer>-330*y**4 - 660*y**3 - 561*y**2</answer>


Question:
Simplify this expression: (17*y + 7)*(26*y**2 - 66)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 442*y**3 + 182*y**2 - 1122*y - 462

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (17*y + 7)*(26*y**2 - 66)
Expanding the part (26*y**2 - 66) using the distributive property, and we got: (26*y**2)*(17*y + 7) - 66*(17*y + 7)
<replace-#Step 1>#Step 2:
Current expression: (26*y**2)*(17*y + 7) - 66*(17*y + 7)</replace>
Simplifying the partial expression: -66*(17*y + 7)
Expanding the part (17*y + 7) using the distributive property, and we got: (17*y)*(-66) + 7*(-66)
Replacing -66*(17*y + 7) with (17*y)*(-66) + 7*(-66) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*y)*(-66) + (26*y**2)*(17*y + 7) - 462</replace>
Simplifying the partial expression: (26*y**2)*(17*y + 7)
Expanding the part (17*y + 7) using the distributive property, and we got: 7*(26*y**2) + (17*y)*(26*y**2)
Replacing (26*y**2)*(17*y + 7) with 7*(26*y**2) + (17*y)*(26*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 7*26*y**2 + (17*y)*(26*y**2) + (17*y)*(-66) - 462</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*y)*-66 = -1122*y
  (17*y)*(26*y**2) = 442*y**3
  7*26*y**2 = 182*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 442*y**3 + 182*y**2 - 1122*y - 462</replace>
No more calculations needed.
<answer>442*y**3 + 182*y**2 - 1122*y - 462</answer>


Question:
Simplify this expression: (12*y**3 + 58)*(-31*y**3 + 11*y + 4)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (12*y**3 + 58)*(-31*y**3 + 11*y + 4)
Expanding the part (12*y**3 + 58) using the distributive property, and we got: (12*y**3)*(-31*y**3 + 11*y + 4) + 58*(-31*y**3 + 11*y + 4)
<replace-#Step 1>#Step 2:
Current expression: (12*y**3)*(-31*y**3 + 11*y + 4) + 58*(-31*y**3 + 11*y + 4)</replace>
Simplifying the partial expression: 58*(-31*y**3 + 11*y + 4)
Expanding the part (-31*y**3 + 11*y + 4) using the distributive property, and we got: (11*y)*58 - 31*y**3*58 + 4*58
Replacing 58*(-31*y**3 + 11*y + 4) with (11*y)*58 - 31*y**3*58 + 4*58 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*y)*58 - 31*y**3*58 + (12*y**3)*(-31*y**3 + 11*y + 4) + 232</replace>
Simplifying the partial expression: (12*y**3)*(-31*y**3 + 11*y + 4)
Expanding the part (-31*y**3 + 11*y + 4) using the distributive property, and we got: 4*(12*y**3) + (11*y)*(12*y**3) + (-31*y**3)*(12*y**3)
Replacing (12*y**3)*(-31*y**3 + 11*y + 4) with 4*(12*y**3) + (11*y)*(12*y**3) + (-31*y**3)*(12*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 4*12*y**3 + (11*y)*(12*y**3) + (11*y)*58 + (-31*y**3)*(12*y**3) - 31*y**3*58 + 232</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-31*y**3)*58 = -1798*y**3
  (-31*y**3)*(12*y**3) = -372*y**6
  (11*y)*58 = 638*y
  (11*y)*(12*y**3) = 132*y**4
  4*12*y**3 = 48*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -372*y**6 + 132*y**4 - 1798*y**3 + 48*y**3 + 638*y + 232</replace>
Combining like terms, got -372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232
<replace-#Step 5>#Step 6:
Current expression: -372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232</replace>
No more calculations needed.
<answer>-372*y**6 + 132*y**4 - 1750*y**3 + 638*y + 232</answer>


Question:
Simplify this expression: (-35*y - 1)*(23*y**3 - 45*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: -805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-35*y - 1)*(23*y**3 - 45*y - 12)
Expanding the part (-35*y - 1) using the distributive property, and we got: (-35*y)*(23*y**3 - 45*y - 12) - (23*y**3 - 45*y - 12)
<replace-#Step 1>#Step 2:
Current expression: (-35*y)*(23*y**3 - 45*y - 12) - (23*y**3 - 45*y - 12)</replace>
Simplifying the partial expression: -(23*y**3 - 45*y - 12)
Expanding the part (23*y**3 - 45*y - 12) using the distributive property, and we got: -45*y*(-1) + (23*y**3)*(-1) - 12*(-1)
Replacing -(23*y**3 - 45*y - 12) with -45*y*(-1) + (23*y**3)*(-1) - 12*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -45*y*(-1) + (-35*y)*(23*y**3 - 45*y - 12) + (23*y**3)*(-1) + 12</replace>
Simplifying the partial expression: (-35*y)*(23*y**3 - 45*y - 12)
Expanding the part (23*y**3 - 45*y - 12) using the distributive property, and we got: (-45*y)*(-35*y) + (-35*y)*(23*y**3) - (-1)*420*y
Replacing (-35*y)*(23*y**3 - 45*y - 12) with (-45*y)*(-35*y) + (-35*y)*(23*y**3) - (-1)*420*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-45*y)*(-35*y) - 45*y*(-1) + (-35*y)*(23*y**3) - 12*(-35)*y + (23*y**3)*(-1) + 12</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*y)*-1 = 45*y
  (-45*y)*(-35*y) = 1575*y**2
  (23*y**3)*-1 = -23*y**3
  (23*y**3)*(-35*y) = -805*y**4
  -12*-35*y = 420*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -805*y**4 - 23*y**3 + 1575*y**2 + 45*y + 420*y + 12</replace>
Combining like terms, got -805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12
<replace-#Step 5>#Step 6:
Current expression: -805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12</replace>
No more calculations needed.
<answer>-805*y**4 - 23*y**3 + 1575*y**2 + 465*y + 12</answer>


Question:
Calculate the following: (-50*z - 25)*(-11*z**3 + 3*z + 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-50*z - 25)*(-11*z**3 + 3*z + 46)
Expanding the part (-50*z - 25) using the distributive property, and we got: (-50*z)*(-11*z**3 + 3*z + 46) - 25*(-11*z**3 + 3*z + 46)
<replace-#Step 1>#Step 2:
Current expression: (-50*z)*(-11*z**3 + 3*z + 46) - 25*(-11*z**3 + 3*z + 46)</replace>
Simplifying the partial expression: -25*(-11*z**3 + 3*z + 46)
Expanding the part (-11*z**3 + 3*z + 46) using the distributive property, and we got: (3*z)*(-25) - 11*z**3*(-25) + 46*(-25)
Replacing -25*(-11*z**3 + 3*z + 46) with (3*z)*(-25) - 11*z**3*(-25) + 46*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-50*z)*(-11*z**3 + 3*z + 46) + (3*z)*(-25) - 11*z**3*(-25) - 1150</replace>
Simplifying the partial expression: (-50*z)*(-11*z**3 + 3*z + 46)
Expanding the part (-11*z**3 + 3*z + 46) using the distributive property, and we got: (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50*z)
Replacing (-50*z)*(-11*z**3 + 3*z + 46) with (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*z)*(3*z) + (-50*z)*(-11*z**3) + 46*(-50)*z + (3*z)*(-25) - 11*z**3*(-25) - 1150</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z**3)*-25 = 275*z**3
  (-11*z**3)*(-50*z) = 550*z**4
  (3*z)*-25 = -75*z
  (3*z)*(-50*z) = -150*z**2
  46*-50*z = -2300*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 550*z**4 + 275*z**3 - 150*z**2 - 2300*z - 75*z - 1150</replace>
Combining like terms, got 550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150
<replace-#Step 5>#Step 6:
Current expression: 550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150</replace>
No more calculations needed.
<answer>550*z**4 + 275*z**3 - 150*z**2 - 2375*z - 1150</answer>


Question:
Simplify this expression: (-45*z**2 - 36*z - 11)*(-13*z**3 + 57*z**2 - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 585*z**5 - 2097*z**4 - 1909*z**3 + 948*z**2 + 1260*z + 385


Question:
Calculate the following: 16*z**3*(16*z**3 - 35*z - 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 256*z**6 - 560*z**4 - 144*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 16*z**3*(16*z**3 - 35*z - 9)
Expanding the part (16*z**3 - 35*z - 9) using the distributive property, and we got: (-35*z)*(16*z**3) - 144*z**3 + (16*z**3)*(16*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-35*z)*(16*z**3) - 144*z**3 + (16*z**3)*(16*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -9*(16*z**3) = -144*z**3
  (-35*z)*(16*z**3) = -560*z**4
  (16*z**3)*(16*z**3) = 256*z**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 256*z**6 - 560*z**4 - 144*z**3</replace>
No more calculations needed.
<answer>256*z**6 - 560*z**4 - 144*z**3</answer>


Question:
Calculate the following: (-4*y**3 - 32*y)*(9*y**3 + 30*y**2 - 29*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: -36*y**6 - 120*y**5 - 172*y**4 - 960*y**3 + 928*y**2


Question:
Simplify this expression: (39*x + 10)*(-22*x**2 - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -858*x**3 - 220*x**2 - 1170*x - 300

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (39*x + 10)*(-22*x**2 - 30)
Expanding the part (-22*x**2 - 30) using the distributive property, and we got: (-22*x**2)*(39*x + 10) - 30*(39*x + 10)
<replace-#Step 1>#Step 2:
Current expression: (-22*x**2)*(39*x + 10) - 30*(39*x + 10)</replace>
Simplifying the partial expression: -30*(39*x + 10)
Expanding the part (39*x + 10) using the distributive property, and we got: (39*x)*(-30) + 10*(-30)
Replacing -30*(39*x + 10) with (39*x)*(-30) + 10*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (39*x)*(-30) + (-22*x**2)*(39*x + 10) - 300</replace>
Simplifying the partial expression: (-22*x**2)*(39*x + 10)
Expanding the part (39*x + 10) using the distributive property, and we got: 10*(-22*x**2) + (39*x)*(-22*x**2)
Replacing (-22*x**2)*(39*x + 10) with 10*(-22*x**2) + (39*x)*(-22*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 10*(-22)*x**2 + (39*x)*(-22*x**2) + (39*x)*(-30) - 300</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (39*x)*-30 = -1170*x
  (39*x)*(-22*x**2) = -858*x**3
  10*-22*x**2 = -220*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -858*x**3 - 220*x**2 - 1170*x - 300</replace>
No more calculations needed.
<answer>-858*x**3 - 220*x**2 - 1170*x - 300</answer>


Question:
Simplify this expression: (45 - 41*y**3)*(-y - 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: 41*y**4 + 738*y**3 - 45*y - 810

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 - 41*y**3)*(-y - 18)
Expanding the part (-y - 18) using the distributive property, and we got: (-y)*(45 - 41*y**3) - 18*(45 - 41*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-y)*(45 - 41*y**3) - 18*(45 - 41*y**3)</replace>
Simplifying the partial expression: -18*(45 - 41*y**3)
Expanding the part (45 - 41*y**3) using the distributive property, and we got: -41*y**3*(-18) + 45*(-18)
Replacing -18*(45 - 41*y**3) with -41*y**3*(-18) + 45*(-18) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-y)*(45 - 41*y**3) - 41*y**3*(-18) - 810</replace>
Simplifying the partial expression: (-y)*(45 - 41*y**3)
Expanding the part (45 - 41*y**3) using the distributive property, and we got: (-y)*(-41*y**3) + 45*(-y)
Replacing (-y)*(45 - 41*y**3) with (-y)*(-41*y**3) + 45*(-y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-y)*(-41*y**3) + 45*(-1)*y - 41*y**3*(-18) - 810</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**3)*-18 = 738*y**3
  (-41*y**3)*(-y) = 41*y**4
  45*-1*y = -45*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 41*y**4 + 738*y**3 - 45*y - 810</replace>
No more calculations needed.
<answer>41*y**4 + 738*y**3 - 45*y - 810</answer>


Question:
Calculate the following: (27 - 41*z)*(73 - 30*z**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: 1230*z**4 - 810*z**3 - 2993*z + 1971

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27 - 41*z)*(73 - 30*z**3)
Expanding the part (27 - 41*z) using the distributive property, and we got: (-41*z)*(73 - 30*z**3) + 27*(73 - 30*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-41*z)*(73 - 30*z**3) + 27*(73 - 30*z**3)</replace>
Simplifying the partial expression: 27*(73 - 30*z**3)
Expanding the part (73 - 30*z**3) using the distributive property, and we got: -30*z**3*27 + 73*27
Replacing 27*(73 - 30*z**3) with -30*z**3*27 + 73*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-41*z)*(73 - 30*z**3) - 30*z**3*27 + 1971</replace>
Simplifying the partial expression: (-41*z)*(73 - 30*z**3)
Expanding the part (73 - 30*z**3) using the distributive property, and we got: (-41*z)*(-30*z**3) + 73*(-41*z)
Replacing (-41*z)*(73 - 30*z**3) with (-41*z)*(-30*z**3) + 73*(-41*z) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*z)*(-30*z**3) + 73*(-41)*z - 30*z**3*27 + 1971</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z**3)*27 = -810*z**3
  (-30*z**3)*(-41*z) = 1230*z**4
  73*-41*z = -2993*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1230*z**4 - 810*z**3 - 2993*z + 1971</replace>
No more calculations needed.
<answer>1230*z**4 - 810*z**3 - 2993*z + 1971</answer>


Question:
Calculate the following: (-44*y**2 + 12*y + 60)*(5*y**3 - 14*y - 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: -220*y**5 + 60*y**4 + 916*y**3 + 1284*y**2 - 1236*y - 1980


Question:
Calculate the following: (57*y**2 + 22*y)*(34*y**2 + 33*y + 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1938*y**4 + 2629*y**3 + 2436*y**2 + 660*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: (57*y**2 + 22*y)*(34*y**2 + 33*y + 30)
Expanding the part (57*y**2 + 22*y) using the distributive property, and we got: (22*y)*(34*y**2 + 33*y + 30) + (57*y**2)*(34*y**2 + 33*y + 30)
<replace-#Step 1>#Step 2:
Current expression: (22*y)*(34*y**2 + 33*y + 30) + (57*y**2)*(34*y**2 + 33*y + 30)</replace>
Simplifying the partial expression: (22*y)*(34*y**2 + 33*y + 30)
Expanding the part (34*y**2 + 33*y + 30) using the distributive property, and we got: 30*(22*y) + (22*y)*(33*y) + (22*y)*(34*y**2)
Replacing (22*y)*(34*y**2 + 33*y + 30) with 30*(22*y) + (22*y)*(33*y) + (22*y)*(34*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 30*22*y + (22*y)*(33*y) + (22*y)*(34*y**2) + (57*y**2)*(34*y**2 + 33*y + 30)</replace>
Simplifying the partial expression: (57*y**2)*(34*y**2 + 33*y + 30)
Expanding the part (34*y**2 + 33*y + 30) using the distributive property, and we got: 30*(57*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2)
Replacing (57*y**2)*(34*y**2 + 33*y + 30) with 30*(57*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 30*57*y**2 + 30*22*y + (22*y)*(33*y) + (22*y)*(34*y**2) + (33*y)*(57*y**2) + (34*y**2)*(57*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (33*y)*(22*y) = 726*y**2
  (33*y)*(57*y**2) = 1881*y**3
  (34*y**2)*(22*y) = 748*y**3
  (34*y**2)*(57*y**2) = 1938*y**4
  30*22*y = 660*y
  30*57*y**2 = 1710*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1938*y**4 + 748*y**3 + 1881*y**3 + 726*y**2 + 1710*y**2 + 660*y</replace>
Combining like terms, got 1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y
<replace-#Step 5>#Step 6:
Current expression: 1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y</replace>
No more calculations needed.
<answer>1938*y**4 + 2629*y**3 + 2436*y**2 + 660*y</answer>