Question:
Simplify this expression: (47 - 25*x**3)*(40*x**3 - 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: -1000*x**6 + 2780*x**3 - 1692

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 - 25*x**3)*(40*x**3 - 36)
Expanding the part (40*x**3 - 36) using the distributive property, and we got: (40*x**3)*(47 - 25*x**3) - 36*(47 - 25*x**3)
<replace-#Step 1>#Step 2:
Current expression: (40*x**3)*(47 - 25*x**3) - 36*(47 - 25*x**3)</replace>
Simplifying the partial expression: -36*(47 - 25*x**3)
Expanding the part (47 - 25*x**3) using the distributive property, and we got: -25*x**3*(-36) + 47*(-36)
Replacing -36*(47 - 25*x**3) with -25*x**3*(-36) + 47*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -25*x**3*(-36) + (40*x**3)*(47 - 25*x**3) - 1692</replace>
Simplifying the partial expression: (40*x**3)*(47 - 25*x**3)
Expanding the part (47 - 25*x**3) using the distributive property, and we got: 47*(40*x**3) + (-25*x**3)*(40*x**3)
Replacing (40*x**3)*(47 - 25*x**3) with 47*(40*x**3) + (-25*x**3)*(40*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*40*x**3 + (-25*x**3)*(40*x**3) - 25*x**3*(-36) - 1692</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x**3)*-36 = 900*x**3
  (-25*x**3)*(40*x**3) = -1000*x**6
  47*40*x**3 = 1880*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1000*x**6 + 900*x**3 + 1880*x**3 - 1692</replace>
Combining like terms, got -1000*x**6 + 2780*x**3 - 1692
<replace-#Step 5>#Step 6:
Current expression: -1000*x**6 + 2780*x**3 - 1692</replace>
No more calculations needed.
<answer>-1000*x**6 + 2780*x**3 - 1692</answer>


Question:
Calculate the following: (7 - 38*z**3)*(39*z**3 - 8*z**2 + 30*z + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1482*z**6 + 304*z**5 - 1140*z**4 - 1437*z**3 - 56*z**2 + 210*z + 315


Question:
Calculate the following: (-10*x - 51)*(-38*x**2 + 24*x + 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 380*x**3 + 1698*x**2 - 1434*x - 1071

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-10*x - 51)*(-38*x**2 + 24*x + 21)
Expanding the part (-10*x - 51) using the distributive property, and we got: (-10*x)*(-38*x**2 + 24*x + 21) - 51*(-38*x**2 + 24*x + 21)
<replace-#Step 1>#Step 2:
Current expression: (-10*x)*(-38*x**2 + 24*x + 21) - 51*(-38*x**2 + 24*x + 21)</replace>
Simplifying the partial expression: -51*(-38*x**2 + 24*x + 21)
Expanding the part (-38*x**2 + 24*x + 21) using the distributive property, and we got: (24*x)*(-51) - 38*x**2*(-51) + 21*(-51)
Replacing -51*(-38*x**2 + 24*x + 21) with (24*x)*(-51) - 38*x**2*(-51) + 21*(-51) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*x)*(-38*x**2 + 24*x + 21) + (24*x)*(-51) - 38*x**2*(-51) - 1071</replace>
Simplifying the partial expression: (-10*x)*(-38*x**2 + 24*x + 21)
Expanding the part (-38*x**2 + 24*x + 21) using the distributive property, and we got: (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10*x)
Replacing (-10*x)*(-38*x**2 + 24*x + 21) with (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*x)*(24*x) + (-10*x)*(-38*x**2) + 21*(-10)*x + (24*x)*(-51) - 38*x**2*(-51) - 1071</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*x**2)*-51 = 1938*x**2
  (-38*x**2)*(-10*x) = 380*x**3
  (24*x)*-51 = -1224*x
  (24*x)*(-10*x) = -240*x**2
  21*-10*x = -210*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 380*x**3 - 240*x**2 + 1938*x**2 - 1224*x - 210*x - 1071</replace>
Combining like terms, got 380*x**3 + 1698*x**2 - 1434*x - 1071
<replace-#Step 5>#Step 6:
Current expression: 380*x**3 + 1698*x**2 - 1434*x - 1071</replace>
No more calculations needed.
<answer>380*x**3 + 1698*x**2 - 1434*x - 1071</answer>


Question:
Simplify this expression: (41*z**2 + 44)*(3*z**3 - 50*z + 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: 123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (41*z**2 + 44)*(3*z**3 - 50*z + 23)
Expanding the part (41*z**2 + 44) using the distributive property, and we got: (41*z**2)*(3*z**3 - 50*z + 23) + 44*(3*z**3 - 50*z + 23)
<replace-#Step 1>#Step 2:
Current expression: (41*z**2)*(3*z**3 - 50*z + 23) + 44*(3*z**3 - 50*z + 23)</replace>
Simplifying the partial expression: 44*(3*z**3 - 50*z + 23)
Expanding the part (3*z**3 - 50*z + 23) using the distributive property, and we got: -50*z*44 + (3*z**3)*44 + 23*44
Replacing 44*(3*z**3 - 50*z + 23) with -50*z*44 + (3*z**3)*44 + 23*44 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -50*z*44 + (41*z**2)*(3*z**3 - 50*z + 23) + (3*z**3)*44 + 1012</replace>
Simplifying the partial expression: (41*z**2)*(3*z**3 - 50*z + 23)
Expanding the part (3*z**3 - 50*z + 23) using the distributive property, and we got: (-50*z)*(41*z**2) + 23*(41*z**2) + (41*z**2)*(3*z**3)
Replacing (41*z**2)*(3*z**3 - 50*z + 23) with (-50*z)*(41*z**2) + 23*(41*z**2) + (41*z**2)*(3*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-50*z)*(41*z**2) - 50*z*44 + 23*41*z**2 + (41*z**2)*(3*z**3) + (3*z**3)*44 + 1012</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*z)*44 = -2200*z
  (-50*z)*(41*z**2) = -2050*z**3
  (3*z**3)*44 = 132*z**3
  (3*z**3)*(41*z**2) = 123*z**5
  23*41*z**2 = 943*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 123*z**5 - 2050*z**3 + 132*z**3 + 943*z**2 - 2200*z + 1012</replace>
Combining like terms, got 123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012
<replace-#Step 5>#Step 6:
Current expression: 123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012</replace>
No more calculations needed.
<answer>123*z**5 - 1918*z**3 + 943*z**2 - 2200*z + 1012</answer>


Question:
Calculate the following: (-72*z**2 + 42*z)*(-17*z**3 - 36*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: 1224*z**5 + 1878*z**4 - 1512*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: (-72*z**2 + 42*z)*(-17*z**3 - 36*z**2)
Expanding the part (-72*z**2 + 42*z) using the distributive property, and we got: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-17*z**3 - 36*z**2)
<replace-#Step 1>#Step 2:
Current expression: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-17*z**3 - 36*z**2)</replace>
Simplifying the partial expression: (-72*z**2)*(-17*z**3 - 36*z**2)
Expanding the part (-17*z**3 - 36*z**2) using the distributive property, and we got: (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)
Replacing (-72*z**2)*(-17*z**3 - 36*z**2) with (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z)*(-17*z**3 - 36*z**2) + (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)</replace>
Simplifying the partial expression: (42*z)*(-17*z**3 - 36*z**2)
Expanding the part (-17*z**3 - 36*z**2) using the distributive property, and we got: (42*z)*(-36*z**2) + (42*z)*(-17*z**3)
Replacing (42*z)*(-17*z**3 - 36*z**2) with (42*z)*(-36*z**2) + (42*z)*(-17*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (42*z)*(-36*z**2) + (42*z)*(-17*z**3) + (-72*z**2)*(-36*z**2) + (-72*z**2)*(-17*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*z**2)*(-72*z**2) = 2592*z**4
  (-36*z**2)*(42*z) = -1512*z**3
  (-17*z**3)*(-72*z**2) = 1224*z**5
  (-17*z**3)*(42*z) = -714*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1224*z**5 - 714*z**4 + 2592*z**4 - 1512*z**3</replace>
Combining like terms, got 1224*z**5 + 1878*z**4 - 1512*z**3
<replace-#Step 5>#Step 6:
Current expression: 1224*z**5 + 1878*z**4 - 1512*z**3</replace>
No more calculations needed.
<answer>1224*z**5 + 1878*z**4 - 1512*z**3</answer>


Question:
Simplify this expression: -1519*x**2 - 341*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: -1519*x**2 - 341*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -1519*x**2 - 341*x
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -1519*x**2 - 341*x</replace>
No more calculations needed.
<answer>-1519*x**2 - 341*x</answer>


Question:
Calculate the following: (-44*x**2 + 13*x)*(7*x**2 + 45*x + 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -308*x**4 - 1889*x**3 - 515*x**2 + 325*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-44*x**2 + 13*x)*(7*x**2 + 45*x + 25)
Expanding the part (-44*x**2 + 13*x) using the distributive property, and we got: (13*x)*(7*x**2 + 45*x + 25) + (-44*x**2)*(7*x**2 + 45*x + 25)
<replace-#Step 1>#Step 2:
Current expression: (13*x)*(7*x**2 + 45*x + 25) + (-44*x**2)*(7*x**2 + 45*x + 25)</replace>
Simplifying the partial expression: (-44*x**2)*(7*x**2 + 45*x + 25)
Expanding the part (7*x**2 + 45*x + 25) using the distributive property, and we got: 25*(-44*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)
Replacing (-44*x**2)*(7*x**2 + 45*x + 25) with 25*(-44*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 25*(-44)*x**2 + (13*x)*(7*x**2 + 45*x + 25) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)</replace>
Simplifying the partial expression: (13*x)*(7*x**2 + 45*x + 25)
Expanding the part (7*x**2 + 45*x + 25) using the distributive property, and we got: 25*(13*x) + (13*x)*(45*x) + (13*x)*(7*x**2)
Replacing (13*x)*(7*x**2 + 45*x + 25) with 25*(13*x) + (13*x)*(45*x) + (13*x)*(7*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 25*(-44)*x**2 + 25*13*x + (13*x)*(45*x) + (13*x)*(7*x**2) + (45*x)*(-44*x**2) + (-44*x**2)*(7*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*x**2)*(-44*x**2) = -308*x**4
  (7*x**2)*(13*x) = 91*x**3
  (45*x)*(-44*x**2) = -1980*x**3
  (45*x)*(13*x) = 585*x**2
  25*-44*x**2 = -1100*x**2
  25*13*x = 325*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -308*x**4 - 1980*x**3 + 91*x**3 - 1100*x**2 + 585*x**2 + 325*x</replace>
Combining like terms, got -308*x**4 - 1889*x**3 - 515*x**2 + 325*x
<replace-#Step 5>#Step 6:
Current expression: -308*x**4 - 1889*x**3 - 515*x**2 + 325*x</replace>
No more calculations needed.
<answer>-308*x**4 - 1889*x**3 - 515*x**2 + 325*x</answer>


Question:
Simplify this expression: (43 - 53*y)*(8*y**3 + 33*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -424*y**4 - 1405*y**3 + 1419*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: (43 - 53*y)*(8*y**3 + 33*y**2)
Expanding the part (43 - 53*y) using the distributive property, and we got: (-53*y)*(8*y**3 + 33*y**2) + 43*(8*y**3 + 33*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-53*y)*(8*y**3 + 33*y**2) + 43*(8*y**3 + 33*y**2)</replace>
Simplifying the partial expression: 43*(8*y**3 + 33*y**2)
Expanding the part (8*y**3 + 33*y**2) using the distributive property, and we got: (33*y**2)*43 + (8*y**3)*43
Replacing 43*(8*y**3 + 33*y**2) with (33*y**2)*43 + (8*y**3)*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-53*y)*(8*y**3 + 33*y**2) + (33*y**2)*43 + (8*y**3)*43</replace>
Simplifying the partial expression: (-53*y)*(8*y**3 + 33*y**2)
Expanding the part (8*y**3 + 33*y**2) using the distributive property, and we got: (-53*y)*(33*y**2) + (-53*y)*(8*y**3)
Replacing (-53*y)*(8*y**3 + 33*y**2) with (-53*y)*(33*y**2) + (-53*y)*(8*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-53*y)*(33*y**2) + (-53*y)*(8*y**3) + (33*y**2)*43 + (8*y**3)*43</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*y**3)*43 = 344*y**3
  (8*y**3)*(-53*y) = -424*y**4
  (33*y**2)*43 = 1419*y**2
  (33*y**2)*(-53*y) = -1749*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -424*y**4 - 1749*y**3 + 344*y**3 + 1419*y**2</replace>
Combining like terms, got -424*y**4 - 1405*y**3 + 1419*y**2
<replace-#Step 5>#Step 6:
Current expression: -424*y**4 - 1405*y**3 + 1419*y**2</replace>
No more calculations needed.
<answer>-424*y**4 - 1405*y**3 + 1419*y**2</answer>


Question:
Calculate the following: 8*y**3*(45*y**3 + 64*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: 360*y**6 + 512*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 8*y**3*(45*y**3 + 64*y)
Expanding the part (45*y**3 + 64*y) using the distributive property, and we got: (64*y)*(8*y**3) + (8*y**3)*(45*y**3)
<replace-#Step 1>#Step 2:
Current expression: (64*y)*(8*y**3) + (8*y**3)*(45*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (45*y**3)*(8*y**3) = 360*y**6
  (64*y)*(8*y**3) = 512*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 360*y**6 + 512*y**4</replace>
No more calculations needed.
<answer>360*y**6 + 512*y**4</answer>


Question:
Simplify this expression: (-13*x**3 - 25)*(27*x**3 - 47*x**2 + 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -351*x**6 + 611*x**5 - 1000*x**3 + 1175*x**2 - 625


Question:
Calculate the following: (57 - 34*y)*(-30*y**3 + 14*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: 1020*y**4 - 2186*y**3 + 1172*y**2 - 627*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 - 34*y)*(-30*y**3 + 14*y**2 - 11*y)
Expanding the part (57 - 34*y) using the distributive property, and we got: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) + 57*(-30*y**3 + 14*y**2 - 11*y)
<replace-#Step 1>#Step 2:
Current expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) + 57*(-30*y**3 + 14*y**2 - 11*y)</replace>
Simplifying the partial expression: 57*(-30*y**3 + 14*y**2 - 11*y)
Expanding the part (-30*y**3 + 14*y**2 - 11*y) using the distributive property, and we got: -11*y*57 + (14*y**2)*57 - 30*y**3*57
Replacing 57*(-30*y**3 + 14*y**2 - 11*y) with -11*y*57 + (14*y**2)*57 - 30*y**3*57 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y) - 11*y*57 + (14*y**2)*57 - 30*y**3*57</replace>
Simplifying the partial expression: (-34*y)*(-30*y**3 + 14*y**2 - 11*y)
Expanding the part (-30*y**3 + 14*y**2 - 11*y) using the distributive property, and we got: (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3)
Replacing (-34*y)*(-30*y**3 + 14*y**2 - 11*y) with (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*y)*(-11*y) + (-34*y)*(14*y**2) + (-34*y)*(-30*y**3) - 11*y*57 + (14*y**2)*57 - 30*y**3*57</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*y**3)*57 = -1710*y**3
  (-30*y**3)*(-34*y) = 1020*y**4
  (-11*y)*57 = -627*y
  (-11*y)*(-34*y) = 374*y**2
  (14*y**2)*57 = 798*y**2
  (14*y**2)*(-34*y) = -476*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1020*y**4 - 1710*y**3 - 476*y**3 + 374*y**2 + 798*y**2 - 627*y</replace>
Combining like terms, got 1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y
<replace-#Step 5>#Step 6:
Current expression: 1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y</replace>
No more calculations needed.
<answer>1020*y**4 - 2186*y**3 + 1172*y**2 - 627*y</answer>


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

Answer: 403*x**5 + 26*x**4 - 620*x**3 - 40*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-31*x**2 - 2*x)*(-13*x**3 + 20*x)
Expanding the part (-31*x**2 - 2*x) using the distributive property, and we got: (-2*x)*(-13*x**3 + 20*x) + (-31*x**2)*(-13*x**3 + 20*x)
<replace-#Step 1>#Step 2:
Current expression: (-2*x)*(-13*x**3 + 20*x) + (-31*x**2)*(-13*x**3 + 20*x)</replace>
Simplifying the partial expression: (-31*x**2)*(-13*x**3 + 20*x)
Expanding the part (-13*x**3 + 20*x) using the distributive property, and we got: (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)
Replacing (-31*x**2)*(-13*x**3 + 20*x) with (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*x)*(-13*x**3 + 20*x) + (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)</replace>
Simplifying the partial expression: (-2*x)*(-13*x**3 + 20*x)
Expanding the part (-13*x**3 + 20*x) using the distributive property, and we got: (-2*x)*(20*x) + (-2*x)*(-13*x**3)
Replacing (-2*x)*(-13*x**3 + 20*x) with (-2*x)*(20*x) + (-2*x)*(-13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*x)*(20*x) + (-2*x)*(-13*x**3) + (20*x)*(-31*x**2) + (-31*x**2)*(-13*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*x**3)*(-31*x**2) = 403*x**5
  (-13*x**3)*(-2*x) = 26*x**4
  (20*x)*(-31*x**2) = -620*x**3
  (20*x)*(-2*x) = -40*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 403*x**5 + 26*x**4 - 620*x**3 - 40*x**2</replace>
No more calculations needed.
<answer>403*x**5 + 26*x**4 - 620*x**3 - 40*x**2</answer>


Question:
Simplify this expression: (34*x**2 + 47)*(28*x**3 + 63*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: 952*x**5 + 2142*x**4 + 1316*x**3 + 2961*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: (34*x**2 + 47)*(28*x**3 + 63*x**2)
Expanding the part (34*x**2 + 47) using the distributive property, and we got: (34*x**2)*(28*x**3 + 63*x**2) + 47*(28*x**3 + 63*x**2)
<replace-#Step 1>#Step 2:
Current expression: (34*x**2)*(28*x**3 + 63*x**2) + 47*(28*x**3 + 63*x**2)</replace>
Simplifying the partial expression: 47*(28*x**3 + 63*x**2)
Expanding the part (28*x**3 + 63*x**2) using the distributive property, and we got: (63*x**2)*47 + (28*x**3)*47
Replacing 47*(28*x**3 + 63*x**2) with (63*x**2)*47 + (28*x**3)*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*x**2)*(28*x**3 + 63*x**2) + (63*x**2)*47 + (28*x**3)*47</replace>
Simplifying the partial expression: (34*x**2)*(28*x**3 + 63*x**2)
Expanding the part (28*x**3 + 63*x**2) using the distributive property, and we got: (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3)
Replacing (34*x**2)*(28*x**3 + 63*x**2) with (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (34*x**2)*(63*x**2) + (34*x**2)*(28*x**3) + (63*x**2)*47 + (28*x**3)*47</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*x**3)*47 = 1316*x**3
  (28*x**3)*(34*x**2) = 952*x**5
  (63*x**2)*47 = 2961*x**2
  (63*x**2)*(34*x**2) = 2142*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2</replace>
No more calculations needed.
<answer>952*x**5 + 2142*x**4 + 1316*x**3 + 2961*x**2</answer>


Question:
Simplify this expression: (-19*y - 65)*(-35*y**3 + 36*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: 665*y**4 + 2275*y**3 - 684*y**2 - 2340*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-19*y - 65)*(-35*y**3 + 36*y)
Expanding the part (-19*y - 65) using the distributive property, and we got: (-19*y)*(-35*y**3 + 36*y) - 65*(-35*y**3 + 36*y)
<replace-#Step 1>#Step 2:
Current expression: (-19*y)*(-35*y**3 + 36*y) - 65*(-35*y**3 + 36*y)</replace>
Simplifying the partial expression: -65*(-35*y**3 + 36*y)
Expanding the part (-35*y**3 + 36*y) using the distributive property, and we got: (36*y)*(-65) - 35*y**3*(-65)
Replacing -65*(-35*y**3 + 36*y) with (36*y)*(-65) - 35*y**3*(-65) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-19*y)*(-35*y**3 + 36*y) + (36*y)*(-65) - 35*y**3*(-65)</replace>
Simplifying the partial expression: (-19*y)*(-35*y**3 + 36*y)
Expanding the part (-35*y**3 + 36*y) using the distributive property, and we got: (-19*y)*(36*y) + (-19*y)*(-35*y**3)
Replacing (-19*y)*(-35*y**3 + 36*y) with (-19*y)*(36*y) + (-19*y)*(-35*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-19*y)*(36*y) + (-19*y)*(-35*y**3) + (36*y)*(-65) - 35*y**3*(-65)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*y**3)*-65 = 2275*y**3
  (-35*y**3)*(-19*y) = 665*y**4
  (36*y)*-65 = -2340*y
  (36*y)*(-19*y) = -684*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 665*y**4 + 2275*y**3 - 684*y**2 - 2340*y</replace>
No more calculations needed.
<answer>665*y**4 + 2275*y**3 - 684*y**2 - 2340*y</answer>


Question:
Simplify this expression: (49*z**3 + 31*z**2)*(-37*z**3 + 27*z**2 - 21*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: -1813*z**6 + 176*z**5 - 192*z**4 - 651*z**3


Question:
Calculate the following: 50*x**3*(4*x**3 - 34*x**2 - 42*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: 200*x**6 - 1700*x**5 - 2100*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 50*x**3*(4*x**3 - 34*x**2 - 42*x)
Expanding the part (4*x**3 - 34*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(50*x**3) + (-34*x**2)*(50*x**3) + (4*x**3)*(50*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-42*x)*(50*x**3) + (-34*x**2)*(50*x**3) + (4*x**3)*(50*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x)*(50*x**3) = -2100*x**4
  (-34*x**2)*(50*x**3) = -1700*x**5
  (4*x**3)*(50*x**3) = 200*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 200*x**6 - 1700*x**5 - 2100*x**4</replace>
No more calculations needed.
<answer>200*x**6 - 1700*x**5 - 2100*x**4</answer>


Question:
Simplify this expression: (2*z**2 - 9*z)*(44*z**3 + 25*z + 59)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2*z**2 - 9*z)*(44*z**3 + 25*z + 59)
Expanding the part (2*z**2 - 9*z) using the distributive property, and we got: (-9*z)*(44*z**3 + 25*z + 59) + (2*z**2)*(44*z**3 + 25*z + 59)
<replace-#Step 1>#Step 2:
Current expression: (-9*z)*(44*z**3 + 25*z + 59) + (2*z**2)*(44*z**3 + 25*z + 59)</replace>
Simplifying the partial expression: (-9*z)*(44*z**3 + 25*z + 59)
Expanding the part (44*z**3 + 25*z + 59) using the distributive property, and we got: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9*z)
Replacing (-9*z)*(44*z**3 + 25*z + 59) with (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9*z) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*(-9)*z + (2*z**2)*(44*z**3 + 25*z + 59)</replace>
Simplifying the partial expression: (2*z**2)*(44*z**3 + 25*z + 59)
Expanding the part (44*z**3 + 25*z + 59) using the distributive property, and we got: 59*(2*z**2) + (25*z)*(2*z**2) + (2*z**2)*(44*z**3)
Replacing (2*z**2)*(44*z**3 + 25*z + 59) with 59*(2*z**2) + (25*z)*(2*z**2) + (2*z**2)*(44*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-9*z)*(25*z) + (-9*z)*(44*z**3) + 59*2*z**2 + 59*(-9)*z + (25*z)*(2*z**2) + (2*z**2)*(44*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (25*z)*(-9*z) = -225*z**2
  (25*z)*(2*z**2) = 50*z**3
  (44*z**3)*(-9*z) = -396*z**4
  (44*z**3)*(2*z**2) = 88*z**5
  59*-9*z = -531*z
  59*2*z**2 = 118*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 88*z**5 - 396*z**4 + 50*z**3 - 225*z**2 + 118*z**2 - 531*z</replace>
Combining like terms, got 88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z
<replace-#Step 5>#Step 6:
Current expression: 88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z</replace>
No more calculations needed.
<answer>88*z**5 - 396*z**4 + 50*z**3 - 107*z**2 - 531*z</answer>


Question:
Simplify this expression: (28*y**3 + y**2 - 22)*(-38*y**3 - 35*y**2 - 17*y + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1064*y**6 - 1018*y**5 - 511*y**4 + 1603*y**3 + 798*y**2 + 374*y - 616


Question:
Simplify this expression: (14 - 41*z**2)*(-13*z**3 - 5*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: 533*z**5 + 23*z**3 - 70*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 - 41*z**2)*(-13*z**3 - 5*z)
Expanding the part (14 - 41*z**2) using the distributive property, and we got: (-41*z**2)*(-13*z**3 - 5*z) + 14*(-13*z**3 - 5*z)
<replace-#Step 1>#Step 2:
Current expression: (-41*z**2)*(-13*z**3 - 5*z) + 14*(-13*z**3 - 5*z)</replace>
Simplifying the partial expression: 14*(-13*z**3 - 5*z)
Expanding the part (-13*z**3 - 5*z) using the distributive property, and we got: -5*z*14 - 13*z**3*14
Replacing 14*(-13*z**3 - 5*z) with -5*z*14 - 13*z**3*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -5*z*14 + (-41*z**2)*(-13*z**3 - 5*z) - 13*z**3*14</replace>
Simplifying the partial expression: (-41*z**2)*(-13*z**3 - 5*z)
Expanding the part (-13*z**3 - 5*z) using the distributive property, and we got: (-5*z)*(-41*z**2) + (-41*z**2)*(-13*z**3)
Replacing (-41*z**2)*(-13*z**3 - 5*z) with (-5*z)*(-41*z**2) + (-41*z**2)*(-13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*z)*(-41*z**2) - 5*z*14 + (-41*z**2)*(-13*z**3) - 13*z**3*14</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-13*z**3)*14 = -182*z**3
  (-13*z**3)*(-41*z**2) = 533*z**5
  (-5*z)*14 = -70*z
  (-5*z)*(-41*z**2) = 205*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 533*z**5 - 182*z**3 + 205*z**3 - 70*z</replace>
Combining like terms, got 533*z**5 + 23*z**3 - 70*z
<replace-#Step 5>#Step 6:
Current expression: 533*z**5 + 23*z**3 - 70*z</replace>
No more calculations needed.
<answer>533*z**5 + 23*z**3 - 70*z</answer>


Question:
Simplify this expression: (28*x + 79)*(-28*x**2 - 28*x - 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -784*x**3 - 2996*x**2 - 3416*x - 3397

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: (28*x + 79)*(-28*x**2 - 28*x - 43)
Expanding the part (28*x + 79) using the distributive property, and we got: (28*x)*(-28*x**2 - 28*x - 43) + 79*(-28*x**2 - 28*x - 43)
<replace-#Step 1>#Step 2:
Current expression: (28*x)*(-28*x**2 - 28*x - 43) + 79*(-28*x**2 - 28*x - 43)</replace>
Simplifying the partial expression: 79*(-28*x**2 - 28*x - 43)
Expanding the part (-28*x**2 - 28*x - 43) using the distributive property, and we got: -28*x*79 - 28*x**2*79 - 43*79
Replacing 79*(-28*x**2 - 28*x - 43) with -28*x*79 - 28*x**2*79 - 43*79 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -28*x*79 + (28*x)*(-28*x**2 - 28*x - 43) - 28*x**2*79 - 3397</replace>
Simplifying the partial expression: (28*x)*(-28*x**2 - 28*x - 43)
Expanding the part (-28*x**2 - 28*x - 43) using the distributive property, and we got: (-28*x)*(28*x) - 1204*x + (28*x)*(-28*x**2)
Replacing (28*x)*(-28*x**2 - 28*x - 43) with (-28*x)*(28*x) - 1204*x + (28*x)*(-28*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-28*x)*(28*x) - 28*x*79 - 43*28*x + (28*x)*(-28*x**2) - 28*x**2*79 - 3397</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*x)*79 = -2212*x
  (-28*x)*(28*x) = -784*x**2
  (-28*x**2)*79 = -2212*x**2
  (-28*x**2)*(28*x) = -784*x**3
  -43*28*x = -1204*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -784*x**3 - 2212*x**2 - 784*x**2 - 2212*x - 1204*x - 3397</replace>
Combining like terms, got -784*x**3 - 2996*x**2 - 3416*x - 3397
<replace-#Step 5>#Step 6:
Current expression: -784*x**3 - 2996*x**2 - 3416*x - 3397</replace>
No more calculations needed.
<answer>-784*x**3 - 2996*x**2 - 3416*x - 3397</answer>


Question:
Calculate the following: (47 - 10*z**2)*(20*z**3 - 63)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -200*z**5 + 940*z**3 + 630*z**2 - 2961

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 - 10*z**2)*(20*z**3 - 63)
Expanding the part (20*z**3 - 63) using the distributive property, and we got: (20*z**3)*(47 - 10*z**2) - 63*(47 - 10*z**2)
<replace-#Step 1>#Step 2:
Current expression: (20*z**3)*(47 - 10*z**2) - 63*(47 - 10*z**2)</replace>
Simplifying the partial expression: -63*(47 - 10*z**2)
Expanding the part (47 - 10*z**2) using the distributive property, and we got: -10*z**2*(-63) + 47*(-63)
Replacing -63*(47 - 10*z**2) with -10*z**2*(-63) + 47*(-63) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -10*z**2*(-63) + (20*z**3)*(47 - 10*z**2) - 2961</replace>
Simplifying the partial expression: (20*z**3)*(47 - 10*z**2)
Expanding the part (47 - 10*z**2) using the distributive property, and we got: 47*(20*z**3) + (-10*z**2)*(20*z**3)
Replacing (20*z**3)*(47 - 10*z**2) with 47*(20*z**3) + (-10*z**2)*(20*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 47*20*z**3 + (-10*z**2)*(20*z**3) - 10*z**2*(-63) - 2961</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-10*z**2)*-63 = 630*z**2
  (-10*z**2)*(20*z**3) = -200*z**5
  47*20*z**3 = 940*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -200*z**5 + 940*z**3 + 630*z**2 - 2961</replace>
No more calculations needed.
<answer>-200*z**5 + 940*z**3 + 630*z**2 - 2961</answer>


Question:
Simplify this expression: -47*x**3*(22*x**2 - 11*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: -1034*x**5 + 517*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -47*x**3*(22*x**2 - 11*x)
Expanding the part (22*x**2 - 11*x) using the distributive property, and we got: (-11*x)*(-47*x**3) + (22*x**2)*(-47*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-11*x)*(-47*x**3) + (22*x**2)*(-47*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*x)*(-47*x**3) = 517*x**4
  (22*x**2)*(-47*x**3) = -1034*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1034*x**5 + 517*x**4</replace>
No more calculations needed.
<answer>-1034*x**5 + 517*x**4</answer>


Question:
Simplify this expression: (-24*y**3 - 4*y**2)*(-14*y**3 - 51*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: 336*y**6 + 1280*y**5 + 204*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-24*y**3 - 4*y**2)*(-14*y**3 - 51*y**2)
Expanding the part (-14*y**3 - 51*y**2) using the distributive property, and we got: (-51*y**2)*(-24*y**3 - 4*y**2) + (-14*y**3)*(-24*y**3 - 4*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-51*y**2)*(-24*y**3 - 4*y**2) + (-14*y**3)*(-24*y**3 - 4*y**2)</replace>
Simplifying the partial expression: (-51*y**2)*(-24*y**3 - 4*y**2)
Expanding the part (-24*y**3 - 4*y**2) using the distributive property, and we got: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3)
Replacing (-51*y**2)*(-24*y**3 - 4*y**2) with (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) + (-14*y**3)*(-24*y**3 - 4*y**2)</replace>
Simplifying the partial expression: (-14*y**3)*(-24*y**3 - 4*y**2)
Expanding the part (-24*y**3 - 4*y**2) using the distributive property, and we got: (-4*y**2)*(-14*y**3) + (-24*y**3)*(-14*y**3)
Replacing (-14*y**3)*(-24*y**3 - 4*y**2) with (-4*y**2)*(-14*y**3) + (-24*y**3)*(-14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-51*y**2)*(-4*y**2) + (-51*y**2)*(-24*y**3) + (-4*y**2)*(-14*y**3) + (-24*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:
  (-24*y**3)*(-51*y**2) = 1224*y**5
  (-24*y**3)*(-14*y**3) = 336*y**6
  (-4*y**2)*(-51*y**2) = 204*y**4
  (-4*y**2)*(-14*y**3) = 56*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 336*y**6 + 56*y**5 + 1224*y**5 + 204*y**4</replace>
Combining like terms, got 336*y**6 + 1280*y**5 + 204*y**4
<replace-#Step 5>#Step 6:
Current expression: 336*y**6 + 1280*y**5 + 204*y**4</replace>
No more calculations needed.
<answer>336*y**6 + 1280*y**5 + 204*y**4</answer>


Question:
Simplify this expression: (12*x**3 + 41*x - 19)*(10*x**3 + 39*x**2 + x - 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: 120*x**6 + 468*x**5 + 422*x**4 + 1169*x**3 - 700*x**2 - 839*x + 380


Question:
Simplify this expression: (15 - 68*z**2)*(9*z**2 - 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: -612*z**4 + 1427*z**2 - 285

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (15 - 68*z**2)*(9*z**2 - 19)
Expanding the part (9*z**2 - 19) using the distributive property, and we got: (9*z**2)*(15 - 68*z**2) - 19*(15 - 68*z**2)
<replace-#Step 1>#Step 2:
Current expression: (9*z**2)*(15 - 68*z**2) - 19*(15 - 68*z**2)</replace>
Simplifying the partial expression: -19*(15 - 68*z**2)
Expanding the part (15 - 68*z**2) using the distributive property, and we got: -68*z**2*(-19) + 15*(-19)
Replacing -19*(15 - 68*z**2) with -68*z**2*(-19) + 15*(-19) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -68*z**2*(-19) + (9*z**2)*(15 - 68*z**2) - 285</replace>
Simplifying the partial expression: (9*z**2)*(15 - 68*z**2)
Expanding the part (15 - 68*z**2) using the distributive property, and we got: 15*(9*z**2) + (-68*z**2)*(9*z**2)
Replacing (9*z**2)*(15 - 68*z**2) with 15*(9*z**2) + (-68*z**2)*(9*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 15*9*z**2 + (-68*z**2)*(9*z**2) - 68*z**2*(-19) - 285</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*z**2)*-19 = 1292*z**2
  (-68*z**2)*(9*z**2) = -612*z**4
  15*9*z**2 = 135*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -612*z**4 + 135*z**2 + 1292*z**2 - 285</replace>
Combining like terms, got -612*z**4 + 1427*z**2 - 285
<replace-#Step 5>#Step 6:
Current expression: -612*z**4 + 1427*z**2 - 285</replace>
No more calculations needed.
<answer>-612*z**4 + 1427*z**2 - 285</answer>


Question:
Calculate the following: (2*x**2 - 27)*(20*x**3 + 21*x**2 + 71*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 40*x**5 + 42*x**4 - 398*x**3 - 567*x**2 - 1917*x


Question:
Calculate the following: (-13*x**3 + 26*x**2)*(-7*x**2 - 8*x - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 91*x**5 - 78*x**4 + 104*x**3 - 624*x**2


Question:
Calculate the following: (9*z**2 + 58)*(45*z**2 - 22)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 405*z**4 + 2412*z**2 - 1276

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (9*z**2 + 58)*(45*z**2 - 22)
Expanding the part (45*z**2 - 22) using the distributive property, and we got: (45*z**2)*(9*z**2 + 58) - 22*(9*z**2 + 58)
<replace-#Step 1>#Step 2:
Current expression: (45*z**2)*(9*z**2 + 58) - 22*(9*z**2 + 58)</replace>
Simplifying the partial expression: -22*(9*z**2 + 58)
Expanding the part (9*z**2 + 58) using the distributive property, and we got: (9*z**2)*(-22) + 58*(-22)
Replacing -22*(9*z**2 + 58) with (9*z**2)*(-22) + 58*(-22) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*z**2)*(-22) + (45*z**2)*(9*z**2 + 58) - 1276</replace>
Simplifying the partial expression: (45*z**2)*(9*z**2 + 58)
Expanding the part (9*z**2 + 58) using the distributive property, and we got: 58*(45*z**2) + (9*z**2)*(45*z**2)
Replacing (45*z**2)*(9*z**2 + 58) with 58*(45*z**2) + (9*z**2)*(45*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 58*45*z**2 + (9*z**2)*(45*z**2) + (9*z**2)*(-22) - 1276</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*z**2)*-22 = -198*z**2
  (9*z**2)*(45*z**2) = 405*z**4
  58*45*z**2 = 2610*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 405*z**4 - 198*z**2 + 2610*z**2 - 1276</replace>
Combining like terms, got 405*z**4 + 2412*z**2 - 1276
<replace-#Step 5>#Step 6:
Current expression: 405*z**4 + 2412*z**2 - 1276</replace>
No more calculations needed.
<answer>405*z**4 + 2412*z**2 - 1276</answer>


Question:
Calculate the following: (48*z**2 - 2*z + 22)*(34*z**3 - 2*z**2 - 49*z + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1632*z**5 - 164*z**4 - 1600*z**3 + 2070*z**2 - 1162*z + 924


Question:
Calculate the following: (107 - 48*y**3)*(14*y**3 + 9*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -672*y**6 - 432*y**5 + 1498*y**3 + 963*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: (107 - 48*y**3)*(14*y**3 + 9*y**2)
Expanding the part (107 - 48*y**3) using the distributive property, and we got: (-48*y**3)*(14*y**3 + 9*y**2) + 107*(14*y**3 + 9*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-48*y**3)*(14*y**3 + 9*y**2) + 107*(14*y**3 + 9*y**2)</replace>
Simplifying the partial expression: 107*(14*y**3 + 9*y**2)
Expanding the part (14*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*107 + (14*y**3)*107
Replacing 107*(14*y**3 + 9*y**2) with (9*y**2)*107 + (14*y**3)*107 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y**2)*107 + (-48*y**3)*(14*y**3 + 9*y**2) + (14*y**3)*107</replace>
Simplifying the partial expression: (-48*y**3)*(14*y**3 + 9*y**2)
Expanding the part (14*y**3 + 9*y**2) using the distributive property, and we got: (9*y**2)*(-48*y**3) + (-48*y**3)*(14*y**3)
Replacing (-48*y**3)*(14*y**3 + 9*y**2) with (9*y**2)*(-48*y**3) + (-48*y**3)*(14*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*y**2)*(-48*y**3) + (9*y**2)*107 + (-48*y**3)*(14*y**3) + (14*y**3)*107</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*y**2)*107 = 963*y**2
  (9*y**2)*(-48*y**3) = -432*y**5
  (14*y**3)*107 = 1498*y**3
  (14*y**3)*(-48*y**3) = -672*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2</replace>
No more calculations needed.
<answer>-672*y**6 - 432*y**5 + 1498*y**3 + 963*y**2</answer>


Question:
Calculate the following: (4 - 15*y**3)*(32*y**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: -480*y**5 - 255*y**3 + 128*y**2 + 68

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (4 - 15*y**3)*(32*y**2 + 17)
Expanding the part (4 - 15*y**3) using the distributive property, and we got: (-15*y**3)*(32*y**2 + 17) + 4*(32*y**2 + 17)
<replace-#Step 1>#Step 2:
Current expression: (-15*y**3)*(32*y**2 + 17) + 4*(32*y**2 + 17)</replace>
Simplifying the partial expression: 4*(32*y**2 + 17)
Expanding the part (32*y**2 + 17) using the distributive property, and we got: (32*y**2)*4 + 17*4
Replacing 4*(32*y**2 + 17) with (32*y**2)*4 + 17*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (32*y**2)*4 + (-15*y**3)*(32*y**2 + 17) + 68</replace>
Simplifying the partial expression: (-15*y**3)*(32*y**2 + 17)
Expanding the part (32*y**2 + 17) using the distributive property, and we got: 17*(-15*y**3) + (32*y**2)*(-15*y**3)
Replacing (-15*y**3)*(32*y**2 + 17) with 17*(-15*y**3) + (32*y**2)*(-15*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*(-15)*y**3 + (32*y**2)*(-15*y**3) + (32*y**2)*4 + 68</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*y**2)*4 = 128*y**2
  (32*y**2)*(-15*y**3) = -480*y**5
  17*-15*y**3 = -255*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -480*y**5 - 255*y**3 + 128*y**2 + 68</replace>
No more calculations needed.
<answer>-480*y**5 - 255*y**3 + 128*y**2 + 68</answer>


Question:
Simplify this expression: (-11*y**3 + y**2)*(45*y**3 + 40*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: -495*y**6 + 45*y**5 - 440*y**4 + 40*y**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-11*y**3 + y**2)*(45*y**3 + 40*y)
Expanding the part (-11*y**3 + y**2) using the distributive property, and we got: y**2*(45*y**3 + 40*y) + (-11*y**3)*(45*y**3 + 40*y)
<replace-#Step 1>#Step 2:
Current expression: y**2*(45*y**3 + 40*y) + (-11*y**3)*(45*y**3 + 40*y)</replace>
Simplifying the partial expression: y**2*(45*y**3 + 40*y)
Expanding the part (45*y**3 + 40*y) using the distributive property, and we got: (40*y)*y**2 + y**2*(45*y**3)
Replacing y**2*(45*y**3 + 40*y) with (40*y)*y**2 + y**2*(45*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*y)*y**2 + y**2*(45*y**3) + (-11*y**3)*(45*y**3 + 40*y)</replace>
Simplifying the partial expression: (-11*y**3)*(45*y**3 + 40*y)
Expanding the part (45*y**3 + 40*y) using the distributive property, and we got: (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3)
Replacing (-11*y**3)*(45*y**3 + 40*y) with (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (40*y)*y**2 + y**2*(45*y**3) + (40*y)*(-11*y**3) + (-11*y**3)*(45*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (40*y)*y**2 = 40*y**3
  (40*y)*(-11*y**3) = -440*y**4
  (45*y**3)*y**2 = 45*y**5
  (45*y**3)*(-11*y**3) = -495*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -495*y**6 + 45*y**5 - 440*y**4 + 40*y**3</replace>
No more calculations needed.
<answer>-495*y**6 + 45*y**5 - 440*y**4 + 40*y**3</answer>


Question:
Calculate the following: -14*y*(-33*y**2 - 61)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 462*y**3 + 854*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: -14*y*(-33*y**2 - 61)
Expanding the part (-33*y**2 - 61) using the distributive property, and we got: (-14*y)*(-33*y**2) - (-1)*854*y
<replace-#Step 1>#Step 2:
Current expression: (-14*y)*(-33*y**2) - (-1)*854*y</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -61*(-14*y) = 854*y
  (-33*y**2)*(-14*y) = 462*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 462*y**3 + 854*y</replace>
No more calculations needed.
<answer>462*y**3 + 854*y</answer>


Question:
Simplify this expression: (-18*z**3 + 19*z)*(-46*z**3 - 59*z - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*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: (-18*z**3 + 19*z)*(-46*z**3 - 59*z - 1)
Expanding the part (-18*z**3 + 19*z) using the distributive property, and we got: (19*z)*(-46*z**3 - 59*z - 1) + (-18*z**3)*(-46*z**3 - 59*z - 1)
<replace-#Step 1>#Step 2:
Current expression: (19*z)*(-46*z**3 - 59*z - 1) + (-18*z**3)*(-46*z**3 - 59*z - 1)</replace>
Simplifying the partial expression: (-18*z**3)*(-46*z**3 - 59*z - 1)
Expanding the part (-46*z**3 - 59*z - 1) using the distributive property, and we got: (-59*z)*(-18*z**3) - (-1)*18*z**3 + (-46*z**3)*(-18*z**3)
Replacing (-18*z**3)*(-46*z**3 - 59*z - 1) with (-59*z)*(-18*z**3) - (-1)*18*z**3 + (-46*z**3)*(-18*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-59*z)*(-18*z**3) - 1*(-18)*z**3 + (19*z)*(-46*z**3 - 59*z - 1) + (-46*z**3)*(-18*z**3)</replace>
Simplifying the partial expression: (19*z)*(-46*z**3 - 59*z - 1)
Expanding the part (-46*z**3 - 59*z - 1) using the distributive property, and we got: (-59*z)*(19*z) - 19*z + (19*z)*(-46*z**3)
Replacing (19*z)*(-46*z**3 - 59*z - 1) with (-59*z)*(19*z) - 19*z + (19*z)*(-46*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-59*z)*(19*z) + (-59*z)*(-18*z**3) - 1*(-18)*z**3 - 1*19*z + (19*z)*(-46*z**3) + (-46*z**3)*(-18*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-59*z)*(-18*z**3) = 1062*z**4
  (-59*z)*(19*z) = -1121*z**2
  (-46*z**3)*(-18*z**3) = 828*z**6
  (-46*z**3)*(19*z) = -874*z**4
  -1*-18*z**3 = 18*z**3
  -1*19*z = -19*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 828*z**6 - 874*z**4 + 1062*z**4 + 18*z**3 - 1121*z**2 - 19*z</replace>
Combining like terms, got 828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z
<replace-#Step 5>#Step 6:
Current expression: 828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z</replace>
No more calculations needed.
<answer>828*z**6 + 188*z**4 + 18*z**3 - 1121*z**2 - 19*z</answer>


Question:
Simplify this expression: (-4*z**3 - 2*z**2)*(3*z**3 + 31*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: -12*z**6 - 6*z**5 - 124*z**4 - 62*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: (-4*z**3 - 2*z**2)*(3*z**3 + 31*z)
Expanding the part (-4*z**3 - 2*z**2) using the distributive property, and we got: (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3 + 31*z)
<replace-#Step 1>#Step 2:
Current expression: (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3 + 31*z)</replace>
Simplifying the partial expression: (-4*z**3)*(3*z**3 + 31*z)
Expanding the part (3*z**3 + 31*z) using the distributive property, and we got: (31*z)*(-4*z**3) + (-4*z**3)*(3*z**3)
Replacing (-4*z**3)*(3*z**3 + 31*z) with (31*z)*(-4*z**3) + (-4*z**3)*(3*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (31*z)*(-4*z**3) + (-2*z**2)*(3*z**3 + 31*z) + (-4*z**3)*(3*z**3)</replace>
Simplifying the partial expression: (-2*z**2)*(3*z**3 + 31*z)
Expanding the part (3*z**3 + 31*z) using the distributive property, and we got: (31*z)*(-2*z**2) + (-2*z**2)*(3*z**3)
Replacing (-2*z**2)*(3*z**3 + 31*z) with (31*z)*(-2*z**2) + (-2*z**2)*(3*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (31*z)*(-2*z**2) + (31*z)*(-4*z**3) + (-2*z**2)*(3*z**3) + (-4*z**3)*(3*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*z**3)*(-4*z**3) = -12*z**6
  (3*z**3)*(-2*z**2) = -6*z**5
  (31*z)*(-4*z**3) = -124*z**4
  (31*z)*(-2*z**2) = -62*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -12*z**6 - 6*z**5 - 124*z**4 - 62*z**3</replace>
No more calculations needed.
<answer>-12*z**6 - 6*z**5 - 124*z**4 - 62*z**3</answer>


Question:
Simplify this expression: (5 - 34*x**2)*(33*x**2 + 23*x - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105

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 - 34*x**2)*(33*x**2 + 23*x - 21)
Expanding the part (5 - 34*x**2) using the distributive property, and we got: (-34*x**2)*(33*x**2 + 23*x - 21) + 5*(33*x**2 + 23*x - 21)
<replace-#Step 1>#Step 2:
Current expression: (-34*x**2)*(33*x**2 + 23*x - 21) + 5*(33*x**2 + 23*x - 21)</replace>
Simplifying the partial expression: 5*(33*x**2 + 23*x - 21)
Expanding the part (33*x**2 + 23*x - 21) using the distributive property, and we got: (23*x)*5 + (33*x**2)*5 - 21*5
Replacing 5*(33*x**2 + 23*x - 21) with (23*x)*5 + (33*x**2)*5 - 21*5 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*x)*5 + (-34*x**2)*(33*x**2 + 23*x - 21) + (33*x**2)*5 - 105</replace>
Simplifying the partial expression: (-34*x**2)*(33*x**2 + 23*x - 21)
Expanding the part (33*x**2 + 23*x - 21) using the distributive property, and we got: -(-1)*714*x**2 + (23*x)*(-34*x**2) + (-34*x**2)*(33*x**2)
Replacing (-34*x**2)*(33*x**2 + 23*x - 21) with -(-1)*714*x**2 + (23*x)*(-34*x**2) + (-34*x**2)*(33*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -21*(-34)*x**2 + (23*x)*(-34*x**2) + (23*x)*5 + (-34*x**2)*(33*x**2) + (33*x**2)*5 - 105</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*x)*5 = 115*x
  (23*x)*(-34*x**2) = -782*x**3
  (33*x**2)*5 = 165*x**2
  (33*x**2)*(-34*x**2) = -1122*x**4
  -21*-34*x**2 = 714*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1122*x**4 - 782*x**3 + 165*x**2 + 714*x**2 + 115*x - 105</replace>
Combining like terms, got -1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105
<replace-#Step 5>#Step 6:
Current expression: -1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105</replace>
No more calculations needed.
<answer>-1122*x**4 - 782*x**3 + 879*x**2 + 115*x - 105</answer>


Question:
Simplify this expression: (-45*x**2 - 47)*(45*x**3 - 35*x + 65)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055

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*x**2 - 47)*(45*x**3 - 35*x + 65)
Expanding the part (-45*x**2 - 47) using the distributive property, and we got: (-45*x**2)*(45*x**3 - 35*x + 65) - 47*(45*x**3 - 35*x + 65)
<replace-#Step 1>#Step 2:
Current expression: (-45*x**2)*(45*x**3 - 35*x + 65) - 47*(45*x**3 - 35*x + 65)</replace>
Simplifying the partial expression: -47*(45*x**3 - 35*x + 65)
Expanding the part (45*x**3 - 35*x + 65) using the distributive property, and we got: -35*x*(-47) + (45*x**3)*(-47) + 65*(-47)
Replacing -47*(45*x**3 - 35*x + 65) with -35*x*(-47) + (45*x**3)*(-47) + 65*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*x*(-47) + (-45*x**2)*(45*x**3 - 35*x + 65) + (45*x**3)*(-47) - 3055</replace>
Simplifying the partial expression: (-45*x**2)*(45*x**3 - 35*x + 65)
Expanding the part (45*x**3 - 35*x + 65) using the distributive property, and we got: (-35*x)*(-45*x**2) + 65*(-45*x**2) + (-45*x**2)*(45*x**3)
Replacing (-45*x**2)*(45*x**3 - 35*x + 65) with (-35*x)*(-45*x**2) + 65*(-45*x**2) + (-45*x**2)*(45*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*x)*(-45*x**2) - 35*x*(-47) + 65*(-45)*x**2 + (-45*x**2)*(45*x**3) + (45*x**3)*(-47) - 3055</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*x)*-47 = 1645*x
  (-35*x)*(-45*x**2) = 1575*x**3
  (45*x**3)*-47 = -2115*x**3
  (45*x**3)*(-45*x**2) = -2025*x**5
  65*-45*x**2 = -2925*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2025*x**5 - 2115*x**3 + 1575*x**3 - 2925*x**2 + 1645*x - 3055</replace>
Combining like terms, got -2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055
<replace-#Step 5>#Step 6:
Current expression: -2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055</replace>
No more calculations needed.
<answer>-2025*x**5 - 540*x**3 - 2925*x**2 + 1645*x - 3055</answer>


Question:
Simplify this expression: (-14*x**2 - 31)*(-22*x**2 + 36*x + 67)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-14*x**2 - 31)*(-22*x**2 + 36*x + 67)
Expanding the part (-14*x**2 - 31) using the distributive property, and we got: (-14*x**2)*(-22*x**2 + 36*x + 67) - 31*(-22*x**2 + 36*x + 67)
<replace-#Step 1>#Step 2:
Current expression: (-14*x**2)*(-22*x**2 + 36*x + 67) - 31*(-22*x**2 + 36*x + 67)</replace>
Simplifying the partial expression: -31*(-22*x**2 + 36*x + 67)
Expanding the part (-22*x**2 + 36*x + 67) using the distributive property, and we got: (36*x)*(-31) - 22*x**2*(-31) + 67*(-31)
Replacing -31*(-22*x**2 + 36*x + 67) with (36*x)*(-31) - 22*x**2*(-31) + 67*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*x)*(-31) - 22*x**2*(-31) + (-14*x**2)*(-22*x**2 + 36*x + 67) - 2077</replace>
Simplifying the partial expression: (-14*x**2)*(-22*x**2 + 36*x + 67)
Expanding the part (-22*x**2 + 36*x + 67) using the distributive property, and we got: 67*(-14*x**2) + (36*x)*(-14*x**2) + (-22*x**2)*(-14*x**2)
Replacing (-14*x**2)*(-22*x**2 + 36*x + 67) with 67*(-14*x**2) + (36*x)*(-14*x**2) + (-22*x**2)*(-14*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 67*(-14)*x**2 + (36*x)*(-14*x**2) + (36*x)*(-31) + (-22*x**2)*(-14*x**2) - 22*x**2*(-31) - 2077</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x**2)*-31 = 682*x**2
  (-22*x**2)*(-14*x**2) = 308*x**4
  (36*x)*-31 = -1116*x
  (36*x)*(-14*x**2) = -504*x**3
  67*-14*x**2 = -938*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 308*x**4 - 504*x**3 - 938*x**2 + 682*x**2 - 1116*x - 2077</replace>
Combining like terms, got 308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077
<replace-#Step 5>#Step 6:
Current expression: 308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077</replace>
No more calculations needed.
<answer>308*x**4 - 504*x**3 - 256*x**2 - 1116*x - 2077</answer>


Question:
Simplify this expression: (46*x**3 + 17*x)*(27*x**3 + 20*x + 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: 1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46*x**3 + 17*x)*(27*x**3 + 20*x + 15)
Expanding the part (46*x**3 + 17*x) using the distributive property, and we got: (17*x)*(27*x**3 + 20*x + 15) + (46*x**3)*(27*x**3 + 20*x + 15)
<replace-#Step 1>#Step 2:
Current expression: (17*x)*(27*x**3 + 20*x + 15) + (46*x**3)*(27*x**3 + 20*x + 15)</replace>
Simplifying the partial expression: (17*x)*(27*x**3 + 20*x + 15)
Expanding the part (27*x**3 + 20*x + 15) using the distributive property, and we got: 15*(17*x) + (17*x)*(20*x) + (17*x)*(27*x**3)
Replacing (17*x)*(27*x**3 + 20*x + 15) with 15*(17*x) + (17*x)*(20*x) + (17*x)*(27*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 15*17*x + (17*x)*(20*x) + (17*x)*(27*x**3) + (46*x**3)*(27*x**3 + 20*x + 15)</replace>
Simplifying the partial expression: (46*x**3)*(27*x**3 + 20*x + 15)
Expanding the part (27*x**3 + 20*x + 15) using the distributive property, and we got: 15*(46*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3)
Replacing (46*x**3)*(27*x**3 + 20*x + 15) with 15*(46*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 15*46*x**3 + 15*17*x + (17*x)*(20*x) + (17*x)*(27*x**3) + (20*x)*(46*x**3) + (27*x**3)*(46*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*x)*(17*x) = 340*x**2
  (20*x)*(46*x**3) = 920*x**4
  (27*x**3)*(17*x) = 459*x**4
  (27*x**3)*(46*x**3) = 1242*x**6
  15*17*x = 255*x
  15*46*x**3 = 690*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1242*x**6 + 459*x**4 + 920*x**4 + 690*x**3 + 340*x**2 + 255*x</replace>
Combining like terms, got 1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x
<replace-#Step 5>#Step 6:
Current expression: 1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x</replace>
No more calculations needed.
<answer>1242*x**6 + 1379*x**4 + 690*x**3 + 340*x**2 + 255*x</answer>


Question:
Calculate the following: (23*z**2 - 35*z + 36)*(72*z**3 - 22*z**2 + 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1656*z**5 - 3026*z**4 + 3362*z**3 - 79*z**2 - 1085*z + 1116


Question:
Simplify this expression: (37 - 35*z**3)*(-17*z**3 - 32*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: 595*z**6 + 1120*z**4 - 629*z**3 - 1184*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: (37 - 35*z**3)*(-17*z**3 - 32*z)
Expanding the part (37 - 35*z**3) using the distributive property, and we got: (-35*z**3)*(-17*z**3 - 32*z) + 37*(-17*z**3 - 32*z)
<replace-#Step 1>#Step 2:
Current expression: (-35*z**3)*(-17*z**3 - 32*z) + 37*(-17*z**3 - 32*z)</replace>
Simplifying the partial expression: 37*(-17*z**3 - 32*z)
Expanding the part (-17*z**3 - 32*z) using the distributive property, and we got: -32*z*37 - 17*z**3*37
Replacing 37*(-17*z**3 - 32*z) with -32*z*37 - 17*z**3*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -32*z*37 + (-35*z**3)*(-17*z**3 - 32*z) - 17*z**3*37</replace>
Simplifying the partial expression: (-35*z**3)*(-17*z**3 - 32*z)
Expanding the part (-17*z**3 - 32*z) using the distributive property, and we got: (-32*z)*(-35*z**3) + (-35*z**3)*(-17*z**3)
Replacing (-35*z**3)*(-17*z**3 - 32*z) with (-32*z)*(-35*z**3) + (-35*z**3)*(-17*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-32*z)*(-35*z**3) - 32*z*37 + (-35*z**3)*(-17*z**3) - 17*z**3*37</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*z)*37 = -1184*z
  (-32*z)*(-35*z**3) = 1120*z**4
  (-17*z**3)*37 = -629*z**3
  (-17*z**3)*(-35*z**3) = 595*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 595*z**6 + 1120*z**4 - 629*z**3 - 1184*z</replace>
No more calculations needed.
<answer>595*z**6 + 1120*z**4 - 629*z**3 - 1184*z</answer>


Question:
Calculate the following: (-47*x**3 - 15)*(32*x**3 + 8*x**2 - 19*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: -1504*x**6 - 376*x**5 + 893*x**4 - 480*x**3 - 120*x**2 + 285*x


Question:
Calculate the following: (10*y**2 + 6)*(-27*y**3 - 16*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: -270*y**5 - 322*y**3 - 96*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: (10*y**2 + 6)*(-27*y**3 - 16*y)
Expanding the part (10*y**2 + 6) using the distributive property, and we got: (10*y**2)*(-27*y**3 - 16*y) + 6*(-27*y**3 - 16*y)
<replace-#Step 1>#Step 2:
Current expression: (10*y**2)*(-27*y**3 - 16*y) + 6*(-27*y**3 - 16*y)</replace>
Simplifying the partial expression: 6*(-27*y**3 - 16*y)
Expanding the part (-27*y**3 - 16*y) using the distributive property, and we got: -16*y*6 - 27*y**3*6
Replacing 6*(-27*y**3 - 16*y) with -16*y*6 - 27*y**3*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -16*y*6 + (10*y**2)*(-27*y**3 - 16*y) - 27*y**3*6</replace>
Simplifying the partial expression: (10*y**2)*(-27*y**3 - 16*y)
Expanding the part (-27*y**3 - 16*y) using the distributive property, and we got: (-16*y)*(10*y**2) + (10*y**2)*(-27*y**3)
Replacing (10*y**2)*(-27*y**3 - 16*y) with (-16*y)*(10*y**2) + (10*y**2)*(-27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-16*y)*(10*y**2) - 16*y*6 + (10*y**2)*(-27*y**3) - 27*y**3*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*y**3)*6 = -162*y**3
  (-27*y**3)*(10*y**2) = -270*y**5
  (-16*y)*6 = -96*y
  (-16*y)*(10*y**2) = -160*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -270*y**5 - 162*y**3 - 160*y**3 - 96*y</replace>
Combining like terms, got -270*y**5 - 322*y**3 - 96*y
<replace-#Step 5>#Step 6:
Current expression: -270*y**5 - 322*y**3 - 96*y</replace>
No more calculations needed.
<answer>-270*y**5 - 322*y**3 - 96*y</answer>


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

Answer: -18*y**4 + 42*y**3 + 2*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: y*(-18*y**3 + 42*y**2 + 2*y)
Expanding the part (-18*y**3 + 42*y**2 + 2*y) using the distributive property, and we got: y*(2*y) + y*(42*y**2) + y*(-18*y**3)
<replace-#Step 1>#Step 2:
Current expression: y*(2*y) + y*(42*y**2) + y*(-18*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*y**3)*y = -18*y**4
  (2*y)*y = 2*y**2
  (42*y**2)*y = 42*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -18*y**4 + 42*y**3 + 2*y**2</replace>
No more calculations needed.
<answer>-18*y**4 + 42*y**3 + 2*y**2</answer>


Question:
Simplify this expression: (27*x**2 - 41*x + 3)*(x**3 + 22*x + 54)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162

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*x**2 - 41*x + 3)*(x**3 + 22*x + 54)
Expanding the part (27*x**2 - 41*x + 3) using the distributive property, and we got: (-41*x)*(x**3 + 22*x + 54) + (27*x**2)*(x**3 + 22*x + 54) + 3*(x**3 + 22*x + 54)
<replace-#Step 1>#Step 2:
Current expression: (-41*x)*(x**3 + 22*x + 54) + (27*x**2)*(x**3 + 22*x + 54) + 3*(x**3 + 22*x + 54)</replace>
Simplifying the partial expression: 3*(x**3 + 22*x + 54)
Expanding the part (x**3 + 22*x + 54) using the distributive property, and we got: x**3*3 + (22*x)*3 + 54*3
Replacing 3*(x**3 + 22*x + 54) with x**3*3 + (22*x)*3 + 54*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-41*x)*(x**3 + 22*x + 54) + x**3*3 + (22*x)*3 + (27*x**2)*(x**3 + 22*x + 54) + 162</replace>
Simplifying the partial expression: (-41*x)*(x**3 + 22*x + 54)
Expanding the part (x**3 + 22*x + 54) using the distributive property, and we got: (-41*x)*x**3 + (-41*x)*(22*x) + 54*(-41*x)
Replacing (-41*x)*(x**3 + 22*x + 54) with (-41*x)*x**3 + (-41*x)*(22*x) + 54*(-41*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*x)*x**3 + (-41*x)*(22*x) + x**3*3 + 54*(-41)*x + (22*x)*3 + (27*x**2)*(x**3 + 22*x + 54) + 162</replace>
Simplifying the partial expression: (27*x**2)*(x**3 + 22*x + 54)
Expanding the part (x**3 + 22*x + 54) using the distributive property, and we got: (27*x**2)*x**3 + 54*(27*x**2) + (22*x)*(27*x**2)
Replacing (27*x**2)*(x**3 + 22*x + 54) with (27*x**2)*x**3 + 54*(27*x**2) + (22*x)*(27*x**2) in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: (-41*x)*x**3 + (-41*x)*(22*x) + (27*x**2)*x**3 + x**3*3 + 54*27*x**2 + 54*(-41)*x + (22*x)*(27*x**2) + (22*x)*3 + 162</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  x**3*3 = 3*x**3
  x**3*(-41*x) = -41*x**4
  x**3*(27*x**2) = 27*x**5
  (22*x)*3 = 66*x
  (22*x)*(-41*x) = -902*x**2
  (22*x)*(27*x**2) = 594*x**3
  54*-41*x = -2214*x
  54*27*x**2 = 1458*x**2
Replacing them in the overall expression.
<replace-#Step 5>#Step 6:
Current expression: 27*x**5 - 41*x**4 + 3*x**3 + 594*x**3 - 902*x**2 + 1458*x**2 - 2214*x + 66*x + 162</replace>
Combining like terms, got 27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162
<replace-#Step 6>#Step 7:
Current expression: 27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162</replace>
No more calculations needed.
<answer>27*x**5 - 41*x**4 + 597*x**3 + 556*x**2 - 2148*x + 162</answer>


Question:
Simplify this expression: (47 - 27*z)*(-30*z**3 - 29*z**2 - 48*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: 810*z**4 - 627*z**3 - 67*z**2 - 2256*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: (47 - 27*z)*(-30*z**3 - 29*z**2 - 48*z)
Expanding the part (47 - 27*z) using the distributive property, and we got: (-27*z)*(-30*z**3 - 29*z**2 - 48*z) + 47*(-30*z**3 - 29*z**2 - 48*z)
<replace-#Step 1>#Step 2:
Current expression: (-27*z)*(-30*z**3 - 29*z**2 - 48*z) + 47*(-30*z**3 - 29*z**2 - 48*z)</replace>
Simplifying the partial expression: 47*(-30*z**3 - 29*z**2 - 48*z)
Expanding the part (-30*z**3 - 29*z**2 - 48*z) using the distributive property, and we got: -48*z*47 - 29*z**2*47 - 30*z**3*47
Replacing 47*(-30*z**3 - 29*z**2 - 48*z) with -48*z*47 - 29*z**2*47 - 30*z**3*47 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*z*47 + (-27*z)*(-30*z**3 - 29*z**2 - 48*z) - 29*z**2*47 - 30*z**3*47</replace>
Simplifying the partial expression: (-27*z)*(-30*z**3 - 29*z**2 - 48*z)
Expanding the part (-30*z**3 - 29*z**2 - 48*z) using the distributive property, and we got: (-48*z)*(-27*z) + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3)
Replacing (-27*z)*(-30*z**3 - 29*z**2 - 48*z) with (-48*z)*(-27*z) + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*z)*(-27*z) - 48*z*47 + (-27*z)*(-29*z**2) + (-27*z)*(-30*z**3) - 29*z**2*47 - 30*z**3*47</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*z)*47 = -2256*z
  (-48*z)*(-27*z) = 1296*z**2
  (-30*z**3)*47 = -1410*z**3
  (-30*z**3)*(-27*z) = 810*z**4
  (-29*z**2)*47 = -1363*z**2
  (-29*z**2)*(-27*z) = 783*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 810*z**4 - 1410*z**3 + 783*z**3 - 1363*z**2 + 1296*z**2 - 2256*z</replace>
Combining like terms, got 810*z**4 - 627*z**3 - 67*z**2 - 2256*z
<replace-#Step 5>#Step 6:
Current expression: 810*z**4 - 627*z**3 - 67*z**2 - 2256*z</replace>
No more calculations needed.
<answer>810*z**4 - 627*z**3 - 67*z**2 - 2256*z</answer>


Question:
Simplify this expression: (-21*y - 42)*(-40*y**3 - 43*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: 840*y**4 + 1680*y**3 + 903*y**2 + 1806*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-21*y - 42)*(-40*y**3 - 43*y)
Expanding the part (-21*y - 42) using the distributive property, and we got: (-21*y)*(-40*y**3 - 43*y) - 42*(-40*y**3 - 43*y)
<replace-#Step 1>#Step 2:
Current expression: (-21*y)*(-40*y**3 - 43*y) - 42*(-40*y**3 - 43*y)</replace>
Simplifying the partial expression: -42*(-40*y**3 - 43*y)
Expanding the part (-40*y**3 - 43*y) using the distributive property, and we got: -43*y*(-42) - 40*y**3*(-42)
Replacing -42*(-40*y**3 - 43*y) with -43*y*(-42) - 40*y**3*(-42) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -43*y*(-42) + (-21*y)*(-40*y**3 - 43*y) - 40*y**3*(-42)</replace>
Simplifying the partial expression: (-21*y)*(-40*y**3 - 43*y)
Expanding the part (-40*y**3 - 43*y) using the distributive property, and we got: (-43*y)*(-21*y) + (-21*y)*(-40*y**3)
Replacing (-21*y)*(-40*y**3 - 43*y) with (-43*y)*(-21*y) + (-21*y)*(-40*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*y)*(-21*y) - 43*y*(-42) + (-21*y)*(-40*y**3) - 40*y**3*(-42)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-43*y)*-42 = 1806*y
  (-43*y)*(-21*y) = 903*y**2
  (-40*y**3)*-42 = 1680*y**3
  (-40*y**3)*(-21*y) = 840*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 840*y**4 + 1680*y**3 + 903*y**2 + 1806*y</replace>
No more calculations needed.
<answer>840*y**4 + 1680*y**3 + 903*y**2 + 1806*y</answer>


Question:
Calculate the following: (-26*x - 23)*(-13*x**3 - 25*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 338*x**4 + 299*x**3 + 650*x**2 + 575*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-26*x - 23)*(-13*x**3 - 25*x)
Expanding the part (-26*x - 23) using the distributive property, and we got: (-26*x)*(-13*x**3 - 25*x) - 23*(-13*x**3 - 25*x)
<replace-#Step 1>#Step 2:
Current expression: (-26*x)*(-13*x**3 - 25*x) - 23*(-13*x**3 - 25*x)</replace>
Simplifying the partial expression: -23*(-13*x**3 - 25*x)
Expanding the part (-13*x**3 - 25*x) using the distributive property, and we got: -25*x*(-23) - 13*x**3*(-23)
Replacing -23*(-13*x**3 - 25*x) with -25*x*(-23) - 13*x**3*(-23) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-26*x)*(-13*x**3 - 25*x) - 25*x*(-23) - 13*x**3*(-23)</replace>
Simplifying the partial expression: (-26*x)*(-13*x**3 - 25*x)
Expanding the part (-13*x**3 - 25*x) using the distributive property, and we got: (-26*x)*(-25*x) + (-26*x)*(-13*x**3)
Replacing (-26*x)*(-13*x**3 - 25*x) with (-26*x)*(-25*x) + (-26*x)*(-13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*x)*(-25*x) + (-26*x)*(-13*x**3) - 25*x*(-23) - 13*x**3*(-23)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x)*-23 = 575*x
  (-25*x)*(-26*x) = 650*x**2
  (-13*x**3)*-23 = 299*x**3
  (-13*x**3)*(-26*x) = 338*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 338*x**4 + 299*x**3 + 650*x**2 + 575*x</replace>
No more calculations needed.
<answer>338*x**4 + 299*x**3 + 650*x**2 + 575*x</answer>


Question:
Simplify this expression: (15*y - 10)*(-29*y**2 - 25*y - 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: -435*y**3 - 85*y**2 + 115*y + 90

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (15*y - 10)*(-29*y**2 - 25*y - 9)
Expanding the part (15*y - 10) using the distributive property, and we got: (15*y)*(-29*y**2 - 25*y - 9) - 10*(-29*y**2 - 25*y - 9)
<replace-#Step 1>#Step 2:
Current expression: (15*y)*(-29*y**2 - 25*y - 9) - 10*(-29*y**2 - 25*y - 9)</replace>
Simplifying the partial expression: -10*(-29*y**2 - 25*y - 9)
Expanding the part (-29*y**2 - 25*y - 9) using the distributive property, and we got: -25*y*(-10) - 29*y**2*(-10) - 9*(-10)
Replacing -10*(-29*y**2 - 25*y - 9) with -25*y*(-10) - 29*y**2*(-10) - 9*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -25*y*(-10) + (15*y)*(-29*y**2 - 25*y - 9) - 29*y**2*(-10) + 90</replace>
Simplifying the partial expression: (15*y)*(-29*y**2 - 25*y - 9)
Expanding the part (-29*y**2 - 25*y - 9) using the distributive property, and we got: (-25*y)*(15*y) - 135*y + (15*y)*(-29*y**2)
Replacing (15*y)*(-29*y**2 - 25*y - 9) with (-25*y)*(15*y) - 135*y + (15*y)*(-29*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-25*y)*(15*y) - 25*y*(-10) - 9*15*y + (15*y)*(-29*y**2) - 29*y**2*(-10) + 90</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-29*y**2)*-10 = 290*y**2
  (-29*y**2)*(15*y) = -435*y**3
  (-25*y)*-10 = 250*y
  (-25*y)*(15*y) = -375*y**2
  -9*15*y = -135*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -435*y**3 - 375*y**2 + 290*y**2 - 135*y + 250*y + 90</replace>
Combining like terms, got -435*y**3 - 85*y**2 + 115*y + 90
<replace-#Step 5>#Step 6:
Current expression: -435*y**3 - 85*y**2 + 115*y + 90</replace>
No more calculations needed.
<answer>-435*y**3 - 85*y**2 + 115*y + 90</answer>


Question:
Simplify this expression: (27 - 36*z**3)*(30*z**3 + 30*z**2 + 19*z - 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: -1080*z**6 - 1080*z**5 - 684*z**4 + 2286*z**3 + 810*z**2 + 513*z - 1107


Question:
Calculate the following: (5*y**3 + 49*y**2)*(19*y**3 - 39*y + 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 95*y**6 + 931*y**5 - 195*y**4 - 1831*y**3 + 784*y**2


Question:
Simplify this expression: (33*y + 39)*(17*y**2 + 37*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: 561*y**3 + 1884*y**2 + 1443*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: (33*y + 39)*(17*y**2 + 37*y)
Expanding the part (33*y + 39) using the distributive property, and we got: (33*y)*(17*y**2 + 37*y) + 39*(17*y**2 + 37*y)
<replace-#Step 1>#Step 2:
Current expression: (33*y)*(17*y**2 + 37*y) + 39*(17*y**2 + 37*y)</replace>
Simplifying the partial expression: 39*(17*y**2 + 37*y)
Expanding the part (17*y**2 + 37*y) using the distributive property, and we got: (37*y)*39 + (17*y**2)*39
Replacing 39*(17*y**2 + 37*y) with (37*y)*39 + (17*y**2)*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*y)*(17*y**2 + 37*y) + (37*y)*39 + (17*y**2)*39</replace>
Simplifying the partial expression: (33*y)*(17*y**2 + 37*y)
Expanding the part (17*y**2 + 37*y) using the distributive property, and we got: (33*y)*(37*y) + (33*y)*(17*y**2)
Replacing (33*y)*(17*y**2 + 37*y) with (33*y)*(37*y) + (33*y)*(17*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (33*y)*(37*y) + (33*y)*(17*y**2) + (37*y)*39 + (17*y**2)*39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*y**2)*39 = 663*y**2
  (17*y**2)*(33*y) = 561*y**3
  (37*y)*39 = 1443*y
  (37*y)*(33*y) = 1221*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 561*y**3 + 663*y**2 + 1221*y**2 + 1443*y</replace>
Combining like terms, got 561*y**3 + 1884*y**2 + 1443*y
<replace-#Step 5>#Step 6:
Current expression: 561*y**3 + 1884*y**2 + 1443*y</replace>
No more calculations needed.
<answer>561*y**3 + 1884*y**2 + 1443*y</answer>


Question:
Calculate the following: (48*x**3 + 4*x)*(14*x**3 + 29*x**2 + 28*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 672*x**6 + 1392*x**5 + 1400*x**4 + 116*x**3 + 112*x**2


Question:
Simplify this expression: 75*z**3*(8*z**3 + 50*z**2 + 27*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 600*z**6 + 3750*z**5 + 2025*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 75*z**3*(8*z**3 + 50*z**2 + 27*z)
Expanding the part (8*z**3 + 50*z**2 + 27*z) using the distributive property, and we got: (27*z)*(75*z**3) + (50*z**2)*(75*z**3) + (8*z**3)*(75*z**3)
<replace-#Step 1>#Step 2:
Current expression: (27*z)*(75*z**3) + (50*z**2)*(75*z**3) + (8*z**3)*(75*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*z**3)*(75*z**3) = 600*z**6
  (27*z)*(75*z**3) = 2025*z**4
  (50*z**2)*(75*z**3) = 3750*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 600*z**6 + 3750*z**5 + 2025*z**4</replace>
No more calculations needed.
<answer>600*z**6 + 3750*z**5 + 2025*z**4</answer>