Question:
Calculate the following: 54*z**2*(28 - 17*z**3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -918*z**5 + 1512*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 54*z**2*(28 - 17*z**3)
Expanding the part (28 - 17*z**3) using the distributive property, and we got: 28*(54*z**2) + (54*z**2)*(-17*z**3)
<replace-#Step 1>#Step 2:
Current expression: 28*(54*z**2) + (54*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:
  28*(54*z**2) = 1512*z**2
  (-17*z**3)*(54*z**2) = -918*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -918*z**5 + 1512*z**2</replace>
No more calculations needed.
<answer>-918*z**5 + 1512*z**2</answer>


Question:
Simplify this expression: -82*x*(22 - 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: 2050*x**2 - 1804*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: -82*x*(22 - 25*x)
Expanding the part (22 - 25*x) using the distributive property, and we got: (-82*x)*(-25*x) + 22*(-82*x)
<replace-#Step 1>#Step 2:
Current expression: (-82*x)*(-25*x) + 22*(-82*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  22*(-82*x) = -1804*x
  (-25*x)*(-82*x) = 2050*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2050*x**2 - 1804*x</replace>
No more calculations needed.
<answer>2050*x**2 - 1804*x</answer>


Question:
Calculate the following: 2520*y - 540
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2520*y - 540

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: 2520*y - 540
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: 2520*y - 540</replace>
No more calculations needed.
<answer>2520*y - 540</answer>


Question:
Calculate the following: (19*x**3 - 1)*(-43*x**2 - 68*x + 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: -817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31

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*x**3 - 1)*(-43*x**2 - 68*x + 31)
Expanding the part (19*x**3 - 1) using the distributive property, and we got: (19*x**3)*(-43*x**2 - 68*x + 31) - (-43*x**2 - 68*x + 31)
<replace-#Step 1>#Step 2:
Current expression: (19*x**3)*(-43*x**2 - 68*x + 31) - (-43*x**2 - 68*x + 31)</replace>
Simplifying the partial expression: -(-43*x**2 - 68*x + 31)
Expanding the part (-43*x**2 - 68*x + 31) using the distributive property, and we got: -68*x*(-1) - 43*x**2*(-1) + 31*(-1)
Replacing -(-43*x**2 - 68*x + 31) with -68*x*(-1) - 43*x**2*(-1) + 31*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -68*x*(-1) - 43*x**2*(-1) + (19*x**3)*(-43*x**2 - 68*x + 31) - 31</replace>
Simplifying the partial expression: (19*x**3)*(-43*x**2 - 68*x + 31)
Expanding the part (-43*x**2 - 68*x + 31) using the distributive property, and we got: (-68*x)*(19*x**3) + 31*(19*x**3) + (-43*x**2)*(19*x**3)
Replacing (19*x**3)*(-43*x**2 - 68*x + 31) with (-68*x)*(19*x**3) + 31*(19*x**3) + (-43*x**2)*(19*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-68*x)*(19*x**3) - 68*x*(-1) + 31*19*x**3 + (-43*x**2)*(19*x**3) - 43*x**2*(-1) - 31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*x)*-1 = 68*x
  (-68*x)*(19*x**3) = -1292*x**4
  (-43*x**2)*-1 = 43*x**2
  (-43*x**2)*(19*x**3) = -817*x**5
  31*19*x**3 = 589*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31</replace>
No more calculations needed.
<answer>-817*x**5 - 1292*x**4 + 589*x**3 + 43*x**2 + 68*x - 31</answer>


Question:
Calculate the following: (-15*x**2 - 43*x)*(6*x**3 + 6*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: -90*x**5 - 348*x**4 - 258*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-15*x**2 - 43*x)*(6*x**3 + 6*x**2)
Expanding the part (-15*x**2 - 43*x) using the distributive property, and we got: (-43*x)*(6*x**3 + 6*x**2) + (-15*x**2)*(6*x**3 + 6*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-43*x)*(6*x**3 + 6*x**2) + (-15*x**2)*(6*x**3 + 6*x**2)</replace>
Simplifying the partial expression: (-43*x)*(6*x**3 + 6*x**2)
Expanding the part (6*x**3 + 6*x**2) using the distributive property, and we got: (-43*x)*(6*x**2) + (-43*x)*(6*x**3)
Replacing (-43*x)*(6*x**3 + 6*x**2) with (-43*x)*(6*x**2) + (-43*x)*(6*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-43*x)*(6*x**2) + (-43*x)*(6*x**3) + (-15*x**2)*(6*x**3 + 6*x**2)</replace>
Simplifying the partial expression: (-15*x**2)*(6*x**3 + 6*x**2)
Expanding the part (6*x**3 + 6*x**2) using the distributive property, and we got: (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3)
Replacing (-15*x**2)*(6*x**3 + 6*x**2) with (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-43*x)*(6*x**2) + (-43*x)*(6*x**3) + (-15*x**2)*(6*x**2) + (-15*x**2)*(6*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**2)*(-43*x) = -258*x**3
  (6*x**2)*(-15*x**2) = -90*x**4
  (6*x**3)*(-43*x) = -258*x**4
  (6*x**3)*(-15*x**2) = -90*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -90*x**5 - 258*x**4 - 90*x**4 - 258*x**3</replace>
Combining like terms, got -90*x**5 - 348*x**4 - 258*x**3
<replace-#Step 5>#Step 6:
Current expression: -90*x**5 - 348*x**4 - 258*x**3</replace>
No more calculations needed.
<answer>-90*x**5 - 348*x**4 - 258*x**3</answer>


Question:
Simplify this expression: (6*x + 77)*(-47*x**2 + 43*x - 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -282*x**3 - 3361*x**2 + 3173*x - 1771

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (6*x + 77)*(-47*x**2 + 43*x - 23)
Expanding the part (6*x + 77) using the distributive property, and we got: (6*x)*(-47*x**2 + 43*x - 23) + 77*(-47*x**2 + 43*x - 23)
<replace-#Step 1>#Step 2:
Current expression: (6*x)*(-47*x**2 + 43*x - 23) + 77*(-47*x**2 + 43*x - 23)</replace>
Simplifying the partial expression: 77*(-47*x**2 + 43*x - 23)
Expanding the part (-47*x**2 + 43*x - 23) using the distributive property, and we got: (43*x)*77 - 47*x**2*77 - 23*77
Replacing 77*(-47*x**2 + 43*x - 23) with (43*x)*77 - 47*x**2*77 - 23*77 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*x)*(-47*x**2 + 43*x - 23) + (43*x)*77 - 47*x**2*77 - 1771</replace>
Simplifying the partial expression: (6*x)*(-47*x**2 + 43*x - 23)
Expanding the part (-47*x**2 + 43*x - 23) using the distributive property, and we got: -138*x + (6*x)*(43*x) + (6*x)*(-47*x**2)
Replacing (6*x)*(-47*x**2 + 43*x - 23) with -138*x + (6*x)*(43*x) + (6*x)*(-47*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -23*6*x + (6*x)*(43*x) + (6*x)*(-47*x**2) + (43*x)*77 - 47*x**2*77 - 1771</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*x**2)*77 = -3619*x**2
  (-47*x**2)*(6*x) = -282*x**3
  (43*x)*77 = 3311*x
  (43*x)*(6*x) = 258*x**2
  -23*6*x = -138*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -282*x**3 - 3619*x**2 + 258*x**2 - 138*x + 3311*x - 1771</replace>
Combining like terms, got -282*x**3 - 3361*x**2 + 3173*x - 1771
<replace-#Step 5>#Step 6:
Current expression: -282*x**3 - 3361*x**2 + 3173*x - 1771</replace>
No more calculations needed.
<answer>-282*x**3 - 3361*x**2 + 3173*x - 1771</answer>


Question:
Calculate the following: (2 - 4*x)*(-48*x**3 - 49*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: 192*x**4 + 100*x**3 + 70*x**2 - 84*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2 - 4*x)*(-48*x**3 - 49*x**2 - 42*x)
Expanding the part (2 - 4*x) using the distributive property, and we got: (-4*x)*(-48*x**3 - 49*x**2 - 42*x) + 2*(-48*x**3 - 49*x**2 - 42*x)
<replace-#Step 1>#Step 2:
Current expression: (-4*x)*(-48*x**3 - 49*x**2 - 42*x) + 2*(-48*x**3 - 49*x**2 - 42*x)</replace>
Simplifying the partial expression: 2*(-48*x**3 - 49*x**2 - 42*x)
Expanding the part (-48*x**3 - 49*x**2 - 42*x) using the distributive property, and we got: -42*x*2 - 49*x**2*2 - 48*x**3*2
Replacing 2*(-48*x**3 - 49*x**2 - 42*x) with -42*x*2 - 49*x**2*2 - 48*x**3*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*x*2 + (-4*x)*(-48*x**3 - 49*x**2 - 42*x) - 49*x**2*2 - 48*x**3*2</replace>
Simplifying the partial expression: (-4*x)*(-48*x**3 - 49*x**2 - 42*x)
Expanding the part (-48*x**3 - 49*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(-4*x) + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3)
Replacing (-4*x)*(-48*x**3 - 49*x**2 - 42*x) with (-42*x)*(-4*x) + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*x)*(-4*x) - 42*x*2 + (-4*x)*(-49*x**2) + (-4*x)*(-48*x**3) - 49*x**2*2 - 48*x**3*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**2)*2 = -98*x**2
  (-49*x**2)*(-4*x) = 196*x**3
  (-48*x**3)*2 = -96*x**3
  (-48*x**3)*(-4*x) = 192*x**4
  (-42*x)*2 = -84*x
  (-42*x)*(-4*x) = 168*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 192*x**4 - 96*x**3 + 196*x**3 - 98*x**2 + 168*x**2 - 84*x</replace>
Combining like terms, got 192*x**4 + 100*x**3 + 70*x**2 - 84*x
<replace-#Step 5>#Step 6:
Current expression: 192*x**4 + 100*x**3 + 70*x**2 - 84*x</replace>
No more calculations needed.
<answer>192*x**4 + 100*x**3 + 70*x**2 - 84*x</answer>


Question:
Simplify this expression: (-36*x - 24)*(45*x**3 + 30*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: -1620*x**4 - 2160*x**3 - 720*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: (-36*x - 24)*(45*x**3 + 30*x**2)
Expanding the part (-36*x - 24) using the distributive property, and we got: (-36*x)*(45*x**3 + 30*x**2) - 24*(45*x**3 + 30*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-36*x)*(45*x**3 + 30*x**2) - 24*(45*x**3 + 30*x**2)</replace>
Simplifying the partial expression: -24*(45*x**3 + 30*x**2)
Expanding the part (45*x**3 + 30*x**2) using the distributive property, and we got: (30*x**2)*(-24) + (45*x**3)*(-24)
Replacing -24*(45*x**3 + 30*x**2) with (30*x**2)*(-24) + (45*x**3)*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*x)*(45*x**3 + 30*x**2) + (30*x**2)*(-24) + (45*x**3)*(-24)</replace>
Simplifying the partial expression: (-36*x)*(45*x**3 + 30*x**2)
Expanding the part (45*x**3 + 30*x**2) using the distributive property, and we got: (-36*x)*(30*x**2) + (-36*x)*(45*x**3)
Replacing (-36*x)*(45*x**3 + 30*x**2) with (-36*x)*(30*x**2) + (-36*x)*(45*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*x)*(30*x**2) + (-36*x)*(45*x**3) + (30*x**2)*(-24) + (45*x**3)*(-24)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*x**2)*-24 = -720*x**2
  (30*x**2)*(-36*x) = -1080*x**3
  (45*x**3)*-24 = -1080*x**3
  (45*x**3)*(-36*x) = -1620*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1620*x**4 - 1080*x**3 - 1080*x**3 - 720*x**2</replace>
Combining like terms, got -1620*x**4 - 2160*x**3 - 720*x**2
<replace-#Step 5>#Step 6:
Current expression: -1620*x**4 - 2160*x**3 - 720*x**2</replace>
No more calculations needed.
<answer>-1620*x**4 - 2160*x**3 - 720*x**2</answer>


Question:
Simplify this expression: (26*z**2 - 30*z)*(25*z**2 - 9*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: 650*z**4 - 984*z**3 + 868*z**2 - 690*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: (26*z**2 - 30*z)*(25*z**2 - 9*z + 23)
Expanding the part (26*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(25*z**2 - 9*z + 23) + (26*z**2)*(25*z**2 - 9*z + 23)
<replace-#Step 1>#Step 2:
Current expression: (-30*z)*(25*z**2 - 9*z + 23) + (26*z**2)*(25*z**2 - 9*z + 23)</replace>
Simplifying the partial expression: (-30*z)*(25*z**2 - 9*z + 23)
Expanding the part (25*z**2 - 9*z + 23) using the distributive property, and we got: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30*z)
Replacing (-30*z)*(25*z**2 - 9*z + 23) with (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30*z) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + 23*(-30)*z + (26*z**2)*(25*z**2 - 9*z + 23)</replace>
Simplifying the partial expression: (26*z**2)*(25*z**2 - 9*z + 23)
Expanding the part (25*z**2 - 9*z + 23) using the distributive property, and we got: (-9*z)*(26*z**2) + 23*(26*z**2) + (25*z**2)*(26*z**2)
Replacing (26*z**2)*(25*z**2 - 9*z + 23) with (-9*z)*(26*z**2) + 23*(26*z**2) + (25*z**2)*(26*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*z)*(-9*z) + (-30*z)*(25*z**2) + (-9*z)*(26*z**2) + 23*26*z**2 + 23*(-30)*z + (25*z**2)*(26*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-9*z)*(-30*z) = 270*z**2
  (-9*z)*(26*z**2) = -234*z**3
  (25*z**2)*(-30*z) = -750*z**3
  (25*z**2)*(26*z**2) = 650*z**4
  23*-30*z = -690*z
  23*26*z**2 = 598*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 650*z**4 - 750*z**3 - 234*z**3 + 270*z**2 + 598*z**2 - 690*z</replace>
Combining like terms, got 650*z**4 - 984*z**3 + 868*z**2 - 690*z
<replace-#Step 5>#Step 6:
Current expression: 650*z**4 - 984*z**3 + 868*z**2 - 690*z</replace>
No more calculations needed.
<answer>650*z**4 - 984*z**3 + 868*z**2 - 690*z</answer>


Question:
Simplify this expression: (50*y - 40)*(47*y**2 + 6*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2350*y**3 - 1580*y**2 - 240*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: (50*y - 40)*(47*y**2 + 6*y)
Expanding the part (50*y - 40) using the distributive property, and we got: (50*y)*(47*y**2 + 6*y) - 40*(47*y**2 + 6*y)
<replace-#Step 1>#Step 2:
Current expression: (50*y)*(47*y**2 + 6*y) - 40*(47*y**2 + 6*y)</replace>
Simplifying the partial expression: -40*(47*y**2 + 6*y)
Expanding the part (47*y**2 + 6*y) using the distributive property, and we got: (6*y)*(-40) + (47*y**2)*(-40)
Replacing -40*(47*y**2 + 6*y) with (6*y)*(-40) + (47*y**2)*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*y)*(-40) + (50*y)*(47*y**2 + 6*y) + (47*y**2)*(-40)</replace>
Simplifying the partial expression: (50*y)*(47*y**2 + 6*y)
Expanding the part (47*y**2 + 6*y) using the distributive property, and we got: (6*y)*(50*y) + (50*y)*(47*y**2)
Replacing (50*y)*(47*y**2 + 6*y) with (6*y)*(50*y) + (50*y)*(47*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*y)*(50*y) + (6*y)*(-40) + (50*y)*(47*y**2) + (47*y**2)*(-40)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*y)*-40 = -240*y
  (6*y)*(50*y) = 300*y**2
  (47*y**2)*-40 = -1880*y**2
  (47*y**2)*(50*y) = 2350*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2350*y**3 - 1880*y**2 + 300*y**2 - 240*y</replace>
Combining like terms, got 2350*y**3 - 1580*y**2 - 240*y
<replace-#Step 5>#Step 6:
Current expression: 2350*y**3 - 1580*y**2 - 240*y</replace>
No more calculations needed.
<answer>2350*y**3 - 1580*y**2 - 240*y</answer>


Question:
Calculate the following: -59*x**2*(-2*x - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 118*x**3 + 2950*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: -59*x**2*(-2*x - 50)
Expanding the part (-2*x - 50) using the distributive property, and we got: (-2*x)*(-59*x**2) - (-1)*2950*x**2
<replace-#Step 1>#Step 2:
Current expression: (-2*x)*(-59*x**2) - (-1)*2950*x**2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -50*(-59*x**2) = 2950*x**2
  (-2*x)*(-59*x**2) = 118*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 118*x**3 + 2950*x**2</replace>
No more calculations needed.
<answer>118*x**3 + 2950*x**2</answer>


Question:
Calculate the following: (35*y**2 + 45*y)*(-10*y**3 - 45*y**2 + 33*y + 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -350*y**5 - 2025*y**4 - 870*y**3 + 3200*y**2 + 2205*y


Question:
Simplify this expression: 28*z*(49 - 23*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: -644*z**3 + 1372*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: 28*z*(49 - 23*z**2)
Expanding the part (49 - 23*z**2) using the distributive property, and we got: 49*(28*z) + (28*z)*(-23*z**2)
<replace-#Step 1>#Step 2:
Current expression: 49*(28*z) + (28*z)*(-23*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  49*(28*z) = 1372*z
  (-23*z**2)*(28*z) = -644*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -644*z**3 + 1372*z</replace>
No more calculations needed.
<answer>-644*z**3 + 1372*z</answer>


Question:
Calculate the following: (17*x**3 - 26)*(26*x**3 - 8*x**2 + 41*x + 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 442*x**6 - 136*x**5 + 697*x**4 - 166*x**3 + 208*x**2 - 1066*x - 780


Question:
Calculate the following: 1056*z + 16
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1056*z + 16

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: 1056*z + 16
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: 1056*z + 16</replace>
No more calculations needed.
<answer>1056*z + 16</answer>


Question:
Calculate the following: (32*z**2 - 24)*(-26*z**3 + 50*z**2 + 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -832*z**5 + 1600*z**4 + 624*z**3 - 176*z**2 - 768


Question:
Calculate the following: (-3*z**2 + 21*z + 3)*(18*z**3 - 34*z**2 - 50*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: -54*z**5 + 480*z**4 - 510*z**3 - 1152*z**2 - 150*z


Question:
Simplify this expression: (-39*z**3 + 42*z - 30)*(-z**3 - z**2 - 23*z - 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 39*z**6 + 39*z**5 + 855*z**4 + 222*z**3 - 936*z**2 + 438*z + 180


Question:
Calculate the following: (10 - 78*y**2)*(45*y**2 + 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3510*y**4 - 2046*y**2 + 320

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 - 78*y**2)*(45*y**2 + 32)
Expanding the part (10 - 78*y**2) using the distributive property, and we got: (-78*y**2)*(45*y**2 + 32) + 10*(45*y**2 + 32)
<replace-#Step 1>#Step 2:
Current expression: (-78*y**2)*(45*y**2 + 32) + 10*(45*y**2 + 32)</replace>
Simplifying the partial expression: 10*(45*y**2 + 32)
Expanding the part (45*y**2 + 32) using the distributive property, and we got: (45*y**2)*10 + 32*10
Replacing 10*(45*y**2 + 32) with (45*y**2)*10 + 32*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-78*y**2)*(45*y**2 + 32) + (45*y**2)*10 + 320</replace>
Simplifying the partial expression: (-78*y**2)*(45*y**2 + 32)
Expanding the part (45*y**2 + 32) using the distributive property, and we got: 32*(-78*y**2) + (-78*y**2)*(45*y**2)
Replacing (-78*y**2)*(45*y**2 + 32) with 32*(-78*y**2) + (-78*y**2)*(45*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 32*(-78)*y**2 + (-78*y**2)*(45*y**2) + (45*y**2)*10 + 320</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (45*y**2)*10 = 450*y**2
  (45*y**2)*(-78*y**2) = -3510*y**4
  32*-78*y**2 = -2496*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3510*y**4 - 2496*y**2 + 450*y**2 + 320</replace>
Combining like terms, got -3510*y**4 - 2046*y**2 + 320
<replace-#Step 5>#Step 6:
Current expression: -3510*y**4 - 2046*y**2 + 320</replace>
No more calculations needed.
<answer>-3510*y**4 - 2046*y**2 + 320</answer>


Question:
Calculate the following: (-27*z**2 - 63)*(-7*z**3 + 3*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 189*z**5 + 360*z**3 - 189*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: (-27*z**2 - 63)*(-7*z**3 + 3*z)
Expanding the part (-27*z**2 - 63) using the distributive property, and we got: (-27*z**2)*(-7*z**3 + 3*z) - 63*(-7*z**3 + 3*z)
<replace-#Step 1>#Step 2:
Current expression: (-27*z**2)*(-7*z**3 + 3*z) - 63*(-7*z**3 + 3*z)</replace>
Simplifying the partial expression: -63*(-7*z**3 + 3*z)
Expanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(-63) - 7*z**3*(-63)
Replacing -63*(-7*z**3 + 3*z) with (3*z)*(-63) - 7*z**3*(-63) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*(-63) + (-27*z**2)*(-7*z**3 + 3*z) - 7*z**3*(-63)</replace>
Simplifying the partial expression: (-27*z**2)*(-7*z**3 + 3*z)
Expanding the part (-7*z**3 + 3*z) using the distributive property, and we got: (3*z)*(-27*z**2) + (-27*z**2)*(-7*z**3)
Replacing (-27*z**2)*(-7*z**3 + 3*z) with (3*z)*(-27*z**2) + (-27*z**2)*(-7*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*z)*(-27*z**2) + (3*z)*(-63) + (-27*z**2)*(-7*z**3) - 7*z**3*(-63)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z**3)*-63 = 441*z**3
  (-7*z**3)*(-27*z**2) = 189*z**5
  (3*z)*-63 = -189*z
  (3*z)*(-27*z**2) = -81*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 189*z**5 - 81*z**3 + 441*z**3 - 189*z</replace>
Combining like terms, got 189*z**5 + 360*z**3 - 189*z
<replace-#Step 5>#Step 6:
Current expression: 189*z**5 + 360*z**3 - 189*z</replace>
No more calculations needed.
<answer>189*z**5 + 360*z**3 - 189*z</answer>


Question:
Simplify this expression: (41*z**2 + 44*z)*(16*z**3 - 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 656*z**5 + 704*z**4 - 1558*z**2 - 1672*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: (41*z**2 + 44*z)*(16*z**3 - 38)
Expanding the part (16*z**3 - 38) using the distributive property, and we got: (16*z**3)*(41*z**2 + 44*z) - 38*(41*z**2 + 44*z)
<replace-#Step 1>#Step 2:
Current expression: (16*z**3)*(41*z**2 + 44*z) - 38*(41*z**2 + 44*z)</replace>
Simplifying the partial expression: -38*(41*z**2 + 44*z)
Expanding the part (41*z**2 + 44*z) using the distributive property, and we got: (44*z)*(-38) + (41*z**2)*(-38)
Replacing -38*(41*z**2 + 44*z) with (44*z)*(-38) + (41*z**2)*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (44*z)*(-38) + (41*z**2)*(-38) + (16*z**3)*(41*z**2 + 44*z)</replace>
Simplifying the partial expression: (16*z**3)*(41*z**2 + 44*z)
Expanding the part (41*z**2 + 44*z) using the distributive property, and we got: (44*z)*(16*z**3) + (41*z**2)*(16*z**3)
Replacing (16*z**3)*(41*z**2 + 44*z) with (44*z)*(16*z**3) + (41*z**2)*(16*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (44*z)*(16*z**3) + (44*z)*(-38) + (41*z**2)*(16*z**3) + (41*z**2)*(-38)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (41*z**2)*-38 = -1558*z**2
  (41*z**2)*(16*z**3) = 656*z**5
  (44*z)*-38 = -1672*z
  (44*z)*(16*z**3) = 704*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 656*z**5 + 704*z**4 - 1558*z**2 - 1672*z</replace>
No more calculations needed.
<answer>656*z**5 + 704*z**4 - 1558*z**2 - 1672*z</answer>


Question:
Simplify this expression: (-45*y**2 - 27)*(-6*y**3 - 7*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 + 477*y**3 + 189*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-45*y**2 - 27)*(-6*y**3 - 7*y)
Expanding the part (-45*y**2 - 27) using the distributive property, and we got: (-45*y**2)*(-6*y**3 - 7*y) - 27*(-6*y**3 - 7*y)
<replace-#Step 1>#Step 2:
Current expression: (-45*y**2)*(-6*y**3 - 7*y) - 27*(-6*y**3 - 7*y)</replace>
Simplifying the partial expression: -27*(-6*y**3 - 7*y)
Expanding the part (-6*y**3 - 7*y) using the distributive property, and we got: -7*y*(-27) - 6*y**3*(-27)
Replacing -27*(-6*y**3 - 7*y) with -7*y*(-27) - 6*y**3*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -7*y*(-27) + (-45*y**2)*(-6*y**3 - 7*y) - 6*y**3*(-27)</replace>
Simplifying the partial expression: (-45*y**2)*(-6*y**3 - 7*y)
Expanding the part (-6*y**3 - 7*y) using the distributive property, and we got: (-7*y)*(-45*y**2) + (-45*y**2)*(-6*y**3)
Replacing (-45*y**2)*(-6*y**3 - 7*y) with (-7*y)*(-45*y**2) + (-45*y**2)*(-6*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*y)*(-45*y**2) - 7*y*(-27) + (-45*y**2)*(-6*y**3) - 6*y**3*(-27)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*y)*-27 = 189*y
  (-7*y)*(-45*y**2) = 315*y**3
  (-6*y**3)*-27 = 162*y**3
  (-6*y**3)*(-45*y**2) = 270*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 270*y**5 + 162*y**3 + 315*y**3 + 189*y</replace>
Combining like terms, got 270*y**5 + 477*y**3 + 189*y
<replace-#Step 5>#Step 6:
Current expression: 270*y**5 + 477*y**3 + 189*y</replace>
No more calculations needed.
<answer>270*y**5 + 477*y**3 + 189*y</answer>


Question:
Calculate the following: -4080*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: -4080*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: -4080*y**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: -4080*y**2</replace>
No more calculations needed.
<answer>-4080*y**2</answer>


Question:
Calculate the following: (12*x**3 + 36*x)*(18*x**3 + 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: 216*x**6 + 648*x**4 + 288*x**3 + 864*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: (12*x**3 + 36*x)*(18*x**3 + 24)
Expanding the part (18*x**3 + 24) using the distributive property, and we got: (18*x**3)*(12*x**3 + 36*x) + 24*(12*x**3 + 36*x)
<replace-#Step 1>#Step 2:
Current expression: (18*x**3)*(12*x**3 + 36*x) + 24*(12*x**3 + 36*x)</replace>
Simplifying the partial expression: 24*(12*x**3 + 36*x)
Expanding the part (12*x**3 + 36*x) using the distributive property, and we got: (36*x)*24 + (12*x**3)*24
Replacing 24*(12*x**3 + 36*x) with (36*x)*24 + (12*x**3)*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*x)*24 + (12*x**3)*24 + (18*x**3)*(12*x**3 + 36*x)</replace>
Simplifying the partial expression: (18*x**3)*(12*x**3 + 36*x)
Expanding the part (12*x**3 + 36*x) using the distributive property, and we got: (36*x)*(18*x**3) + (12*x**3)*(18*x**3)
Replacing (18*x**3)*(12*x**3 + 36*x) with (36*x)*(18*x**3) + (12*x**3)*(18*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (36*x)*(18*x**3) + (36*x)*24 + (12*x**3)*(18*x**3) + (12*x**3)*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*x**3)*24 = 288*x**3
  (12*x**3)*(18*x**3) = 216*x**6
  (36*x)*24 = 864*x
  (36*x)*(18*x**3) = 648*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 216*x**6 + 648*x**4 + 288*x**3 + 864*x</replace>
No more calculations needed.
<answer>216*x**6 + 648*x**4 + 288*x**3 + 864*x</answer>


Question:
Simplify this expression: -8*x**3*(21*x**3 + 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: -168*x**6 - 184*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -8*x**3*(21*x**3 + 23)
Expanding the part (21*x**3 + 23) using the distributive property, and we got: 23*(-8*x**3) + (-8*x**3)*(21*x**3)
<replace-#Step 1>#Step 2:
Current expression: 23*(-8*x**3) + (-8*x**3)*(21*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  23*(-8*x**3) = -184*x**3
  (21*x**3)*(-8*x**3) = -168*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -168*x**6 - 184*x**3</replace>
No more calculations needed.
<answer>-168*x**6 - 184*x**3</answer>


Question:
Calculate the following: (92*y + 35)*(-41*y**3 + 45*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -3772*y**4 + 2705*y**3 + 1575*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: (92*y + 35)*(-41*y**3 + 45*y**2)
Expanding the part (92*y + 35) using the distributive property, and we got: (92*y)*(-41*y**3 + 45*y**2) + 35*(-41*y**3 + 45*y**2)
<replace-#Step 1>#Step 2:
Current expression: (92*y)*(-41*y**3 + 45*y**2) + 35*(-41*y**3 + 45*y**2)</replace>
Simplifying the partial expression: 35*(-41*y**3 + 45*y**2)
Expanding the part (-41*y**3 + 45*y**2) using the distributive property, and we got: (45*y**2)*35 - 41*y**3*35
Replacing 35*(-41*y**3 + 45*y**2) with (45*y**2)*35 - 41*y**3*35 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (92*y)*(-41*y**3 + 45*y**2) + (45*y**2)*35 - 41*y**3*35</replace>
Simplifying the partial expression: (92*y)*(-41*y**3 + 45*y**2)
Expanding the part (-41*y**3 + 45*y**2) using the distributive property, and we got: (92*y)*(45*y**2) + (92*y)*(-41*y**3)
Replacing (92*y)*(-41*y**3 + 45*y**2) with (92*y)*(45*y**2) + (92*y)*(-41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (92*y)*(45*y**2) + (92*y)*(-41*y**3) + (45*y**2)*35 - 41*y**3*35</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**3)*35 = -1435*y**3
  (-41*y**3)*(92*y) = -3772*y**4
  (45*y**2)*35 = 1575*y**2
  (45*y**2)*(92*y) = 4140*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -3772*y**4 - 1435*y**3 + 4140*y**3 + 1575*y**2</replace>
Combining like terms, got -3772*y**4 + 2705*y**3 + 1575*y**2
<replace-#Step 5>#Step 6:
Current expression: -3772*y**4 + 2705*y**3 + 1575*y**2</replace>
No more calculations needed.
<answer>-3772*y**4 + 2705*y**3 + 1575*y**2</answer>


Question:
Simplify this expression: (2*z - 53)*(-44*z**2 + 19*z - 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: -88*z**3 + 2370*z**2 - 1137*z + 3445

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 - 53)*(-44*z**2 + 19*z - 65)
Expanding the part (2*z - 53) using the distributive property, and we got: (2*z)*(-44*z**2 + 19*z - 65) - 53*(-44*z**2 + 19*z - 65)
<replace-#Step 1>#Step 2:
Current expression: (2*z)*(-44*z**2 + 19*z - 65) - 53*(-44*z**2 + 19*z - 65)</replace>
Simplifying the partial expression: -53*(-44*z**2 + 19*z - 65)
Expanding the part (-44*z**2 + 19*z - 65) using the distributive property, and we got: (19*z)*(-53) - 44*z**2*(-53) - 65*(-53)
Replacing -53*(-44*z**2 + 19*z - 65) with (19*z)*(-53) - 44*z**2*(-53) - 65*(-53) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*z)*(-44*z**2 + 19*z - 65) + (19*z)*(-53) - 44*z**2*(-53) + 3445</replace>
Simplifying the partial expression: (2*z)*(-44*z**2 + 19*z - 65)
Expanding the part (-44*z**2 + 19*z - 65) using the distributive property, and we got: -130*z + (2*z)*(19*z) + (2*z)*(-44*z**2)
Replacing (2*z)*(-44*z**2 + 19*z - 65) with -130*z + (2*z)*(19*z) + (2*z)*(-44*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -65*2*z + (2*z)*(19*z) + (2*z)*(-44*z**2) + (19*z)*(-53) - 44*z**2*(-53) + 3445</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*z**2)*-53 = 2332*z**2
  (-44*z**2)*(2*z) = -88*z**3
  (19*z)*-53 = -1007*z
  (19*z)*(2*z) = 38*z**2
  -65*2*z = -130*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -88*z**3 + 38*z**2 + 2332*z**2 - 1007*z - 130*z + 3445</replace>
Combining like terms, got -88*z**3 + 2370*z**2 - 1137*z + 3445
<replace-#Step 5>#Step 6:
Current expression: -88*z**3 + 2370*z**2 - 1137*z + 3445</replace>
No more calculations needed.
<answer>-88*z**3 + 2370*z**2 - 1137*z + 3445</answer>


Question:
Simplify this expression: (-38*y**3 - 27*y + 7)*(62*y**3 + 49*y**2 - 10*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: -2356*y**6 - 1862*y**5 - 1294*y**4 - 889*y**3 + 613*y**2 - 70*y


Question:
Calculate the following: (38*z**3 - 38*z**2 - 5*z)*(44*z**3 - 44*z**2 - 2*z - 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: 1672*z**6 - 3344*z**5 + 1376*z**4 - 1338*z**3 + 1644*z**2 + 215*z


Question:
Simplify this expression: 72*y**2*(-11*y**2 + 12*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -792*y**4 + 864*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: 72*y**2*(-11*y**2 + 12*y)
Expanding the part (-11*y**2 + 12*y) using the distributive property, and we got: (12*y)*(72*y**2) + (-11*y**2)*(72*y**2)
<replace-#Step 1>#Step 2:
Current expression: (12*y)*(72*y**2) + (-11*y**2)*(72*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*y**2)*(72*y**2) = -792*y**4
  (12*y)*(72*y**2) = 864*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -792*y**4 + 864*y**3</replace>
No more calculations needed.
<answer>-792*y**4 + 864*y**3</answer>


Question:
Calculate the following: (-33*x**2 - 24)*(-8*x**2 + 37*x + 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936

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*x**2 - 24)*(-8*x**2 + 37*x + 39)
Expanding the part (-33*x**2 - 24) using the distributive property, and we got: (-33*x**2)*(-8*x**2 + 37*x + 39) - 24*(-8*x**2 + 37*x + 39)
<replace-#Step 1>#Step 2:
Current expression: (-33*x**2)*(-8*x**2 + 37*x + 39) - 24*(-8*x**2 + 37*x + 39)</replace>
Simplifying the partial expression: -24*(-8*x**2 + 37*x + 39)
Expanding the part (-8*x**2 + 37*x + 39) using the distributive property, and we got: (37*x)*(-24) - 8*x**2*(-24) + 39*(-24)
Replacing -24*(-8*x**2 + 37*x + 39) with (37*x)*(-24) - 8*x**2*(-24) + 39*(-24) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*x)*(-24) + (-33*x**2)*(-8*x**2 + 37*x + 39) - 8*x**2*(-24) - 936</replace>
Simplifying the partial expression: (-33*x**2)*(-8*x**2 + 37*x + 39)
Expanding the part (-8*x**2 + 37*x + 39) using the distributive property, and we got: 39*(-33*x**2) + (37*x)*(-33*x**2) + (-33*x**2)*(-8*x**2)
Replacing (-33*x**2)*(-8*x**2 + 37*x + 39) with 39*(-33*x**2) + (37*x)*(-33*x**2) + (-33*x**2)*(-8*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 39*(-33)*x**2 + (37*x)*(-33*x**2) + (37*x)*(-24) + (-33*x**2)*(-8*x**2) - 8*x**2*(-24) - 936</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*x**2)*-24 = 192*x**2
  (-8*x**2)*(-33*x**2) = 264*x**4
  (37*x)*-24 = -888*x
  (37*x)*(-33*x**2) = -1221*x**3
  39*-33*x**2 = -1287*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 264*x**4 - 1221*x**3 - 1287*x**2 + 192*x**2 - 888*x - 936</replace>
Combining like terms, got 264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936
<replace-#Step 5>#Step 6:
Current expression: 264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936</replace>
No more calculations needed.
<answer>264*x**4 - 1221*x**3 - 1095*x**2 - 888*x - 936</answer>


Question:
Calculate the following: -62*z**3*(21*z**3 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1302*z**6 + 1922*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: -62*z**3*(21*z**3 - 31)
Expanding the part (21*z**3 - 31) using the distributive property, and we got: -(-1)*1922*z**3 + (-62*z**3)*(21*z**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*1922*z**3 + (-62*z**3)*(21*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -31*(-62*z**3) = 1922*z**3
  (21*z**3)*(-62*z**3) = -1302*z**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1302*z**6 + 1922*z**3</replace>
No more calculations needed.
<answer>-1302*z**6 + 1922*z**3</answer>


Question:
Calculate the following: (-50*x**3 - 27*x - 3)*(26*x**3 + 45*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: -1300*x**6 - 2952*x**4 + 672*x**3 - 1215*x**2 + 270*x + 45


Question:
Simplify this expression: 41*z**3*(40*z**3 + 44*z + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1640*z**6 + 1804*z**4 + 1804*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: 41*z**3*(40*z**3 + 44*z + 44)
Expanding the part (40*z**3 + 44*z + 44) using the distributive property, and we got: 44*(41*z**3) + (44*z)*(41*z**3) + (40*z**3)*(41*z**3)
<replace-#Step 1>#Step 2:
Current expression: 44*(41*z**3) + (44*z)*(41*z**3) + (40*z**3)*(41*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  44*(41*z**3) = 1804*z**3
  (40*z**3)*(41*z**3) = 1640*z**6
  (44*z)*(41*z**3) = 1804*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1640*z**6 + 1804*z**4 + 1804*z**3</replace>
No more calculations needed.
<answer>1640*z**6 + 1804*z**4 + 1804*z**3</answer>


Question:
Calculate the following: (42*z + 62)*(-32*z**3 + 14*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: -1344*z**4 - 1396*z**3 + 868*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (42*z + 62)*(-32*z**3 + 14*z**2)
Expanding the part (42*z + 62) using the distributive property, and we got: (42*z)*(-32*z**3 + 14*z**2) + 62*(-32*z**3 + 14*z**2)
<replace-#Step 1>#Step 2:
Current expression: (42*z)*(-32*z**3 + 14*z**2) + 62*(-32*z**3 + 14*z**2)</replace>
Simplifying the partial expression: 62*(-32*z**3 + 14*z**2)
Expanding the part (-32*z**3 + 14*z**2) using the distributive property, and we got: (14*z**2)*62 - 32*z**3*62
Replacing 62*(-32*z**3 + 14*z**2) with (14*z**2)*62 - 32*z**3*62 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (42*z)*(-32*z**3 + 14*z**2) + (14*z**2)*62 - 32*z**3*62</replace>
Simplifying the partial expression: (42*z)*(-32*z**3 + 14*z**2)
Expanding the part (-32*z**3 + 14*z**2) using the distributive property, and we got: (42*z)*(14*z**2) + (42*z)*(-32*z**3)
Replacing (42*z)*(-32*z**3 + 14*z**2) with (42*z)*(14*z**2) + (42*z)*(-32*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (42*z)*(14*z**2) + (42*z)*(-32*z**3) + (14*z**2)*62 - 32*z**3*62</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-32*z**3)*62 = -1984*z**3
  (-32*z**3)*(42*z) = -1344*z**4
  (14*z**2)*62 = 868*z**2
  (14*z**2)*(42*z) = 588*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1344*z**4 - 1984*z**3 + 588*z**3 + 868*z**2</replace>
Combining like terms, got -1344*z**4 - 1396*z**3 + 868*z**2
<replace-#Step 5>#Step 6:
Current expression: -1344*z**4 - 1396*z**3 + 868*z**2</replace>
No more calculations needed.
<answer>-1344*z**4 - 1396*z**3 + 868*z**2</answer>


Question:
Simplify this expression: (40*z**2 + 41*z + 31)*(-21*z**3 + 43*z**2 - 53*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: -840*z**5 + 859*z**4 - 1008*z**3 - 840*z**2 - 1643*z


Question:
Simplify this expression: (-37*y**3 + 29*y**2 + 34*y)*(4*y**3 + 47*y + 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -148*y**6 + 116*y**5 - 1603*y**4 + 364*y**3 + 2381*y**2 + 918*y


Question:
Simplify this expression: (33 - 19*y**2)*(47*y**2 + 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -893*y**4 + 1247*y**2 + 528

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 - 19*y**2)*(47*y**2 + 16)
Expanding the part (47*y**2 + 16) using the distributive property, and we got: (47*y**2)*(33 - 19*y**2) + 16*(33 - 19*y**2)
<replace-#Step 1>#Step 2:
Current expression: (47*y**2)*(33 - 19*y**2) + 16*(33 - 19*y**2)</replace>
Simplifying the partial expression: 16*(33 - 19*y**2)
Expanding the part (33 - 19*y**2) using the distributive property, and we got: -19*y**2*16 + 33*16
Replacing 16*(33 - 19*y**2) with -19*y**2*16 + 33*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -19*y**2*16 + (47*y**2)*(33 - 19*y**2) + 528</replace>
Simplifying the partial expression: (47*y**2)*(33 - 19*y**2)
Expanding the part (33 - 19*y**2) using the distributive property, and we got: 33*(47*y**2) + (-19*y**2)*(47*y**2)
Replacing (47*y**2)*(33 - 19*y**2) with 33*(47*y**2) + (-19*y**2)*(47*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*47*y**2 + (-19*y**2)*(47*y**2) - 19*y**2*16 + 528</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**2)*16 = -304*y**2
  (-19*y**2)*(47*y**2) = -893*y**4
  33*47*y**2 = 1551*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -893*y**4 - 304*y**2 + 1551*y**2 + 528</replace>
Combining like terms, got -893*y**4 + 1247*y**2 + 528
<replace-#Step 5>#Step 6:
Current expression: -893*y**4 + 1247*y**2 + 528</replace>
No more calculations needed.
<answer>-893*y**4 + 1247*y**2 + 528</answer>


Question:
Simplify this expression: (-40*z**2 + 46*z + 63)*(34*z**3 + 18*z**2 + 29*z - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1360*z**5 + 844*z**4 + 1810*z**3 + 4468*z**2 - 473*z - 3150


Question:
Calculate the following: (-38*z - 61)*(41*z**2 - 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1558*z**3 - 2501*z**2 + 228*z + 366

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-38*z - 61)*(41*z**2 - 6)
Expanding the part (-38*z - 61) using the distributive property, and we got: (-38*z)*(41*z**2 - 6) - 61*(41*z**2 - 6)
<replace-#Step 1>#Step 2:
Current expression: (-38*z)*(41*z**2 - 6) - 61*(41*z**2 - 6)</replace>
Simplifying the partial expression: -61*(41*z**2 - 6)
Expanding the part (41*z**2 - 6) using the distributive property, and we got: (41*z**2)*(-61) - 6*(-61)
Replacing -61*(41*z**2 - 6) with (41*z**2)*(-61) - 6*(-61) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-38*z)*(41*z**2 - 6) + (41*z**2)*(-61) + 366</replace>
Simplifying the partial expression: (-38*z)*(41*z**2 - 6)
Expanding the part (41*z**2 - 6) using the distributive property, and we got: (-38*z)*(41*z**2) - (-1)*228*z
Replacing (-38*z)*(41*z**2 - 6) with (-38*z)*(41*z**2) - (-1)*228*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-38*z)*(41*z**2) - 6*(-38)*z + (41*z**2)*(-61) + 366</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (41*z**2)*-61 = -2501*z**2
  (41*z**2)*(-38*z) = -1558*z**3
  -6*-38*z = 228*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1558*z**3 - 2501*z**2 + 228*z + 366</replace>
No more calculations needed.
<answer>-1558*z**3 - 2501*z**2 + 228*z + 366</answer>


Question:
Simplify this expression: 85*z**2*(35*z**2 - 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2975*z**4 - 935*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 85*z**2*(35*z**2 - 11)
Expanding the part (35*z**2 - 11) using the distributive property, and we got: -935*z**2 + (35*z**2)*(85*z**2)
<replace-#Step 1>#Step 2:
Current expression: -935*z**2 + (35*z**2)*(85*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -11*(85*z**2) = -935*z**2
  (35*z**2)*(85*z**2) = 2975*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2975*z**4 - 935*z**2</replace>
No more calculations needed.
<answer>2975*z**4 - 935*z**2</answer>


Question:
Calculate the following: (11*y**2 - 20*y)*(41*y**3 + 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 451*y**5 - 820*y**4 + 374*y**2 - 680*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: (11*y**2 - 20*y)*(41*y**3 + 34)
Expanding the part (41*y**3 + 34) using the distributive property, and we got: (41*y**3)*(11*y**2 - 20*y) + 34*(11*y**2 - 20*y)
<replace-#Step 1>#Step 2:
Current expression: (41*y**3)*(11*y**2 - 20*y) + 34*(11*y**2 - 20*y)</replace>
Simplifying the partial expression: 34*(11*y**2 - 20*y)
Expanding the part (11*y**2 - 20*y) using the distributive property, and we got: -20*y*34 + (11*y**2)*34
Replacing 34*(11*y**2 - 20*y) with -20*y*34 + (11*y**2)*34 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*y*34 + (11*y**2)*34 + (41*y**3)*(11*y**2 - 20*y)</replace>
Simplifying the partial expression: (41*y**3)*(11*y**2 - 20*y)
Expanding the part (11*y**2 - 20*y) using the distributive property, and we got: (-20*y)*(41*y**3) + (11*y**2)*(41*y**3)
Replacing (41*y**3)*(11*y**2 - 20*y) with (-20*y)*(41*y**3) + (11*y**2)*(41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*y)*(41*y**3) - 20*y*34 + (11*y**2)*(41*y**3) + (11*y**2)*34</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*y)*34 = -680*y
  (-20*y)*(41*y**3) = -820*y**4
  (11*y**2)*34 = 374*y**2
  (11*y**2)*(41*y**3) = 451*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 451*y**5 - 820*y**4 + 374*y**2 - 680*y</replace>
No more calculations needed.
<answer>451*y**5 - 820*y**4 + 374*y**2 - 680*y</answer>


Question:
Simplify this expression: (60*y**2 + 23*y)*(-27*y**3 - 90)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1620*y**5 - 621*y**4 - 5400*y**2 - 2070*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: (60*y**2 + 23*y)*(-27*y**3 - 90)
Expanding the part (-27*y**3 - 90) using the distributive property, and we got: (-27*y**3)*(60*y**2 + 23*y) - 90*(60*y**2 + 23*y)
<replace-#Step 1>#Step 2:
Current expression: (-27*y**3)*(60*y**2 + 23*y) - 90*(60*y**2 + 23*y)</replace>
Simplifying the partial expression: -90*(60*y**2 + 23*y)
Expanding the part (60*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-90) + (60*y**2)*(-90)
Replacing -90*(60*y**2 + 23*y) with (23*y)*(-90) + (60*y**2)*(-90) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*y)*(-90) + (60*y**2)*(-90) + (-27*y**3)*(60*y**2 + 23*y)</replace>
Simplifying the partial expression: (-27*y**3)*(60*y**2 + 23*y)
Expanding the part (60*y**2 + 23*y) using the distributive property, and we got: (23*y)*(-27*y**3) + (60*y**2)*(-27*y**3)
Replacing (-27*y**3)*(60*y**2 + 23*y) with (23*y)*(-27*y**3) + (60*y**2)*(-27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (23*y)*(-27*y**3) + (23*y)*(-90) + (60*y**2)*(-27*y**3) + (60*y**2)*(-90)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*y)*-90 = -2070*y
  (23*y)*(-27*y**3) = -621*y**4
  (60*y**2)*-90 = -5400*y**2
  (60*y**2)*(-27*y**3) = -1620*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y</replace>
No more calculations needed.
<answer>-1620*y**5 - 621*y**4 - 5400*y**2 - 2070*y</answer>


Question:
Calculate the following: (23*x**3 + 59)*(-27*x**3 - 48*x**2 - 42*x + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -621*x**6 - 1104*x**5 - 966*x**4 - 489*x**3 - 2832*x**2 - 2478*x + 2832


Question:
Simplify this expression: (20*z**3 - 26*z)*(34*z**3 + 37*z**2 - 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 680*z**6 + 740*z**5 - 884*z**4 - 1702*z**3 + 962*z


Question:
Calculate the following: (-63*x**3 - 40)*(-23*x**3 + 6*x**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: 1449*x**6 - 378*x**5 - 466*x**3 - 240*x**2 - 880


Question:
Simplify this expression: (14*y**3 - 17*y**2)*(42*y**2 + 30*y + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 588*y**5 - 294*y**4 - 426*y**3 - 102*y**2


Question:
Calculate the following: (-30*y**3 - 40*y)*(-23*y**3 - y**2 + 35*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: 690*y**6 + 30*y**5 - 130*y**4 + 100*y**3 - 1400*y**2 + 80*y


Question:
Calculate the following: (-38*x**2 + 34*x - 5)*(x**3 - 25*x**2 - 39*x + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -38*x**5 + 984*x**4 + 627*x**3 - 1505*x**2 + 467*x - 40


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

Answer: 1880*z**4 + 861*z**3 + 54*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-47*z**2 - 18*z)*(-40*z**2 - 3*z)
Expanding the part (-47*z**2 - 18*z) using the distributive property, and we got: (-18*z)*(-40*z**2 - 3*z) + (-47*z**2)*(-40*z**2 - 3*z)
<replace-#Step 1>#Step 2:
Current expression: (-18*z)*(-40*z**2 - 3*z) + (-47*z**2)*(-40*z**2 - 3*z)</replace>
Simplifying the partial expression: (-47*z**2)*(-40*z**2 - 3*z)
Expanding the part (-40*z**2 - 3*z) using the distributive property, and we got: (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)
Replacing (-47*z**2)*(-40*z**2 - 3*z) with (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*z)*(-40*z**2 - 3*z) + (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)</replace>
Simplifying the partial expression: (-18*z)*(-40*z**2 - 3*z)
Expanding the part (-40*z**2 - 3*z) using the distributive property, and we got: (-18*z)*(-3*z) + (-18*z)*(-40*z**2)
Replacing (-18*z)*(-40*z**2 - 3*z) with (-18*z)*(-3*z) + (-18*z)*(-40*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*z)*(-3*z) + (-18*z)*(-40*z**2) + (-3*z)*(-47*z**2) + (-47*z**2)*(-40*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*z**2)*(-47*z**2) = 1880*z**4
  (-40*z**2)*(-18*z) = 720*z**3
  (-3*z)*(-47*z**2) = 141*z**3
  (-3*z)*(-18*z) = 54*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1880*z**4 + 141*z**3 + 720*z**3 + 54*z**2</replace>
Combining like terms, got 1880*z**4 + 861*z**3 + 54*z**2
<replace-#Step 5>#Step 6:
Current expression: 1880*z**4 + 861*z**3 + 54*z**2</replace>
No more calculations needed.
<answer>1880*z**4 + 861*z**3 + 54*z**2</answer>


Question:
Calculate the following: (-3*z**3 - 47*z**2)*(-68*z**3 + 17*z**2 + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 204*z**6 + 3145*z**5 - 799*z**4 - 18*z**3 - 282*z**2


Question:
Simplify this expression: 46*x**2*(46*x - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2116*x**3 - 1840*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: 46*x**2*(46*x - 40)
Expanding the part (46*x - 40) using the distributive property, and we got: -1840*x**2 + (46*x)*(46*x**2)
<replace-#Step 1>#Step 2:
Current expression: -1840*x**2 + (46*x)*(46*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -40*(46*x**2) = -1840*x**2
  (46*x)*(46*x**2) = 2116*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 2116*x**3 - 1840*x**2</replace>
No more calculations needed.
<answer>2116*x**3 - 1840*x**2</answer>


Question:
Calculate the following: (-16*y**2 + 7*y)*(4*y**3 + 41*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: -64*y**5 + 28*y**4 - 656*y**3 + 287*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: (-16*y**2 + 7*y)*(4*y**3 + 41*y)
Expanding the part (-16*y**2 + 7*y) using the distributive property, and we got: (7*y)*(4*y**3 + 41*y) + (-16*y**2)*(4*y**3 + 41*y)
<replace-#Step 1>#Step 2:
Current expression: (7*y)*(4*y**3 + 41*y) + (-16*y**2)*(4*y**3 + 41*y)</replace>
Simplifying the partial expression: (-16*y**2)*(4*y**3 + 41*y)
Expanding the part (4*y**3 + 41*y) using the distributive property, and we got: (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)
Replacing (-16*y**2)*(4*y**3 + 41*y) with (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*y)*(4*y**3 + 41*y) + (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)</replace>
Simplifying the partial expression: (7*y)*(4*y**3 + 41*y)
Expanding the part (4*y**3 + 41*y) using the distributive property, and we got: (7*y)*(41*y) + (7*y)*(4*y**3)
Replacing (7*y)*(4*y**3 + 41*y) with (7*y)*(41*y) + (7*y)*(4*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*y)*(41*y) + (7*y)*(4*y**3) + (41*y)*(-16*y**2) + (-16*y**2)*(4*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (4*y**3)*(-16*y**2) = -64*y**5
  (4*y**3)*(7*y) = 28*y**4
  (41*y)*(-16*y**2) = -656*y**3
  (41*y)*(7*y) = 287*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -64*y**5 + 28*y**4 - 656*y**3 + 287*y**2</replace>
No more calculations needed.
<answer>-64*y**5 + 28*y**4 - 656*y**3 + 287*y**2</answer>


Question:
Simplify this expression: (-47*x**2 - 1)*(22*x**3 - 23*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1034*x**5 + 1081*x**4 - 22*x**3 + 23*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: (-47*x**2 - 1)*(22*x**3 - 23*x**2)
Expanding the part (-47*x**2 - 1) using the distributive property, and we got: (-47*x**2)*(22*x**3 - 23*x**2) - (22*x**3 - 23*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-47*x**2)*(22*x**3 - 23*x**2) - (22*x**3 - 23*x**2)</replace>
Simplifying the partial expression: -(22*x**3 - 23*x**2)
Expanding the part (22*x**3 - 23*x**2) using the distributive property, and we got: -23*x**2*(-1) + (22*x**3)*(-1)
Replacing -(22*x**3 - 23*x**2) with -23*x**2*(-1) + (22*x**3)*(-1) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*x**2)*(22*x**3 - 23*x**2) - 23*x**2*(-1) + (22*x**3)*(-1)</replace>
Simplifying the partial expression: (-47*x**2)*(22*x**3 - 23*x**2)
Expanding the part (22*x**3 - 23*x**2) using the distributive property, and we got: (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3)
Replacing (-47*x**2)*(22*x**3 - 23*x**2) with (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*x**2)*(-23*x**2) + (-47*x**2)*(22*x**3) - 23*x**2*(-1) + (22*x**3)*(-1)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*x**2)*-1 = 23*x**2
  (-23*x**2)*(-47*x**2) = 1081*x**4
  (22*x**3)*-1 = -22*x**3
  (22*x**3)*(-47*x**2) = -1034*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2</replace>
No more calculations needed.
<answer>-1034*x**5 + 1081*x**4 - 22*x**3 + 23*x**2</answer>


Question:
Calculate the following: 3950*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: 3950*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: 3950*z
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 3950*z</replace>
No more calculations needed.
<answer>3950*z</answer>


Question:
Simplify this expression: (-23*z - 46)*(32*z**2 + 67*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: -736*z**3 - 3013*z**2 - 3082*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: (-23*z - 46)*(32*z**2 + 67*z)
Expanding the part (-23*z - 46) using the distributive property, and we got: (-23*z)*(32*z**2 + 67*z) - 46*(32*z**2 + 67*z)
<replace-#Step 1>#Step 2:
Current expression: (-23*z)*(32*z**2 + 67*z) - 46*(32*z**2 + 67*z)</replace>
Simplifying the partial expression: -46*(32*z**2 + 67*z)
Expanding the part (32*z**2 + 67*z) using the distributive property, and we got: (67*z)*(-46) + (32*z**2)*(-46)
Replacing -46*(32*z**2 + 67*z) with (67*z)*(-46) + (32*z**2)*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-23*z)*(32*z**2 + 67*z) + (67*z)*(-46) + (32*z**2)*(-46)</replace>
Simplifying the partial expression: (-23*z)*(32*z**2 + 67*z)
Expanding the part (32*z**2 + 67*z) using the distributive property, and we got: (-23*z)*(67*z) + (-23*z)*(32*z**2)
Replacing (-23*z)*(32*z**2 + 67*z) with (-23*z)*(67*z) + (-23*z)*(32*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*z)*(67*z) + (-23*z)*(32*z**2) + (67*z)*(-46) + (32*z**2)*(-46)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*z**2)*-46 = -1472*z**2
  (32*z**2)*(-23*z) = -736*z**3
  (67*z)*-46 = -3082*z
  (67*z)*(-23*z) = -1541*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -736*z**3 - 1541*z**2 - 1472*z**2 - 3082*z</replace>
Combining like terms, got -736*z**3 - 3013*z**2 - 3082*z
<replace-#Step 5>#Step 6:
Current expression: -736*z**3 - 3013*z**2 - 3082*z</replace>
No more calculations needed.
<answer>-736*z**3 - 3013*z**2 - 3082*z</answer>


Question:
Calculate the following: (41*y**3 + 42)*(-21*y**3 - 48*y**2 + 22*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: -861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*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: (41*y**3 + 42)*(-21*y**3 - 48*y**2 + 22*y)
Expanding the part (41*y**3 + 42) using the distributive property, and we got: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) + 42*(-21*y**3 - 48*y**2 + 22*y)
<replace-#Step 1>#Step 2:
Current expression: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) + 42*(-21*y**3 - 48*y**2 + 22*y)</replace>
Simplifying the partial expression: 42*(-21*y**3 - 48*y**2 + 22*y)
Expanding the part (-21*y**3 - 48*y**2 + 22*y) using the distributive property, and we got: (22*y)*42 - 48*y**2*42 - 21*y**3*42
Replacing 42*(-21*y**3 - 48*y**2 + 22*y) with (22*y)*42 - 48*y**2*42 - 21*y**3*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (22*y)*42 - 48*y**2*42 - 21*y**3*42 + (41*y**3)*(-21*y**3 - 48*y**2 + 22*y)</replace>
Simplifying the partial expression: (41*y**3)*(-21*y**3 - 48*y**2 + 22*y)
Expanding the part (-21*y**3 - 48*y**2 + 22*y) using the distributive property, and we got: (22*y)*(41*y**3) + (-48*y**2)*(41*y**3) + (-21*y**3)*(41*y**3)
Replacing (41*y**3)*(-21*y**3 - 48*y**2 + 22*y) with (22*y)*(41*y**3) + (-48*y**2)*(41*y**3) + (-21*y**3)*(41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (22*y)*(41*y**3) + (22*y)*42 + (-48*y**2)*(41*y**3) - 48*y**2*42 + (-21*y**3)*(41*y**3) - 21*y**3*42</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*y**2)*42 = -2016*y**2
  (-48*y**2)*(41*y**3) = -1968*y**5
  (-21*y**3)*42 = -882*y**3
  (-21*y**3)*(41*y**3) = -861*y**6
  (22*y)*42 = 924*y
  (22*y)*(41*y**3) = 902*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y</replace>
No more calculations needed.
<answer>-861*y**6 - 1968*y**5 + 902*y**4 - 882*y**3 - 2016*y**2 + 924*y</answer>


Question:
Calculate the following: 18*x**3*(25*x**2 - 22*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: 450*x**5 - 396*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: 18*x**3*(25*x**2 - 22*x)
Expanding the part (25*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(18*x**3) + (25*x**2)*(18*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(18*x**3) + (25*x**2)*(18*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x)*(18*x**3) = -396*x**4
  (25*x**2)*(18*x**3) = 450*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 450*x**5 - 396*x**4</replace>
No more calculations needed.
<answer>450*x**5 - 396*x**4</answer>


Question:
Simplify this expression: (-18*x**3 + 17*x)*(-48*x**3 - 18*x**2 + 2*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: 864*x**6 + 324*x**5 - 852*x**4 - 306*x**3 + 34*x**2


Question:
Simplify this expression: (45*y**2 + 30)*(27*y**3 + 18*y**2 + 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45*y**2 + 30)*(27*y**3 + 18*y**2 + 33)
Expanding the part (45*y**2 + 30) using the distributive property, and we got: (45*y**2)*(27*y**3 + 18*y**2 + 33) + 30*(27*y**3 + 18*y**2 + 33)
<replace-#Step 1>#Step 2:
Current expression: (45*y**2)*(27*y**3 + 18*y**2 + 33) + 30*(27*y**3 + 18*y**2 + 33)</replace>
Simplifying the partial expression: 30*(27*y**3 + 18*y**2 + 33)
Expanding the part (27*y**3 + 18*y**2 + 33) using the distributive property, and we got: (18*y**2)*30 + (27*y**3)*30 + 33*30
Replacing 30*(27*y**3 + 18*y**2 + 33) with (18*y**2)*30 + (27*y**3)*30 + 33*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*y**2)*30 + (45*y**2)*(27*y**3 + 18*y**2 + 33) + (27*y**3)*30 + 990</replace>
Simplifying the partial expression: (45*y**2)*(27*y**3 + 18*y**2 + 33)
Expanding the part (27*y**3 + 18*y**2 + 33) using the distributive property, and we got: 33*(45*y**2) + (18*y**2)*(45*y**2) + (45*y**2)*(27*y**3)
Replacing (45*y**2)*(27*y**3 + 18*y**2 + 33) with 33*(45*y**2) + (18*y**2)*(45*y**2) + (45*y**2)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 33*45*y**2 + (18*y**2)*(45*y**2) + (18*y**2)*30 + (45*y**2)*(27*y**3) + (27*y**3)*30 + 990</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (18*y**2)*30 = 540*y**2
  (18*y**2)*(45*y**2) = 810*y**4
  (27*y**3)*30 = 810*y**3
  (27*y**3)*(45*y**2) = 1215*y**5
  33*45*y**2 = 1485*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1215*y**5 + 810*y**4 + 810*y**3 + 540*y**2 + 1485*y**2 + 990</replace>
Combining like terms, got 1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990
<replace-#Step 5>#Step 6:
Current expression: 1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990</replace>
No more calculations needed.
<answer>1215*y**5 + 810*y**4 + 810*y**3 + 2025*y**2 + 990</answer>


Question:
Calculate the following: (46 - 3*z)*(69*z**3 + 42*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: -207*z**4 + 3048*z**3 + 1932*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (46 - 3*z)*(69*z**3 + 42*z**2)
Expanding the part (46 - 3*z) using the distributive property, and we got: (-3*z)*(69*z**3 + 42*z**2) + 46*(69*z**3 + 42*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-3*z)*(69*z**3 + 42*z**2) + 46*(69*z**3 + 42*z**2)</replace>
Simplifying the partial expression: 46*(69*z**3 + 42*z**2)
Expanding the part (69*z**3 + 42*z**2) using the distributive property, and we got: (42*z**2)*46 + (69*z**3)*46
Replacing 46*(69*z**3 + 42*z**2) with (42*z**2)*46 + (69*z**3)*46 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-3*z)*(69*z**3 + 42*z**2) + (42*z**2)*46 + (69*z**3)*46</replace>
Simplifying the partial expression: (-3*z)*(69*z**3 + 42*z**2)
Expanding the part (69*z**3 + 42*z**2) using the distributive property, and we got: (-3*z)*(42*z**2) + (-3*z)*(69*z**3)
Replacing (-3*z)*(69*z**3 + 42*z**2) with (-3*z)*(42*z**2) + (-3*z)*(69*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*z)*(42*z**2) + (-3*z)*(69*z**3) + (42*z**2)*46 + (69*z**3)*46</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (42*z**2)*46 = 1932*z**2
  (42*z**2)*(-3*z) = -126*z**3
  (69*z**3)*46 = 3174*z**3
  (69*z**3)*(-3*z) = -207*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -207*z**4 - 126*z**3 + 3174*z**3 + 1932*z**2</replace>
Combining like terms, got -207*z**4 + 3048*z**3 + 1932*z**2
<replace-#Step 5>#Step 6:
Current expression: -207*z**4 + 3048*z**3 + 1932*z**2</replace>
No more calculations needed.
<answer>-207*z**4 + 3048*z**3 + 1932*z**2</answer>


Question:
Simplify this expression: 78*x*(9*x**3 + 45*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: 702*x**4 + 3510*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 78*x*(9*x**3 + 45*x**2)
Expanding the part (9*x**3 + 45*x**2) using the distributive property, and we got: (78*x)*(45*x**2) + (78*x)*(9*x**3)
<replace-#Step 1>#Step 2:
Current expression: (78*x)*(45*x**2) + (78*x)*(9*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*x**3)*(78*x) = 702*x**4
  (45*x**2)*(78*x) = 3510*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 702*x**4 + 3510*x**3</replace>
No more calculations needed.
<answer>702*x**4 + 3510*x**3</answer>


Question:
Simplify this expression: (15*y**3 - 23*y**2)*(31*y**3 - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 465*y**6 - 713*y**5 - 375*y**3 + 575*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: (15*y**3 - 23*y**2)*(31*y**3 - 25)
Expanding the part (31*y**3 - 25) using the distributive property, and we got: (31*y**3)*(15*y**3 - 23*y**2) - 25*(15*y**3 - 23*y**2)
<replace-#Step 1>#Step 2:
Current expression: (31*y**3)*(15*y**3 - 23*y**2) - 25*(15*y**3 - 23*y**2)</replace>
Simplifying the partial expression: -25*(15*y**3 - 23*y**2)
Expanding the part (15*y**3 - 23*y**2) using the distributive property, and we got: -23*y**2*(-25) + (15*y**3)*(-25)
Replacing -25*(15*y**3 - 23*y**2) with -23*y**2*(-25) + (15*y**3)*(-25) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*y**2*(-25) + (15*y**3)*(-25) + (31*y**3)*(15*y**3 - 23*y**2)</replace>
Simplifying the partial expression: (31*y**3)*(15*y**3 - 23*y**2)
Expanding the part (15*y**3 - 23*y**2) using the distributive property, and we got: (-23*y**2)*(31*y**3) + (15*y**3)*(31*y**3)
Replacing (31*y**3)*(15*y**3 - 23*y**2) with (-23*y**2)*(31*y**3) + (15*y**3)*(31*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-23*y**2)*(31*y**3) - 23*y**2*(-25) + (15*y**3)*(31*y**3) + (15*y**3)*(-25)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*y**2)*-25 = 575*y**2
  (-23*y**2)*(31*y**3) = -713*y**5
  (15*y**3)*-25 = -375*y**3
  (15*y**3)*(31*y**3) = 465*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 465*y**6 - 713*y**5 - 375*y**3 + 575*y**2</replace>
No more calculations needed.
<answer>465*y**6 - 713*y**5 - 375*y**3 + 575*y**2</answer>


Question:
Simplify this expression: -1750*x**2 + 1120*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: -1750*x**2 + 1120*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: -1750*x**2 + 1120*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: -1750*x**2 + 1120*x</replace>
No more calculations needed.
<answer>-1750*x**2 + 1120*x</answer>


Question:
Simplify this expression: 55*x**2*(29*x**3 - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1595*x**5 - 2420*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: 55*x**2*(29*x**3 - 44)
Expanding the part (29*x**3 - 44) using the distributive property, and we got: -2420*x**2 + (55*x**2)*(29*x**3)
<replace-#Step 1>#Step 2:
Current expression: -2420*x**2 + (55*x**2)*(29*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -44*(55*x**2) = -2420*x**2
  (29*x**3)*(55*x**2) = 1595*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1595*x**5 - 2420*x**2</replace>
No more calculations needed.
<answer>1595*x**5 - 2420*x**2</answer>


Question:
Simplify this expression: (15*y**3 - 60*y**2)*(-43*y**3 + 33*y**2 + 11*y + 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: -645*y**6 + 3075*y**5 - 1815*y**4 - 645*y**3 - 60*y**2


Question:
Calculate the following: (-24*x**2 - 3*x + 8)*(-30*x**3 + 14*x**2 - 62*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 720*x**5 - 246*x**4 + 1206*x**3 + 298*x**2 - 496*x