Question:
Simplify this expression: (7*z**3 + 8*z**2)*(57*z**3 + 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: 399*z**6 + 456*z**5 + 336*z**3 + 384*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: (7*z**3 + 8*z**2)*(57*z**3 + 48)
Expanding the part (57*z**3 + 48) using the distributive property, and we got: (57*z**3)*(7*z**3 + 8*z**2) + 48*(7*z**3 + 8*z**2)
<replace-#Step 1>#Step 2:
Current expression: (57*z**3)*(7*z**3 + 8*z**2) + 48*(7*z**3 + 8*z**2)</replace>
Simplifying the partial expression: 48*(7*z**3 + 8*z**2)
Expanding the part (7*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*48 + (7*z**3)*48
Replacing 48*(7*z**3 + 8*z**2) with (8*z**2)*48 + (7*z**3)*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (8*z**2)*48 + (7*z**3)*48 + (57*z**3)*(7*z**3 + 8*z**2)</replace>
Simplifying the partial expression: (57*z**3)*(7*z**3 + 8*z**2)
Expanding the part (7*z**3 + 8*z**2) using the distributive property, and we got: (8*z**2)*(57*z**3) + (7*z**3)*(57*z**3)
Replacing (57*z**3)*(7*z**3 + 8*z**2) with (8*z**2)*(57*z**3) + (7*z**3)*(57*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (8*z**2)*(57*z**3) + (8*z**2)*48 + (7*z**3)*(57*z**3) + (7*z**3)*48</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (7*z**3)*48 = 336*z**3
  (7*z**3)*(57*z**3) = 399*z**6
  (8*z**2)*48 = 384*z**2
  (8*z**2)*(57*z**3) = 456*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 399*z**6 + 456*z**5 + 336*z**3 + 384*z**2</replace>
No more calculations needed.
<answer>399*z**6 + 456*z**5 + 336*z**3 + 384*z**2</answer>


Question:
Calculate the following: -30*y**2 + 190*y - 220
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*y**2 + 190*y - 220

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -30*y**2 + 190*y - 220
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: -30*y**2 + 190*y - 220</replace>
No more calculations needed.
<answer>-30*y**2 + 190*y - 220</answer>


Question:
Calculate the following: (-6*y**3 + 6*y)*(-3*y**3 + 34*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: 18*y**6 - 204*y**5 - 18*y**4 + 204*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: (-6*y**3 + 6*y)*(-3*y**3 + 34*y**2)
Expanding the part (-6*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-3*y**3 + 34*y**2) + (-6*y**3)*(-3*y**3 + 34*y**2)
<replace-#Step 1>#Step 2:
Current expression: (6*y)*(-3*y**3 + 34*y**2) + (-6*y**3)*(-3*y**3 + 34*y**2)</replace>
Simplifying the partial expression: (-6*y**3)*(-3*y**3 + 34*y**2)
Expanding the part (-3*y**3 + 34*y**2) using the distributive property, and we got: (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)
Replacing (-6*y**3)*(-3*y**3 + 34*y**2) with (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*y)*(-3*y**3 + 34*y**2) + (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)</replace>
Simplifying the partial expression: (6*y)*(-3*y**3 + 34*y**2)
Expanding the part (-3*y**3 + 34*y**2) using the distributive property, and we got: (6*y)*(34*y**2) + (6*y)*(-3*y**3)
Replacing (6*y)*(-3*y**3 + 34*y**2) with (6*y)*(34*y**2) + (6*y)*(-3*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*y)*(34*y**2) + (6*y)*(-3*y**3) + (34*y**2)*(-6*y**3) + (-6*y**3)*(-3*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*y**3)*(-6*y**3) = 18*y**6
  (-3*y**3)*(6*y) = -18*y**4
  (34*y**2)*(-6*y**3) = -204*y**5
  (34*y**2)*(6*y) = 204*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 18*y**6 - 204*y**5 - 18*y**4 + 204*y**3</replace>
No more calculations needed.
<answer>18*y**6 - 204*y**5 - 18*y**4 + 204*y**3</answer>


Question:
Simplify this expression: (22*x**2 + 2)*(33*x**3 + 30*x**2 + 56*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: 726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*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: (22*x**2 + 2)*(33*x**3 + 30*x**2 + 56*x)
Expanding the part (22*x**2 + 2) using the distributive property, and we got: (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + 2*(33*x**3 + 30*x**2 + 56*x)
<replace-#Step 1>#Step 2:
Current expression: (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + 2*(33*x**3 + 30*x**2 + 56*x)</replace>
Simplifying the partial expression: 2*(33*x**3 + 30*x**2 + 56*x)
Expanding the part (33*x**3 + 30*x**2 + 56*x) using the distributive property, and we got: (56*x)*2 + (30*x**2)*2 + (33*x**3)*2
Replacing 2*(33*x**3 + 30*x**2 + 56*x) with (56*x)*2 + (30*x**2)*2 + (33*x**3)*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (56*x)*2 + (22*x**2)*(33*x**3 + 30*x**2 + 56*x) + (30*x**2)*2 + (33*x**3)*2</replace>
Simplifying the partial expression: (22*x**2)*(33*x**3 + 30*x**2 + 56*x)
Expanding the part (33*x**3 + 30*x**2 + 56*x) using the distributive property, and we got: (56*x)*(22*x**2) + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3)
Replacing (22*x**2)*(33*x**3 + 30*x**2 + 56*x) with (56*x)*(22*x**2) + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (56*x)*(22*x**2) + (56*x)*2 + (22*x**2)*(30*x**2) + (22*x**2)*(33*x**3) + (30*x**2)*2 + (33*x**3)*2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*x**2)*2 = 60*x**2
  (30*x**2)*(22*x**2) = 660*x**4
  (33*x**3)*2 = 66*x**3
  (33*x**3)*(22*x**2) = 726*x**5
  (56*x)*2 = 112*x
  (56*x)*(22*x**2) = 1232*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 726*x**5 + 660*x**4 + 66*x**3 + 1232*x**3 + 60*x**2 + 112*x</replace>
Combining like terms, got 726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x
<replace-#Step 5>#Step 6:
Current expression: 726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x</replace>
No more calculations needed.
<answer>726*x**5 + 660*x**4 + 1298*x**3 + 60*x**2 + 112*x</answer>


Question:
Calculate the following: 34*y**2*(-37*y - 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: -1258*y**3 - 374*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: 34*y**2*(-37*y - 11)
Expanding the part (-37*y - 11) using the distributive property, and we got: (-37*y)*(34*y**2) - 374*y**2
<replace-#Step 1>#Step 2:
Current expression: (-37*y)*(34*y**2) - 374*y**2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -11*(34*y**2) = -374*y**2
  (-37*y)*(34*y**2) = -1258*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1258*y**3 - 374*y**2</replace>
No more calculations needed.
<answer>-1258*y**3 - 374*y**2</answer>


Question:
Simplify this expression: (6 - 18*x**3)*(-4*x**3 - 45*x**2 - 30*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: 72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*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: (6 - 18*x**3)*(-4*x**3 - 45*x**2 - 30*x)
Expanding the part (6 - 18*x**3) using the distributive property, and we got: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) + 6*(-4*x**3 - 45*x**2 - 30*x)
<replace-#Step 1>#Step 2:
Current expression: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) + 6*(-4*x**3 - 45*x**2 - 30*x)</replace>
Simplifying the partial expression: 6*(-4*x**3 - 45*x**2 - 30*x)
Expanding the part (-4*x**3 - 45*x**2 - 30*x) using the distributive property, and we got: -30*x*6 - 45*x**2*6 - 4*x**3*6
Replacing 6*(-4*x**3 - 45*x**2 - 30*x) with -30*x*6 - 45*x**2*6 - 4*x**3*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -30*x*6 - 45*x**2*6 + (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) - 4*x**3*6</replace>
Simplifying the partial expression: (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x)
Expanding the part (-4*x**3 - 45*x**2 - 30*x) using the distributive property, and we got: (-30*x)*(-18*x**3) + (-45*x**2)*(-18*x**3) + (-18*x**3)*(-4*x**3)
Replacing (-18*x**3)*(-4*x**3 - 45*x**2 - 30*x) with (-30*x)*(-18*x**3) + (-45*x**2)*(-18*x**3) + (-18*x**3)*(-4*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*x)*(-18*x**3) - 30*x*6 + (-45*x**2)*(-18*x**3) - 45*x**2*6 + (-18*x**3)*(-4*x**3) - 4*x**3*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*x**2)*6 = -270*x**2
  (-45*x**2)*(-18*x**3) = 810*x**5
  (-30*x)*6 = -180*x
  (-30*x)*(-18*x**3) = 540*x**4
  (-4*x**3)*6 = -24*x**3
  (-4*x**3)*(-18*x**3) = 72*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x</replace>
No more calculations needed.
<answer>72*x**6 + 810*x**5 + 540*x**4 - 24*x**3 - 270*x**2 - 180*x</answer>


Question:
Calculate the following: (41*z - 34)*(-14*z**3 + 6*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: -574*z**4 + 476*z**3 + 246*z**2 - 204*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 - 34)*(-14*z**3 + 6*z)
Expanding the part (41*z - 34) using the distributive property, and we got: (41*z)*(-14*z**3 + 6*z) - 34*(-14*z**3 + 6*z)
<replace-#Step 1>#Step 2:
Current expression: (41*z)*(-14*z**3 + 6*z) - 34*(-14*z**3 + 6*z)</replace>
Simplifying the partial expression: -34*(-14*z**3 + 6*z)
Expanding the part (-14*z**3 + 6*z) using the distributive property, and we got: (6*z)*(-34) - 14*z**3*(-34)
Replacing -34*(-14*z**3 + 6*z) with (6*z)*(-34) - 14*z**3*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*z)*(-34) + (41*z)*(-14*z**3 + 6*z) - 14*z**3*(-34)</replace>
Simplifying the partial expression: (41*z)*(-14*z**3 + 6*z)
Expanding the part (-14*z**3 + 6*z) using the distributive property, and we got: (6*z)*(41*z) + (41*z)*(-14*z**3)
Replacing (41*z)*(-14*z**3 + 6*z) with (6*z)*(41*z) + (41*z)*(-14*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*z)*(41*z) + (6*z)*(-34) + (41*z)*(-14*z**3) - 14*z**3*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**3)*-34 = 476*z**3
  (-14*z**3)*(41*z) = -574*z**4
  (6*z)*-34 = -204*z
  (6*z)*(41*z) = 246*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -574*z**4 + 476*z**3 + 246*z**2 - 204*z</replace>
No more calculations needed.
<answer>-574*z**4 + 476*z**3 + 246*z**2 - 204*z</answer>


Question:
Calculate the following: (-19*z**2 - 10)*(13*z**3 - 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -247*z**5 - 130*z**3 + 608*z**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: (-19*z**2 - 10)*(13*z**3 - 32)
Expanding the part (13*z**3 - 32) using the distributive property, and we got: (13*z**3)*(-19*z**2 - 10) - 32*(-19*z**2 - 10)
<replace-#Step 1>#Step 2:
Current expression: (13*z**3)*(-19*z**2 - 10) - 32*(-19*z**2 - 10)</replace>
Simplifying the partial expression: -32*(-19*z**2 - 10)
Expanding the part (-19*z**2 - 10) using the distributive property, and we got: -19*z**2*(-32) - 10*(-32)
Replacing -32*(-19*z**2 - 10) with -19*z**2*(-32) - 10*(-32) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -19*z**2*(-32) + (13*z**3)*(-19*z**2 - 10) + 320</replace>
Simplifying the partial expression: (13*z**3)*(-19*z**2 - 10)
Expanding the part (-19*z**2 - 10) using the distributive property, and we got: -130*z**3 + (-19*z**2)*(13*z**3)
Replacing (13*z**3)*(-19*z**2 - 10) with -130*z**3 + (-19*z**2)*(13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -10*13*z**3 + (-19*z**2)*(13*z**3) - 19*z**2*(-32) + 320</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*z**2)*-32 = 608*z**2
  (-19*z**2)*(13*z**3) = -247*z**5
  -10*13*z**3 = -130*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -247*z**5 - 130*z**3 + 608*z**2 + 320</replace>
No more calculations needed.
<answer>-247*z**5 - 130*z**3 + 608*z**2 + 320</answer>


Question:
Calculate the following: (14*x**3 + 50*x**2 - 22)*(5*x**3 + 47*x**2 - 44*x - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 70*x**6 + 908*x**5 + 1734*x**4 - 2772*x**3 - 2684*x**2 + 968*x + 726


Question:
Calculate the following: (36 - 21*y)*(-3*y**2 + y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 63*y**3 - 129*y**2 + 36*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: (36 - 21*y)*(-3*y**2 + y)
Expanding the part (36 - 21*y) using the distributive property, and we got: (-21*y)*(-3*y**2 + y) + 36*(-3*y**2 + y)
<replace-#Step 1>#Step 2:
Current expression: (-21*y)*(-3*y**2 + y) + 36*(-3*y**2 + y)</replace>
Simplifying the partial expression: 36*(-3*y**2 + y)
Expanding the part (-3*y**2 + y) using the distributive property, and we got: y*36 - 3*y**2*36
Replacing 36*(-3*y**2 + y) with y*36 - 3*y**2*36 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-21*y)*(-3*y**2 + y) + y*36 - 3*y**2*36</replace>
Simplifying the partial expression: (-21*y)*(-3*y**2 + y)
Expanding the part (-3*y**2 + y) using the distributive property, and we got: (-21*y)*y + (-21*y)*(-3*y**2)
Replacing (-21*y)*(-3*y**2 + y) with (-21*y)*y + (-21*y)*(-3*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*y)*y + (-21*y)*(-3*y**2) + y*36 - 3*y**2*36</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  y*36 = 36*y
  y*(-21*y) = -21*y**2
  (-3*y**2)*36 = -108*y**2
  (-3*y**2)*(-21*y) = 63*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 63*y**3 - 108*y**2 - 21*y**2 + 36*y</replace>
Combining like terms, got 63*y**3 - 129*y**2 + 36*y
<replace-#Step 5>#Step 6:
Current expression: 63*y**3 - 129*y**2 + 36*y</replace>
No more calculations needed.
<answer>63*y**3 - 129*y**2 + 36*y</answer>


Question:
Calculate the following: 78*x**2*(4*x**3 - 12*x**2 + 23*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: 312*x**5 - 936*x**4 + 1794*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**2*(4*x**3 - 12*x**2 + 23*x)
Expanding the part (4*x**3 - 12*x**2 + 23*x) using the distributive property, and we got: (23*x)*(78*x**2) + (-12*x**2)*(78*x**2) + (78*x**2)*(4*x**3)
<replace-#Step 1>#Step 2:
Current expression: (23*x)*(78*x**2) + (-12*x**2)*(78*x**2) + (78*x**2)*(4*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**2)*(78*x**2) = -936*x**4
  (4*x**3)*(78*x**2) = 312*x**5
  (23*x)*(78*x**2) = 1794*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 312*x**5 - 936*x**4 + 1794*x**3</replace>
No more calculations needed.
<answer>312*x**5 - 936*x**4 + 1794*x**3</answer>


Question:
Simplify this expression: (28 - 5*y)*(39 - 12*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: 60*y**3 - 336*y**2 - 195*y + 1092

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 - 5*y)*(39 - 12*y**2)
Expanding the part (28 - 5*y) using the distributive property, and we got: (-5*y)*(39 - 12*y**2) + 28*(39 - 12*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-5*y)*(39 - 12*y**2) + 28*(39 - 12*y**2)</replace>
Simplifying the partial expression: 28*(39 - 12*y**2)
Expanding the part (39 - 12*y**2) using the distributive property, and we got: -12*y**2*28 + 39*28
Replacing 28*(39 - 12*y**2) with -12*y**2*28 + 39*28 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-5*y)*(39 - 12*y**2) - 12*y**2*28 + 1092</replace>
Simplifying the partial expression: (-5*y)*(39 - 12*y**2)
Expanding the part (39 - 12*y**2) using the distributive property, and we got: (-5*y)*(-12*y**2) + 39*(-5*y)
Replacing (-5*y)*(39 - 12*y**2) with (-5*y)*(-12*y**2) + 39*(-5*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-5*y)*(-12*y**2) + 39*(-5)*y - 12*y**2*28 + 1092</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*y**2)*28 = -336*y**2
  (-12*y**2)*(-5*y) = 60*y**3
  39*-5*y = -195*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 60*y**3 - 336*y**2 - 195*y + 1092</replace>
No more calculations needed.
<answer>60*y**3 - 336*y**2 - 195*y + 1092</answer>


Question:
Simplify this expression: (-27*x**3 + 35*x**2)*(-21*x**3 - 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 567*x**6 - 735*x**5 + 1107*x**3 - 1435*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: (-27*x**3 + 35*x**2)*(-21*x**3 - 41)
Expanding the part (-21*x**3 - 41) using the distributive property, and we got: (-21*x**3)*(-27*x**3 + 35*x**2) - 41*(-27*x**3 + 35*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-21*x**3)*(-27*x**3 + 35*x**2) - 41*(-27*x**3 + 35*x**2)</replace>
Simplifying the partial expression: -41*(-27*x**3 + 35*x**2)
Expanding the part (-27*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-41) - 27*x**3*(-41)
Replacing -41*(-27*x**3 + 35*x**2) with (35*x**2)*(-41) - 27*x**3*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (35*x**2)*(-41) - 27*x**3*(-41) + (-21*x**3)*(-27*x**3 + 35*x**2)</replace>
Simplifying the partial expression: (-21*x**3)*(-27*x**3 + 35*x**2)
Expanding the part (-27*x**3 + 35*x**2) using the distributive property, and we got: (35*x**2)*(-21*x**3) + (-27*x**3)*(-21*x**3)
Replacing (-21*x**3)*(-27*x**3 + 35*x**2) with (35*x**2)*(-21*x**3) + (-27*x**3)*(-21*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (35*x**2)*(-21*x**3) + (35*x**2)*(-41) + (-27*x**3)*(-21*x**3) - 27*x**3*(-41)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-27*x**3)*-41 = 1107*x**3
  (-27*x**3)*(-21*x**3) = 567*x**6
  (35*x**2)*-41 = -1435*x**2
  (35*x**2)*(-21*x**3) = -735*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2</replace>
No more calculations needed.
<answer>567*x**6 - 735*x**5 + 1107*x**3 - 1435*x**2</answer>


Question:
Simplify this expression: (-95*y**2 + 14*y)*(53*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: -5035*y**4 - 398*y**3 + 168*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: (-95*y**2 + 14*y)*(53*y**2 + 12*y)
Expanding the part (-95*y**2 + 14*y) using the distributive property, and we got: (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2 + 12*y)
<replace-#Step 1>#Step 2:
Current expression: (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2 + 12*y)</replace>
Simplifying the partial expression: (-95*y**2)*(53*y**2 + 12*y)
Expanding the part (53*y**2 + 12*y) using the distributive property, and we got: (12*y)*(-95*y**2) + (-95*y**2)*(53*y**2)
Replacing (-95*y**2)*(53*y**2 + 12*y) with (12*y)*(-95*y**2) + (-95*y**2)*(53*y**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (12*y)*(-95*y**2) + (14*y)*(53*y**2 + 12*y) + (-95*y**2)*(53*y**2)</replace>
Simplifying the partial expression: (14*y)*(53*y**2 + 12*y)
Expanding the part (53*y**2 + 12*y) using the distributive property, and we got: (12*y)*(14*y) + (14*y)*(53*y**2)
Replacing (14*y)*(53*y**2 + 12*y) with (12*y)*(14*y) + (14*y)*(53*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (12*y)*(14*y) + (12*y)*(-95*y**2) + (14*y)*(53*y**2) + (-95*y**2)*(53*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*y)*(-95*y**2) = -1140*y**3
  (12*y)*(14*y) = 168*y**2
  (53*y**2)*(-95*y**2) = -5035*y**4
  (53*y**2)*(14*y) = 742*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -5035*y**4 - 1140*y**3 + 742*y**3 + 168*y**2</replace>
Combining like terms, got -5035*y**4 - 398*y**3 + 168*y**2
<replace-#Step 5>#Step 6:
Current expression: -5035*y**4 - 398*y**3 + 168*y**2</replace>
No more calculations needed.
<answer>-5035*y**4 - 398*y**3 + 168*y**2</answer>


Question:
Simplify this expression: (-34*z - 47)*(27*z**3 - 41*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: -918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-34*z - 47)*(27*z**3 - 41*z)
Expanding the part (-34*z - 47) using the distributive property, and we got: (-34*z)*(27*z**3 - 41*z) - 47*(27*z**3 - 41*z)
<replace-#Step 1>#Step 2:
Current expression: (-34*z)*(27*z**3 - 41*z) - 47*(27*z**3 - 41*z)</replace>
Simplifying the partial expression: -47*(27*z**3 - 41*z)
Expanding the part (27*z**3 - 41*z) using the distributive property, and we got: -41*z*(-47) + (27*z**3)*(-47)
Replacing -47*(27*z**3 - 41*z) with -41*z*(-47) + (27*z**3)*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*z*(-47) + (-34*z)*(27*z**3 - 41*z) + (27*z**3)*(-47)</replace>
Simplifying the partial expression: (-34*z)*(27*z**3 - 41*z)
Expanding the part (27*z**3 - 41*z) using the distributive property, and we got: (-41*z)*(-34*z) + (-34*z)*(27*z**3)
Replacing (-34*z)*(27*z**3 - 41*z) with (-41*z)*(-34*z) + (-34*z)*(27*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-41*z)*(-34*z) - 41*z*(-47) + (-34*z)*(27*z**3) + (27*z**3)*(-47)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*z)*-47 = 1927*z
  (-41*z)*(-34*z) = 1394*z**2
  (27*z**3)*-47 = -1269*z**3
  (27*z**3)*(-34*z) = -918*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z</replace>
No more calculations needed.
<answer>-918*z**4 - 1269*z**3 + 1394*z**2 + 1927*z</answer>


Question:
Simplify this expression: (18*x**2 - 4)*(-55*x**3 + 43*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: -990*x**5 + 994*x**3 - 172*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: (18*x**2 - 4)*(-55*x**3 + 43*x)
Expanding the part (18*x**2 - 4) using the distributive property, and we got: (18*x**2)*(-55*x**3 + 43*x) - 4*(-55*x**3 + 43*x)
<replace-#Step 1>#Step 2:
Current expression: (18*x**2)*(-55*x**3 + 43*x) - 4*(-55*x**3 + 43*x)</replace>
Simplifying the partial expression: -4*(-55*x**3 + 43*x)
Expanding the part (-55*x**3 + 43*x) using the distributive property, and we got: (43*x)*(-4) - 55*x**3*(-4)
Replacing -4*(-55*x**3 + 43*x) with (43*x)*(-4) - 55*x**3*(-4) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (43*x)*(-4) + (18*x**2)*(-55*x**3 + 43*x) - 55*x**3*(-4)</replace>
Simplifying the partial expression: (18*x**2)*(-55*x**3 + 43*x)
Expanding the part (-55*x**3 + 43*x) using the distributive property, and we got: (43*x)*(18*x**2) + (18*x**2)*(-55*x**3)
Replacing (18*x**2)*(-55*x**3 + 43*x) with (43*x)*(18*x**2) + (18*x**2)*(-55*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (43*x)*(18*x**2) + (43*x)*(-4) + (18*x**2)*(-55*x**3) - 55*x**3*(-4)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-55*x**3)*-4 = 220*x**3
  (-55*x**3)*(18*x**2) = -990*x**5
  (43*x)*-4 = -172*x
  (43*x)*(18*x**2) = 774*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -990*x**5 + 220*x**3 + 774*x**3 - 172*x</replace>
Combining like terms, got -990*x**5 + 994*x**3 - 172*x
<replace-#Step 5>#Step 6:
Current expression: -990*x**5 + 994*x**3 - 172*x</replace>
No more calculations needed.
<answer>-990*x**5 + 994*x**3 - 172*x</answer>


Question:
Simplify this expression: (10*y + 44)*(-3*y**3 - 21*y - 80)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*y + 44)*(-3*y**3 - 21*y - 80)
Expanding the part (10*y + 44) using the distributive property, and we got: (10*y)*(-3*y**3 - 21*y - 80) + 44*(-3*y**3 - 21*y - 80)
<replace-#Step 1>#Step 2:
Current expression: (10*y)*(-3*y**3 - 21*y - 80) + 44*(-3*y**3 - 21*y - 80)</replace>
Simplifying the partial expression: 44*(-3*y**3 - 21*y - 80)
Expanding the part (-3*y**3 - 21*y - 80) using the distributive property, and we got: -21*y*44 - 3*y**3*44 - 80*44
Replacing 44*(-3*y**3 - 21*y - 80) with -21*y*44 - 3*y**3*44 - 80*44 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -21*y*44 + (10*y)*(-3*y**3 - 21*y - 80) - 3*y**3*44 - 3520</replace>
Simplifying the partial expression: (10*y)*(-3*y**3 - 21*y - 80)
Expanding the part (-3*y**3 - 21*y - 80) using the distributive property, and we got: (-21*y)*(10*y) - 800*y + (10*y)*(-3*y**3)
Replacing (10*y)*(-3*y**3 - 21*y - 80) with (-21*y)*(10*y) - 800*y + (10*y)*(-3*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-21*y)*(10*y) - 21*y*44 - 80*10*y + (10*y)*(-3*y**3) - 3*y**3*44 - 3520</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-21*y)*44 = -924*y
  (-21*y)*(10*y) = -210*y**2
  (-3*y**3)*44 = -132*y**3
  (-3*y**3)*(10*y) = -30*y**4
  -80*10*y = -800*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -30*y**4 - 132*y**3 - 210*y**2 - 924*y - 800*y - 3520</replace>
Combining like terms, got -30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520
<replace-#Step 5>#Step 6:
Current expression: -30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520</replace>
No more calculations needed.
<answer>-30*y**4 - 132*y**3 - 210*y**2 - 1724*y - 3520</answer>


Question:
Calculate the following: (-7*x**2 - 54)*(6*x**2 - 34*x + 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: -42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-7*x**2 - 54)*(6*x**2 - 34*x + 38)
Expanding the part (-7*x**2 - 54) using the distributive property, and we got: (-7*x**2)*(6*x**2 - 34*x + 38) - 54*(6*x**2 - 34*x + 38)
<replace-#Step 1>#Step 2:
Current expression: (-7*x**2)*(6*x**2 - 34*x + 38) - 54*(6*x**2 - 34*x + 38)</replace>
Simplifying the partial expression: -54*(6*x**2 - 34*x + 38)
Expanding the part (6*x**2 - 34*x + 38) using the distributive property, and we got: -34*x*(-54) + (6*x**2)*(-54) + 38*(-54)
Replacing -54*(6*x**2 - 34*x + 38) with -34*x*(-54) + (6*x**2)*(-54) + 38*(-54) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -34*x*(-54) + (-7*x**2)*(6*x**2 - 34*x + 38) + (6*x**2)*(-54) - 2052</replace>
Simplifying the partial expression: (-7*x**2)*(6*x**2 - 34*x + 38)
Expanding the part (6*x**2 - 34*x + 38) using the distributive property, and we got: (-34*x)*(-7*x**2) + 38*(-7*x**2) + (-7*x**2)*(6*x**2)
Replacing (-7*x**2)*(6*x**2 - 34*x + 38) with (-34*x)*(-7*x**2) + 38*(-7*x**2) + (-7*x**2)*(6*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*x)*(-7*x**2) - 34*x*(-54) + 38*(-7)*x**2 + (-7*x**2)*(6*x**2) + (6*x**2)*(-54) - 2052</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x)*-54 = 1836*x
  (-34*x)*(-7*x**2) = 238*x**3
  (6*x**2)*-54 = -324*x**2
  (6*x**2)*(-7*x**2) = -42*x**4
  38*-7*x**2 = -266*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -42*x**4 + 238*x**3 - 324*x**2 - 266*x**2 + 1836*x - 2052</replace>
Combining like terms, got -42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052
<replace-#Step 5>#Step 6:
Current expression: -42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052</replace>
No more calculations needed.
<answer>-42*x**4 + 238*x**3 - 590*x**2 + 1836*x - 2052</answer>


Question:
Calculate the following: (3 - 2*z)*(14*z**2 + 44*z - 95)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -28*z**3 - 46*z**2 + 322*z - 285

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (3 - 2*z)*(14*z**2 + 44*z - 95)
Expanding the part (3 - 2*z) using the distributive property, and we got: (-2*z)*(14*z**2 + 44*z - 95) + 3*(14*z**2 + 44*z - 95)
<replace-#Step 1>#Step 2:
Current expression: (-2*z)*(14*z**2 + 44*z - 95) + 3*(14*z**2 + 44*z - 95)</replace>
Simplifying the partial expression: 3*(14*z**2 + 44*z - 95)
Expanding the part (14*z**2 + 44*z - 95) using the distributive property, and we got: (44*z)*3 + (14*z**2)*3 - 95*3
Replacing 3*(14*z**2 + 44*z - 95) with (44*z)*3 + (14*z**2)*3 - 95*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*z)*(14*z**2 + 44*z - 95) + (44*z)*3 + (14*z**2)*3 - 285</replace>
Simplifying the partial expression: (-2*z)*(14*z**2 + 44*z - 95)
Expanding the part (14*z**2 + 44*z - 95) using the distributive property, and we got: (-2*z)*(44*z) + (-2*z)*(14*z**2) - (-1)*190*z
Replacing (-2*z)*(14*z**2 + 44*z - 95) with (-2*z)*(44*z) + (-2*z)*(14*z**2) - (-1)*190*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-2*z)*(44*z) + (-2*z)*(14*z**2) - 95*(-2)*z + (44*z)*3 + (14*z**2)*3 - 285</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*z**2)*3 = 42*z**2
  (14*z**2)*(-2*z) = -28*z**3
  (44*z)*3 = 132*z
  (44*z)*(-2*z) = -88*z**2
  -95*-2*z = 190*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -28*z**3 - 88*z**2 + 42*z**2 + 132*z + 190*z - 285</replace>
Combining like terms, got -28*z**3 - 46*z**2 + 322*z - 285
<replace-#Step 5>#Step 6:
Current expression: -28*z**3 - 46*z**2 + 322*z - 285</replace>
No more calculations needed.
<answer>-28*z**3 - 46*z**2 + 322*z - 285</answer>


Question:
Calculate the following: (6 - 43*x**3)*(7*x**3 - 45*x**2 + 40*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: -301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*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: (6 - 43*x**3)*(7*x**3 - 45*x**2 + 40*x)
Expanding the part (6 - 43*x**3) using the distributive property, and we got: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + 6*(7*x**3 - 45*x**2 + 40*x)
<replace-#Step 1>#Step 2:
Current expression: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + 6*(7*x**3 - 45*x**2 + 40*x)</replace>
Simplifying the partial expression: 6*(7*x**3 - 45*x**2 + 40*x)
Expanding the part (7*x**3 - 45*x**2 + 40*x) using the distributive property, and we got: (40*x)*6 - 45*x**2*6 + (7*x**3)*6
Replacing 6*(7*x**3 - 45*x**2 + 40*x) with (40*x)*6 - 45*x**2*6 + (7*x**3)*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (40*x)*6 - 45*x**2*6 + (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) + (7*x**3)*6</replace>
Simplifying the partial expression: (-43*x**3)*(7*x**3 - 45*x**2 + 40*x)
Expanding the part (7*x**3 - 45*x**2 + 40*x) using the distributive property, and we got: (40*x)*(-43*x**3) + (-45*x**2)*(-43*x**3) + (-43*x**3)*(7*x**3)
Replacing (-43*x**3)*(7*x**3 - 45*x**2 + 40*x) with (40*x)*(-43*x**3) + (-45*x**2)*(-43*x**3) + (-43*x**3)*(7*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (40*x)*(-43*x**3) + (40*x)*6 + (-45*x**2)*(-43*x**3) - 45*x**2*6 + (-43*x**3)*(7*x**3) + (7*x**3)*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-45*x**2)*6 = -270*x**2
  (-45*x**2)*(-43*x**3) = 1935*x**5
  (7*x**3)*6 = 42*x**3
  (7*x**3)*(-43*x**3) = -301*x**6
  (40*x)*6 = 240*x
  (40*x)*(-43*x**3) = -1720*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x</replace>
No more calculations needed.
<answer>-301*x**6 + 1935*x**5 - 1720*x**4 + 42*x**3 - 270*x**2 + 240*x</answer>


Question:
Simplify this expression: (75 - 23*z**3)*(16*z**2 + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -368*z**5 - 161*z**3 + 1200*z**2 + 525

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (75 - 23*z**3)*(16*z**2 + 7)
Expanding the part (16*z**2 + 7) using the distributive property, and we got: (16*z**2)*(75 - 23*z**3) + 7*(75 - 23*z**3)
<replace-#Step 1>#Step 2:
Current expression: (16*z**2)*(75 - 23*z**3) + 7*(75 - 23*z**3)</replace>
Simplifying the partial expression: 7*(75 - 23*z**3)
Expanding the part (75 - 23*z**3) using the distributive property, and we got: -23*z**3*7 + 75*7
Replacing 7*(75 - 23*z**3) with -23*z**3*7 + 75*7 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (16*z**2)*(75 - 23*z**3) - 23*z**3*7 + 525</replace>
Simplifying the partial expression: (16*z**2)*(75 - 23*z**3)
Expanding the part (75 - 23*z**3) using the distributive property, and we got: 75*(16*z**2) + (16*z**2)*(-23*z**3)
Replacing (16*z**2)*(75 - 23*z**3) with 75*(16*z**2) + (16*z**2)*(-23*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 75*16*z**2 + (16*z**2)*(-23*z**3) - 23*z**3*7 + 525</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*z**3)*7 = -161*z**3
  (-23*z**3)*(16*z**2) = -368*z**5
  75*16*z**2 = 1200*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -368*z**5 - 161*z**3 + 1200*z**2 + 525</replace>
No more calculations needed.
<answer>-368*z**5 - 161*z**3 + 1200*z**2 + 525</answer>


Question:
Simplify this expression: (37 - y**2)*(12*y**3 + 8*y**2 - 35*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: -12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*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: (37 - y**2)*(12*y**3 + 8*y**2 - 35*y)
Expanding the part (37 - y**2) using the distributive property, and we got: (-y**2)*(12*y**3 + 8*y**2 - 35*y) + 37*(12*y**3 + 8*y**2 - 35*y)
<replace-#Step 1>#Step 2:
Current expression: (-y**2)*(12*y**3 + 8*y**2 - 35*y) + 37*(12*y**3 + 8*y**2 - 35*y)</replace>
Simplifying the partial expression: 37*(12*y**3 + 8*y**2 - 35*y)
Expanding the part (12*y**3 + 8*y**2 - 35*y) using the distributive property, and we got: -35*y*37 + (8*y**2)*37 + (12*y**3)*37
Replacing 37*(12*y**3 + 8*y**2 - 35*y) with -35*y*37 + (8*y**2)*37 + (12*y**3)*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -35*y*37 + (-y**2)*(12*y**3 + 8*y**2 - 35*y) + (8*y**2)*37 + (12*y**3)*37</replace>
Simplifying the partial expression: (-y**2)*(12*y**3 + 8*y**2 - 35*y)
Expanding the part (12*y**3 + 8*y**2 - 35*y) using the distributive property, and we got: (-35*y)*(-y**2) + (-y**2)*(8*y**2) + (-y**2)*(12*y**3)
Replacing (-y**2)*(12*y**3 + 8*y**2 - 35*y) with (-35*y)*(-y**2) + (-y**2)*(8*y**2) + (-y**2)*(12*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-35*y)*(-y**2) - 35*y*37 + (-y**2)*(8*y**2) + (-y**2)*(12*y**3) + (8*y**2)*37 + (12*y**3)*37</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-35*y)*37 = -1295*y
  (-35*y)*(-y**2) = 35*y**3
  (8*y**2)*37 = 296*y**2
  (8*y**2)*(-y**2) = -8*y**4
  (12*y**3)*37 = 444*y**3
  (12*y**3)*(-y**2) = -12*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -12*y**5 - 8*y**4 + 35*y**3 + 444*y**3 + 296*y**2 - 1295*y</replace>
Combining like terms, got -12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y
<replace-#Step 5>#Step 6:
Current expression: -12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y</replace>
No more calculations needed.
<answer>-12*y**5 - 8*y**4 + 479*y**3 + 296*y**2 - 1295*y</answer>


Question:
Simplify this expression: (-23*x**3 - 36*x**2)*(13*x**3 + 10*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -299*x**6 - 468*x**5 - 230*x**4 - 360*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: (-23*x**3 - 36*x**2)*(13*x**3 + 10*x)
Expanding the part (-23*x**3 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(13*x**3 + 10*x) + (-23*x**3)*(13*x**3 + 10*x)
<replace-#Step 1>#Step 2:
Current expression: (-36*x**2)*(13*x**3 + 10*x) + (-23*x**3)*(13*x**3 + 10*x)</replace>
Simplifying the partial expression: (-36*x**2)*(13*x**3 + 10*x)
Expanding the part (13*x**3 + 10*x) using the distributive property, and we got: (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3)
Replacing (-36*x**2)*(13*x**3 + 10*x) with (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*x)*(-36*x**2) + (-36*x**2)*(13*x**3) + (-23*x**3)*(13*x**3 + 10*x)</replace>
Simplifying the partial expression: (-23*x**3)*(13*x**3 + 10*x)
Expanding the part (13*x**3 + 10*x) using the distributive property, and we got: (10*x)*(-23*x**3) + (-23*x**3)*(13*x**3)
Replacing (-23*x**3)*(13*x**3 + 10*x) with (10*x)*(-23*x**3) + (-23*x**3)*(13*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*x)*(-36*x**2) + (10*x)*(-23*x**3) + (-36*x**2)*(13*x**3) + (-23*x**3)*(13*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*x)*(-36*x**2) = -360*x**3
  (10*x)*(-23*x**3) = -230*x**4
  (13*x**3)*(-36*x**2) = -468*x**5
  (13*x**3)*(-23*x**3) = -299*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -299*x**6 - 468*x**5 - 230*x**4 - 360*x**3</replace>
No more calculations needed.
<answer>-299*x**6 - 468*x**5 - 230*x**4 - 360*x**3</answer>


Question:
Simplify this expression: (10*y**3 - 31)*(-19*y**2 + 27*y + 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: -190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*y**3 - 31)*(-19*y**2 + 27*y + 25)
Expanding the part (10*y**3 - 31) using the distributive property, and we got: (10*y**3)*(-19*y**2 + 27*y + 25) - 31*(-19*y**2 + 27*y + 25)
<replace-#Step 1>#Step 2:
Current expression: (10*y**3)*(-19*y**2 + 27*y + 25) - 31*(-19*y**2 + 27*y + 25)</replace>
Simplifying the partial expression: -31*(-19*y**2 + 27*y + 25)
Expanding the part (-19*y**2 + 27*y + 25) using the distributive property, and we got: (27*y)*(-31) - 19*y**2*(-31) + 25*(-31)
Replacing -31*(-19*y**2 + 27*y + 25) with (27*y)*(-31) - 19*y**2*(-31) + 25*(-31) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (27*y)*(-31) - 19*y**2*(-31) + (10*y**3)*(-19*y**2 + 27*y + 25) - 775</replace>
Simplifying the partial expression: (10*y**3)*(-19*y**2 + 27*y + 25)
Expanding the part (-19*y**2 + 27*y + 25) using the distributive property, and we got: 25*(10*y**3) + (27*y)*(10*y**3) + (-19*y**2)*(10*y**3)
Replacing (10*y**3)*(-19*y**2 + 27*y + 25) with 25*(10*y**3) + (27*y)*(10*y**3) + (-19*y**2)*(10*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 25*10*y**3 + (27*y)*(10*y**3) + (27*y)*(-31) + (-19*y**2)*(10*y**3) - 19*y**2*(-31) - 775</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*y**2)*-31 = 589*y**2
  (-19*y**2)*(10*y**3) = -190*y**5
  (27*y)*-31 = -837*y
  (27*y)*(10*y**3) = 270*y**4
  25*10*y**3 = 250*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775</replace>
No more calculations needed.
<answer>-190*y**5 + 270*y**4 + 250*y**3 + 589*y**2 - 837*y - 775</answer>


Question:
Calculate the following: (19*z + 26)*(33*z**3 - 14*z**2 + 14*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: 627*z**4 + 592*z**3 - 98*z**2 + 364*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: (19*z + 26)*(33*z**3 - 14*z**2 + 14*z)
Expanding the part (19*z + 26) using the distributive property, and we got: (19*z)*(33*z**3 - 14*z**2 + 14*z) + 26*(33*z**3 - 14*z**2 + 14*z)
<replace-#Step 1>#Step 2:
Current expression: (19*z)*(33*z**3 - 14*z**2 + 14*z) + 26*(33*z**3 - 14*z**2 + 14*z)</replace>
Simplifying the partial expression: 26*(33*z**3 - 14*z**2 + 14*z)
Expanding the part (33*z**3 - 14*z**2 + 14*z) using the distributive property, and we got: (14*z)*26 - 14*z**2*26 + (33*z**3)*26
Replacing 26*(33*z**3 - 14*z**2 + 14*z) with (14*z)*26 - 14*z**2*26 + (33*z**3)*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*26 + (19*z)*(33*z**3 - 14*z**2 + 14*z) - 14*z**2*26 + (33*z**3)*26</replace>
Simplifying the partial expression: (19*z)*(33*z**3 - 14*z**2 + 14*z)
Expanding the part (33*z**3 - 14*z**2 + 14*z) using the distributive property, and we got: (14*z)*(19*z) + (19*z)*(-14*z**2) + (19*z)*(33*z**3)
Replacing (19*z)*(33*z**3 - 14*z**2 + 14*z) with (14*z)*(19*z) + (19*z)*(-14*z**2) + (19*z)*(33*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*z)*(19*z) + (14*z)*26 + (19*z)*(-14*z**2) + (19*z)*(33*z**3) - 14*z**2*26 + (33*z**3)*26</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-14*z**2)*26 = -364*z**2
  (-14*z**2)*(19*z) = -266*z**3
  (14*z)*26 = 364*z
  (14*z)*(19*z) = 266*z**2
  (33*z**3)*26 = 858*z**3
  (33*z**3)*(19*z) = 627*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 627*z**4 - 266*z**3 + 858*z**3 - 364*z**2 + 266*z**2 + 364*z</replace>
Combining like terms, got 627*z**4 + 592*z**3 - 98*z**2 + 364*z
<replace-#Step 5>#Step 6:
Current expression: 627*z**4 + 592*z**3 - 98*z**2 + 364*z</replace>
No more calculations needed.
<answer>627*z**4 + 592*z**3 - 98*z**2 + 364*z</answer>


Question:
Simplify this expression: (10*y**2 - 48*y)*(-39*y**3 + 9*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: -390*y**5 + 1962*y**4 - 432*y**3 + 330*y**2 - 1584*y


Question:
Calculate the following: (26 - 47*x)*(43*x + 54)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2021*x**2 - 1420*x + 1404

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 - 47*x)*(43*x + 54)
Expanding the part (26 - 47*x) using the distributive property, and we got: (-47*x)*(43*x + 54) + 26*(43*x + 54)
<replace-#Step 1>#Step 2:
Current expression: (-47*x)*(43*x + 54) + 26*(43*x + 54)</replace>
Simplifying the partial expression: 26*(43*x + 54)
Expanding the part (43*x + 54) using the distributive property, and we got: (43*x)*26 + 54*26
Replacing 26*(43*x + 54) with (43*x)*26 + 54*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*x)*(43*x + 54) + (43*x)*26 + 1404</replace>
Simplifying the partial expression: (-47*x)*(43*x + 54)
Expanding the part (43*x + 54) using the distributive property, and we got: (-47*x)*(43*x) + 54*(-47*x)
Replacing (-47*x)*(43*x + 54) with (-47*x)*(43*x) + 54*(-47*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*x)*(43*x) + 54*(-47)*x + (43*x)*26 + 1404</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*x)*26 = 1118*x
  (43*x)*(-47*x) = -2021*x**2
  54*-47*x = -2538*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2021*x**2 - 2538*x + 1118*x + 1404</replace>
Combining like terms, got -2021*x**2 - 1420*x + 1404
<replace-#Step 5>#Step 6:
Current expression: -2021*x**2 - 1420*x + 1404</replace>
No more calculations needed.
<answer>-2021*x**2 - 1420*x + 1404</answer>


Question:
Calculate the following: (49*z - 77)*(20*z**2 + 36*z - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 980*z**3 + 224*z**2 - 3360*z + 924

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (49*z - 77)*(20*z**2 + 36*z - 12)
Expanding the part (49*z - 77) using the distributive property, and we got: (49*z)*(20*z**2 + 36*z - 12) - 77*(20*z**2 + 36*z - 12)
<replace-#Step 1>#Step 2:
Current expression: (49*z)*(20*z**2 + 36*z - 12) - 77*(20*z**2 + 36*z - 12)</replace>
Simplifying the partial expression: -77*(20*z**2 + 36*z - 12)
Expanding the part (20*z**2 + 36*z - 12) using the distributive property, and we got: (36*z)*(-77) + (20*z**2)*(-77) - 12*(-77)
Replacing -77*(20*z**2 + 36*z - 12) with (36*z)*(-77) + (20*z**2)*(-77) - 12*(-77) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (36*z)*(-77) + (49*z)*(20*z**2 + 36*z - 12) + (20*z**2)*(-77) + 924</replace>
Simplifying the partial expression: (49*z)*(20*z**2 + 36*z - 12)
Expanding the part (20*z**2 + 36*z - 12) using the distributive property, and we got: -588*z + (36*z)*(49*z) + (49*z)*(20*z**2)
Replacing (49*z)*(20*z**2 + 36*z - 12) with -588*z + (36*z)*(49*z) + (49*z)*(20*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -12*49*z + (36*z)*(49*z) + (36*z)*(-77) + (49*z)*(20*z**2) + (20*z**2)*(-77) + 924</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*z**2)*-77 = -1540*z**2
  (20*z**2)*(49*z) = 980*z**3
  (36*z)*-77 = -2772*z
  (36*z)*(49*z) = 1764*z**2
  -12*49*z = -588*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 980*z**3 - 1540*z**2 + 1764*z**2 - 2772*z - 588*z + 924</replace>
Combining like terms, got 980*z**3 + 224*z**2 - 3360*z + 924
<replace-#Step 5>#Step 6:
Current expression: 980*z**3 + 224*z**2 - 3360*z + 924</replace>
No more calculations needed.
<answer>980*z**3 + 224*z**2 - 3360*z + 924</answer>


Question:
Simplify this expression: (37*x**2 + 6)*(35*x**3 - 41*x**2 - 45*x - 33)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1295*x**5 - 1517*x**4 - 1455*x**3 - 1467*x**2 - 270*x - 198


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

Answer: 144*x**6 + 216*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: -12*x**3*(-12*x**3 - 18)
Expanding the part (-12*x**3 - 18) using the distributive property, and we got: -(-1)*216*x**3 + (-12*x**3)*(-12*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*216*x**3 + (-12*x**3)*(-12*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -18*(-12*x**3) = 216*x**3
  (-12*x**3)*(-12*x**3) = 144*x**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 144*x**6 + 216*x**3</replace>
No more calculations needed.
<answer>144*x**6 + 216*x**3</answer>


Question:
Simplify this expression: (7*x**3 - 36)*(16*x**3 + 23*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: 112*x**6 + 161*x**4 - 576*x**3 - 828*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: (7*x**3 - 36)*(16*x**3 + 23*x)
Expanding the part (7*x**3 - 36) using the distributive property, and we got: (7*x**3)*(16*x**3 + 23*x) - 36*(16*x**3 + 23*x)
<replace-#Step 1>#Step 2:
Current expression: (7*x**3)*(16*x**3 + 23*x) - 36*(16*x**3 + 23*x)</replace>
Simplifying the partial expression: -36*(16*x**3 + 23*x)
Expanding the part (16*x**3 + 23*x) using the distributive property, and we got: (23*x)*(-36) + (16*x**3)*(-36)
Replacing -36*(16*x**3 + 23*x) with (23*x)*(-36) + (16*x**3)*(-36) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*x)*(-36) + (7*x**3)*(16*x**3 + 23*x) + (16*x**3)*(-36)</replace>
Simplifying the partial expression: (7*x**3)*(16*x**3 + 23*x)
Expanding the part (16*x**3 + 23*x) using the distributive property, and we got: (23*x)*(7*x**3) + (7*x**3)*(16*x**3)
Replacing (7*x**3)*(16*x**3 + 23*x) with (23*x)*(7*x**3) + (7*x**3)*(16*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (23*x)*(7*x**3) + (23*x)*(-36) + (7*x**3)*(16*x**3) + (16*x**3)*(-36)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*x**3)*-36 = -576*x**3
  (16*x**3)*(7*x**3) = 112*x**6
  (23*x)*-36 = -828*x
  (23*x)*(7*x**3) = 161*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 112*x**6 + 161*x**4 - 576*x**3 - 828*x</replace>
No more calculations needed.
<answer>112*x**6 + 161*x**4 - 576*x**3 - 828*x</answer>


Question:
Calculate the following: (23*y**2 + 7*y)*(-18*y**3 + 16*y**2 - 14*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -414*y**5 + 242*y**4 - 210*y**3 - 98*y**2


Question:
Calculate the following: (-26*y - 45)*(30*y**3 + 27*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: -780*y**4 - 1350*y**3 - 702*y**2 - 1215*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: (-26*y - 45)*(30*y**3 + 27*y)
Expanding the part (-26*y - 45) using the distributive property, and we got: (-26*y)*(30*y**3 + 27*y) - 45*(30*y**3 + 27*y)
<replace-#Step 1>#Step 2:
Current expression: (-26*y)*(30*y**3 + 27*y) - 45*(30*y**3 + 27*y)</replace>
Simplifying the partial expression: -45*(30*y**3 + 27*y)
Expanding the part (30*y**3 + 27*y) using the distributive property, and we got: (27*y)*(-45) + (30*y**3)*(-45)
Replacing -45*(30*y**3 + 27*y) with (27*y)*(-45) + (30*y**3)*(-45) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-26*y)*(30*y**3 + 27*y) + (27*y)*(-45) + (30*y**3)*(-45)</replace>
Simplifying the partial expression: (-26*y)*(30*y**3 + 27*y)
Expanding the part (30*y**3 + 27*y) using the distributive property, and we got: (-26*y)*(27*y) + (-26*y)*(30*y**3)
Replacing (-26*y)*(30*y**3 + 27*y) with (-26*y)*(27*y) + (-26*y)*(30*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-26*y)*(27*y) + (-26*y)*(30*y**3) + (27*y)*(-45) + (30*y**3)*(-45)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (27*y)*-45 = -1215*y
  (27*y)*(-26*y) = -702*y**2
  (30*y**3)*-45 = -1350*y**3
  (30*y**3)*(-26*y) = -780*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -780*y**4 - 1350*y**3 - 702*y**2 - 1215*y</replace>
No more calculations needed.
<answer>-780*y**4 - 1350*y**3 - 702*y**2 - 1215*y</answer>


Question:
Calculate the following: (23*z**3 - 32)*(-11*z**3 - 11*z**2 + 13*z + 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -253*z**6 - 253*z**5 + 299*z**4 + 1042*z**3 + 352*z**2 - 416*z - 960


Question:
Simplify this expression: (18*y**3 - 22*y**2)*(11*y**3 - 20*y**2 - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 198*y**6 - 602*y**5 + 440*y**4 - 720*y**3 + 880*y**2


Question:
Simplify this expression: -31*x**3*(-57*x**3 + 26*x**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: 1767*x**6 - 806*x**5 + 496*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: -31*x**3*(-57*x**3 + 26*x**2 - 16)
Expanding the part (-57*x**3 + 26*x**2 - 16) using the distributive property, and we got: -(-1)*496*x**3 + (26*x**2)*(-31*x**3) + (-57*x**3)*(-31*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*496*x**3 + (26*x**2)*(-31*x**3) + (-57*x**3)*(-31*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -16*(-31*x**3) = 496*x**3
  (-57*x**3)*(-31*x**3) = 1767*x**6
  (26*x**2)*(-31*x**3) = -806*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1767*x**6 - 806*x**5 + 496*x**3</replace>
No more calculations needed.
<answer>1767*x**6 - 806*x**5 + 496*x**3</answer>


Question:
Calculate the following: (6*x**3 - 24*x**2)*(48*x**3 - 11*x**2 - 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: 288*x**6 - 1218*x**5 + 264*x**4 - 138*x**3 + 552*x**2


Question:
Simplify this expression: -129*x*(4*x**3 - x**2 + 37*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: -516*x**4 + 129*x**3 - 4773*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: -129*x*(4*x**3 - x**2 + 37*x)
Expanding the part (4*x**3 - x**2 + 37*x) using the distributive property, and we got: (-129*x)*(37*x) + (-129*x)*(-x**2) + (-129*x)*(4*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-129*x)*(37*x) + (-129*x)*(-x**2) + (-129*x)*(4*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-x**2)*(-129*x) = 129*x**3
  (4*x**3)*(-129*x) = -516*x**4
  (37*x)*(-129*x) = -4773*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -516*x**4 + 129*x**3 - 4773*x**2</replace>
No more calculations needed.
<answer>-516*x**4 + 129*x**3 - 4773*x**2</answer>


Question:
Simplify this expression: (47*y**3 - 47)*(-37*y**3 - 11*y**2 - 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: -1739*y**6 - 517*y**5 - 517*y**3 + 517*y**2 + 2256


Question:
Simplify this expression: (7*x + 4)*(-49*x**2 + 23*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: -343*x**3 - 35*x**2 + 92*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: (7*x + 4)*(-49*x**2 + 23*x)
Expanding the part (7*x + 4) using the distributive property, and we got: (7*x)*(-49*x**2 + 23*x) + 4*(-49*x**2 + 23*x)
<replace-#Step 1>#Step 2:
Current expression: (7*x)*(-49*x**2 + 23*x) + 4*(-49*x**2 + 23*x)</replace>
Simplifying the partial expression: 4*(-49*x**2 + 23*x)
Expanding the part (-49*x**2 + 23*x) using the distributive property, and we got: (23*x)*4 - 49*x**2*4
Replacing 4*(-49*x**2 + 23*x) with (23*x)*4 - 49*x**2*4 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*x)*(-49*x**2 + 23*x) + (23*x)*4 - 49*x**2*4</replace>
Simplifying the partial expression: (7*x)*(-49*x**2 + 23*x)
Expanding the part (-49*x**2 + 23*x) using the distributive property, and we got: (7*x)*(23*x) + (7*x)*(-49*x**2)
Replacing (7*x)*(-49*x**2 + 23*x) with (7*x)*(23*x) + (7*x)*(-49*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*x)*(23*x) + (7*x)*(-49*x**2) + (23*x)*4 - 49*x**2*4</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*x**2)*4 = -196*x**2
  (-49*x**2)*(7*x) = -343*x**3
  (23*x)*4 = 92*x
  (23*x)*(7*x) = 161*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -343*x**3 - 196*x**2 + 161*x**2 + 92*x</replace>
Combining like terms, got -343*x**3 - 35*x**2 + 92*x
<replace-#Step 5>#Step 6:
Current expression: -343*x**3 - 35*x**2 + 92*x</replace>
No more calculations needed.
<answer>-343*x**3 - 35*x**2 + 92*x</answer>


Question:
Calculate the following: (19*y**2 - 38)*(45*y**3 + 46*y**2 + 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (19*y**2 - 38)*(45*y**3 + 46*y**2 + 17)
Expanding the part (19*y**2 - 38) using the distributive property, and we got: (19*y**2)*(45*y**3 + 46*y**2 + 17) - 38*(45*y**3 + 46*y**2 + 17)
<replace-#Step 1>#Step 2:
Current expression: (19*y**2)*(45*y**3 + 46*y**2 + 17) - 38*(45*y**3 + 46*y**2 + 17)</replace>
Simplifying the partial expression: -38*(45*y**3 + 46*y**2 + 17)
Expanding the part (45*y**3 + 46*y**2 + 17) using the distributive property, and we got: (46*y**2)*(-38) + (45*y**3)*(-38) + 17*(-38)
Replacing -38*(45*y**3 + 46*y**2 + 17) with (46*y**2)*(-38) + (45*y**3)*(-38) + 17*(-38) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (19*y**2)*(45*y**3 + 46*y**2 + 17) + (46*y**2)*(-38) + (45*y**3)*(-38) - 646</replace>
Simplifying the partial expression: (19*y**2)*(45*y**3 + 46*y**2 + 17)
Expanding the part (45*y**3 + 46*y**2 + 17) using the distributive property, and we got: 17*(19*y**2) + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3)
Replacing (19*y**2)*(45*y**3 + 46*y**2 + 17) with 17*(19*y**2) + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 17*19*y**2 + (19*y**2)*(46*y**2) + (19*y**2)*(45*y**3) + (46*y**2)*(-38) + (45*y**3)*(-38) - 646</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (45*y**3)*-38 = -1710*y**3
  (45*y**3)*(19*y**2) = 855*y**5
  (46*y**2)*-38 = -1748*y**2
  (46*y**2)*(19*y**2) = 874*y**4
  17*19*y**2 = 323*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 855*y**5 + 874*y**4 - 1710*y**3 - 1748*y**2 + 323*y**2 - 646</replace>
Combining like terms, got 855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646
<replace-#Step 5>#Step 6:
Current expression: 855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646</replace>
No more calculations needed.
<answer>855*y**5 + 874*y**4 - 1710*y**3 - 1425*y**2 - 646</answer>


Question:
Calculate the following: (13*y**3 - 49*y**2)*(-19*y**3 - 35*y - 59)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -247*y**6 + 931*y**5 - 455*y**4 + 948*y**3 + 2891*y**2


Question:
Simplify this expression: 44*x**3*(-39*x**3 + 8*x**2 + 11*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1716*x**6 + 352*x**5 + 484*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: 44*x**3*(-39*x**3 + 8*x**2 + 11*x)
Expanding the part (-39*x**3 + 8*x**2 + 11*x) using the distributive property, and we got: (11*x)*(44*x**3) + (8*x**2)*(44*x**3) + (-39*x**3)*(44*x**3)
<replace-#Step 1>#Step 2:
Current expression: (11*x)*(44*x**3) + (8*x**2)*(44*x**3) + (-39*x**3)*(44*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*(44*x**3) = -1716*x**6
  (8*x**2)*(44*x**3) = 352*x**5
  (11*x)*(44*x**3) = 484*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1716*x**6 + 352*x**5 + 484*x**4</replace>
No more calculations needed.
<answer>-1716*x**6 + 352*x**5 + 484*x**4</answer>


Question:
Simplify this expression: -16*y**3*(-47*y**3 + 49*y**2 - 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: 752*y**6 - 784*y**5 + 768*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: -16*y**3*(-47*y**3 + 49*y**2 - 48)
Expanding the part (-47*y**3 + 49*y**2 - 48) using the distributive property, and we got: -(-1)*768*y**3 + (49*y**2)*(-16*y**3) + (-47*y**3)*(-16*y**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*768*y**3 + (49*y**2)*(-16*y**3) + (-47*y**3)*(-16*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -48*(-16*y**3) = 768*y**3
  (-47*y**3)*(-16*y**3) = 752*y**6
  (49*y**2)*(-16*y**3) = -784*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 752*y**6 - 784*y**5 + 768*y**3</replace>
No more calculations needed.
<answer>752*y**6 - 784*y**5 + 768*y**3</answer>


Question:
Simplify this expression: (32*x**3 + 33*x)*(50*x**3 + 7*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: 1600*x**6 + 1874*x**4 + 231*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (32*x**3 + 33*x)*(50*x**3 + 7*x)
Expanding the part (50*x**3 + 7*x) using the distributive property, and we got: (7*x)*(32*x**3 + 33*x) + (50*x**3)*(32*x**3 + 33*x)
<replace-#Step 1>#Step 2:
Current expression: (7*x)*(32*x**3 + 33*x) + (50*x**3)*(32*x**3 + 33*x)</replace>
Simplifying the partial expression: (7*x)*(32*x**3 + 33*x)
Expanding the part (32*x**3 + 33*x) using the distributive property, and we got: (7*x)*(33*x) + (7*x)*(32*x**3)
Replacing (7*x)*(32*x**3 + 33*x) with (7*x)*(33*x) + (7*x)*(32*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (7*x)*(33*x) + (7*x)*(32*x**3) + (50*x**3)*(32*x**3 + 33*x)</replace>
Simplifying the partial expression: (50*x**3)*(32*x**3 + 33*x)
Expanding the part (32*x**3 + 33*x) using the distributive property, and we got: (33*x)*(50*x**3) + (32*x**3)*(50*x**3)
Replacing (50*x**3)*(32*x**3 + 33*x) with (33*x)*(50*x**3) + (32*x**3)*(50*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (7*x)*(33*x) + (7*x)*(32*x**3) + (33*x)*(50*x**3) + (32*x**3)*(50*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*x**3)*(7*x) = 224*x**4
  (32*x**3)*(50*x**3) = 1600*x**6
  (33*x)*(7*x) = 231*x**2
  (33*x)*(50*x**3) = 1650*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1600*x**6 + 224*x**4 + 1650*x**4 + 231*x**2</replace>
Combining like terms, got 1600*x**6 + 1874*x**4 + 231*x**2
<replace-#Step 5>#Step 6:
Current expression: 1600*x**6 + 1874*x**4 + 231*x**2</replace>
No more calculations needed.
<answer>1600*x**6 + 1874*x**4 + 231*x**2</answer>


Question:
Calculate the following: (29*x**2 - 28*x)*(-35*x**2 - 49*x + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1015*x**4 - 441*x**3 + 2677*x**2 - 1260*x


Question:
Simplify this expression: (20 - 48*x**2)*(-22*x - 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1056*x**3 + 768*x**2 - 440*x - 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: (20 - 48*x**2)*(-22*x - 16)
Expanding the part (-22*x - 16) using the distributive property, and we got: (-22*x)*(20 - 48*x**2) - 16*(20 - 48*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(20 - 48*x**2) - 16*(20 - 48*x**2)</replace>
Simplifying the partial expression: -16*(20 - 48*x**2)
Expanding the part (20 - 48*x**2) using the distributive property, and we got: -48*x**2*(-16) + 20*(-16)
Replacing -16*(20 - 48*x**2) with -48*x**2*(-16) + 20*(-16) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-22*x)*(20 - 48*x**2) - 48*x**2*(-16) - 320</replace>
Simplifying the partial expression: (-22*x)*(20 - 48*x**2)
Expanding the part (20 - 48*x**2) using the distributive property, and we got: (-22*x)*(-48*x**2) + 20*(-22*x)
Replacing (-22*x)*(20 - 48*x**2) with (-22*x)*(-48*x**2) + 20*(-22*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*x)*(-48*x**2) + 20*(-22)*x - 48*x**2*(-16) - 320</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x**2)*-16 = 768*x**2
  (-48*x**2)*(-22*x) = 1056*x**3
  20*-22*x = -440*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1056*x**3 + 768*x**2 - 440*x - 320</replace>
No more calculations needed.
<answer>1056*x**3 + 768*x**2 - 440*x - 320</answer>


Question:
Simplify this expression: (18*y + 15)*(-8*y**3 + 3*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -144*y**4 - 66*y**3 + 45*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (18*y + 15)*(-8*y**3 + 3*y**2)
Expanding the part (18*y + 15) using the distributive property, and we got: (18*y)*(-8*y**3 + 3*y**2) + 15*(-8*y**3 + 3*y**2)
<replace-#Step 1>#Step 2:
Current expression: (18*y)*(-8*y**3 + 3*y**2) + 15*(-8*y**3 + 3*y**2)</replace>
Simplifying the partial expression: 15*(-8*y**3 + 3*y**2)
Expanding the part (-8*y**3 + 3*y**2) using the distributive property, and we got: (3*y**2)*15 - 8*y**3*15
Replacing 15*(-8*y**3 + 3*y**2) with (3*y**2)*15 - 8*y**3*15 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (18*y)*(-8*y**3 + 3*y**2) + (3*y**2)*15 - 8*y**3*15</replace>
Simplifying the partial expression: (18*y)*(-8*y**3 + 3*y**2)
Expanding the part (-8*y**3 + 3*y**2) using the distributive property, and we got: (18*y)*(3*y**2) + (18*y)*(-8*y**3)
Replacing (18*y)*(-8*y**3 + 3*y**2) with (18*y)*(3*y**2) + (18*y)*(-8*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (18*y)*(3*y**2) + (18*y)*(-8*y**3) + (3*y**2)*15 - 8*y**3*15</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-8*y**3)*15 = -120*y**3
  (-8*y**3)*(18*y) = -144*y**4
  (3*y**2)*15 = 45*y**2
  (3*y**2)*(18*y) = 54*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -144*y**4 - 120*y**3 + 54*y**3 + 45*y**2</replace>
Combining like terms, got -144*y**4 - 66*y**3 + 45*y**2
<replace-#Step 5>#Step 6:
Current expression: -144*y**4 - 66*y**3 + 45*y**2</replace>
No more calculations needed.
<answer>-144*y**4 - 66*y**3 + 45*y**2</answer>


Question:
Simplify this expression: (-29*z - 40)*(45*z**3 - 10*z**2 - 37*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: -1305*z**4 - 1510*z**3 + 1473*z**2 + 1480*z


Question:
Simplify this expression: (34*x**3 + x**2)*(-4*x**3 + 27*x + 28)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (34*x**3 + x**2)*(-4*x**3 + 27*x + 28)
Expanding the part (34*x**3 + x**2) using the distributive property, and we got: x**2*(-4*x**3 + 27*x + 28) + (34*x**3)*(-4*x**3 + 27*x + 28)
<replace-#Step 1>#Step 2:
Current expression: x**2*(-4*x**3 + 27*x + 28) + (34*x**3)*(-4*x**3 + 27*x + 28)</replace>
Simplifying the partial expression: x**2*(-4*x**3 + 27*x + 28)
Expanding the part (-4*x**3 + 27*x + 28) using the distributive property, and we got: (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2
Replacing x**2*(-4*x**3 + 27*x + 28) with (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 + (34*x**3)*(-4*x**3 + 27*x + 28)</replace>
Simplifying the partial expression: (34*x**3)*(-4*x**3 + 27*x + 28)
Expanding the part (-4*x**3 + 27*x + 28) using the distributive property, and we got: 28*(34*x**3) + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3)
Replacing (34*x**3)*(-4*x**3 + 27*x + 28) with 28*(34*x**3) + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 28*34*x**3 + (27*x)*x**2 + x**2*(-4*x**3) + 28*x**2 + (27*x)*(34*x**3) + (-4*x**3)*(34*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x**3)*x**2 = -4*x**5
  (-4*x**3)*(34*x**3) = -136*x**6
  (27*x)*x**2 = 27*x**3
  (27*x)*(34*x**3) = 918*x**4
  28*34*x**3 = 952*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -136*x**6 - 4*x**5 + 918*x**4 + 27*x**3 + 952*x**3 + 28*x**2</replace>
Combining like terms, got -136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2
<replace-#Step 5>#Step 6:
Current expression: -136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2</replace>
No more calculations needed.
<answer>-136*x**6 - 4*x**5 + 918*x**4 + 979*x**3 + 28*x**2</answer>


Question:
Simplify this expression: (-37*y**2 - 32*y + 29)*(10*y**3 + 33*y**2 - 13*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: -370*y**5 - 1541*y**4 - 285*y**3 + 1373*y**2 - 377*y


Question:
Simplify this expression: (4*x + 1)*(-17*x**3 + 51*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: -68*x**4 - 17*x**3 + 204*x**2 + 51*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: (4*x + 1)*(-17*x**3 + 51*x)
Expanding the part (4*x + 1) using the distributive property, and we got: (4*x)*(-17*x**3 + 51*x) + 1*(-17*x**3 + 51*x)
<replace-#Step 1>#Step 2:
Current expression: (4*x)*(-17*x**3 + 51*x) + 1*(-17*x**3 + 51*x)</replace>
Simplifying the partial expression: 1*(-17*x**3 + 51*x)
Expanding the part (-17*x**3 + 51*x) using the distributive property, and we got: (51*x)*1 - 17*x**3*1
Replacing 1*(-17*x**3 + 51*x) with (51*x)*1 - 17*x**3*1 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*x)*(-17*x**3 + 51*x) + (51*x)*1 - 17*x**3*1</replace>
Simplifying the partial expression: (4*x)*(-17*x**3 + 51*x)
Expanding the part (-17*x**3 + 51*x) using the distributive property, and we got: (4*x)*(51*x) + (4*x)*(-17*x**3)
Replacing (4*x)*(-17*x**3 + 51*x) with (4*x)*(51*x) + (4*x)*(-17*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (4*x)*(51*x) + (4*x)*(-17*x**3) + (51*x)*1 - 17*x**3*1</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*x**3)*1 = -17*x**3
  (-17*x**3)*(4*x) = -68*x**4
  (51*x)*1 = 51*x
  (51*x)*(4*x) = 204*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -68*x**4 - 17*x**3 + 204*x**2 + 51*x</replace>
No more calculations needed.
<answer>-68*x**4 - 17*x**3 + 204*x**2 + 51*x</answer>


Question:
Simplify this expression: (-8*z**2 + 25*z)*(26*z**2 - 37*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: -208*z**4 + 946*z**3 - 925*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: (-8*z**2 + 25*z)*(26*z**2 - 37*z)
Expanding the part (26*z**2 - 37*z) using the distributive property, and we got: (-37*z)*(-8*z**2 + 25*z) + (26*z**2)*(-8*z**2 + 25*z)
<replace-#Step 1>#Step 2:
Current expression: (-37*z)*(-8*z**2 + 25*z) + (26*z**2)*(-8*z**2 + 25*z)</replace>
Simplifying the partial expression: (-37*z)*(-8*z**2 + 25*z)
Expanding the part (-8*z**2 + 25*z) using the distributive property, and we got: (-37*z)*(25*z) + (-37*z)*(-8*z**2)
Replacing (-37*z)*(-8*z**2 + 25*z) with (-37*z)*(25*z) + (-37*z)*(-8*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*z)*(25*z) + (-37*z)*(-8*z**2) + (26*z**2)*(-8*z**2 + 25*z)</replace>
Simplifying the partial expression: (26*z**2)*(-8*z**2 + 25*z)
Expanding the part (-8*z**2 + 25*z) using the distributive property, and we got: (25*z)*(26*z**2) + (-8*z**2)*(26*z**2)
Replacing (26*z**2)*(-8*z**2 + 25*z) with (25*z)*(26*z**2) + (-8*z**2)*(26*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*z)*(25*z) + (-37*z)*(-8*z**2) + (25*z)*(26*z**2) + (-8*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:
  (-8*z**2)*(-37*z) = 296*z**3
  (-8*z**2)*(26*z**2) = -208*z**4
  (25*z)*(-37*z) = -925*z**2
  (25*z)*(26*z**2) = 650*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -208*z**4 + 296*z**3 + 650*z**3 - 925*z**2</replace>
Combining like terms, got -208*z**4 + 946*z**3 - 925*z**2
<replace-#Step 5>#Step 6:
Current expression: -208*z**4 + 946*z**3 - 925*z**2</replace>
No more calculations needed.
<answer>-208*z**4 + 946*z**3 - 925*z**2</answer>


Question:
Simplify this expression: (2*x + 2)*(6*x**3 + 44*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: 12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44

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*x + 2)*(6*x**3 + 44*x**2 + 22)
Expanding the part (2*x + 2) using the distributive property, and we got: (2*x)*(6*x**3 + 44*x**2 + 22) + 2*(6*x**3 + 44*x**2 + 22)
<replace-#Step 1>#Step 2:
Current expression: (2*x)*(6*x**3 + 44*x**2 + 22) + 2*(6*x**3 + 44*x**2 + 22)</replace>
Simplifying the partial expression: 2*(6*x**3 + 44*x**2 + 22)
Expanding the part (6*x**3 + 44*x**2 + 22) using the distributive property, and we got: (44*x**2)*2 + (6*x**3)*2 + 22*2
Replacing 2*(6*x**3 + 44*x**2 + 22) with (44*x**2)*2 + (6*x**3)*2 + 22*2 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*x)*(6*x**3 + 44*x**2 + 22) + (44*x**2)*2 + (6*x**3)*2 + 44</replace>
Simplifying the partial expression: (2*x)*(6*x**3 + 44*x**2 + 22)
Expanding the part (6*x**3 + 44*x**2 + 22) using the distributive property, and we got: 22*(2*x) + (2*x)*(44*x**2) + (2*x)*(6*x**3)
Replacing (2*x)*(6*x**3 + 44*x**2 + 22) with 22*(2*x) + (2*x)*(44*x**2) + (2*x)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 22*2*x + (2*x)*(44*x**2) + (2*x)*(6*x**3) + (44*x**2)*2 + (6*x**3)*2 + 44</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**3)*2 = 12*x**3
  (6*x**3)*(2*x) = 12*x**4
  (44*x**2)*2 = 88*x**2
  (44*x**2)*(2*x) = 88*x**3
  22*2*x = 44*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 12*x**4 + 12*x**3 + 88*x**3 + 88*x**2 + 44*x + 44</replace>
Combining like terms, got 12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44
<replace-#Step 5>#Step 6:
Current expression: 12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44</replace>
No more calculations needed.
<answer>12*x**4 + 100*x**3 + 88*x**2 + 44*x + 44</answer>


Question:
Calculate the following: (-37*y**2 - 12)*(-41*y**3 + 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: 1517*y**5 + 270*y**3 - 72*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: (-37*y**2 - 12)*(-41*y**3 + 6*y)
Expanding the part (-37*y**2 - 12) using the distributive property, and we got: (-37*y**2)*(-41*y**3 + 6*y) - 12*(-41*y**3 + 6*y)
<replace-#Step 1>#Step 2:
Current expression: (-37*y**2)*(-41*y**3 + 6*y) - 12*(-41*y**3 + 6*y)</replace>
Simplifying the partial expression: -12*(-41*y**3 + 6*y)
Expanding the part (-41*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-12) - 41*y**3*(-12)
Replacing -12*(-41*y**3 + 6*y) with (6*y)*(-12) - 41*y**3*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*y)*(-12) + (-37*y**2)*(-41*y**3 + 6*y) - 41*y**3*(-12)</replace>
Simplifying the partial expression: (-37*y**2)*(-41*y**3 + 6*y)
Expanding the part (-41*y**3 + 6*y) using the distributive property, and we got: (6*y)*(-37*y**2) + (-37*y**2)*(-41*y**3)
Replacing (-37*y**2)*(-41*y**3 + 6*y) with (6*y)*(-37*y**2) + (-37*y**2)*(-41*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (6*y)*(-37*y**2) + (6*y)*(-12) + (-37*y**2)*(-41*y**3) - 41*y**3*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*y**3)*-12 = 492*y**3
  (-41*y**3)*(-37*y**2) = 1517*y**5
  (6*y)*-12 = -72*y
  (6*y)*(-37*y**2) = -222*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1517*y**5 - 222*y**3 + 492*y**3 - 72*y</replace>
Combining like terms, got 1517*y**5 + 270*y**3 - 72*y
<replace-#Step 5>#Step 6:
Current expression: 1517*y**5 + 270*y**3 - 72*y</replace>
No more calculations needed.
<answer>1517*y**5 + 270*y**3 - 72*y</answer>