Question:
Calculate the following: (-x**2 - 37)*(-18*x**3 - 30*x**2 - 6*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: 18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*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: (-x**2 - 37)*(-18*x**3 - 30*x**2 - 6*x)
Expanding the part (-x**2 - 37) using the distributive property, and we got: (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 37*(-18*x**3 - 30*x**2 - 6*x)
<replace-#Step 1>#Step 2:
Current expression: (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 37*(-18*x**3 - 30*x**2 - 6*x)</replace>
Simplifying the partial expression: -37*(-18*x**3 - 30*x**2 - 6*x)
Expanding the part (-18*x**3 - 30*x**2 - 6*x) using the distributive property, and we got: -6*x*(-37) - 30*x**2*(-37) - 18*x**3*(-37)
Replacing -37*(-18*x**3 - 30*x**2 - 6*x) with -6*x*(-37) - 30*x**2*(-37) - 18*x**3*(-37) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -6*x*(-37) - 30*x**2*(-37) + (-x**2)*(-18*x**3 - 30*x**2 - 6*x) - 18*x**3*(-37)</replace>
Simplifying the partial expression: (-x**2)*(-18*x**3 - 30*x**2 - 6*x)
Expanding the part (-18*x**3 - 30*x**2 - 6*x) using the distributive property, and we got: (-6*x)*(-x**2) + (-30*x**2)*(-x**2) + (-x**2)*(-18*x**3)
Replacing (-x**2)*(-18*x**3 - 30*x**2 - 6*x) with (-6*x)*(-x**2) + (-30*x**2)*(-x**2) + (-x**2)*(-18*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-6*x)*(-x**2) - 6*x*(-37) + (-30*x**2)*(-x**2) - 30*x**2*(-37) + (-x**2)*(-18*x**3) - 18*x**3*(-37)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*x**2)*-37 = 1110*x**2
  (-30*x**2)*(-x**2) = 30*x**4
  (-18*x**3)*-37 = 666*x**3
  (-18*x**3)*(-x**2) = 18*x**5
  (-6*x)*-37 = 222*x
  (-6*x)*(-x**2) = 6*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 18*x**5 + 30*x**4 + 6*x**3 + 666*x**3 + 1110*x**2 + 222*x</replace>
Combining like terms, got 18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x
<replace-#Step 5>#Step 6:
Current expression: 18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x</replace>
No more calculations needed.
<answer>18*x**5 + 30*x**4 + 672*x**3 + 1110*x**2 + 222*x</answer>


Question:
Simplify this expression: (29 - 50*z**2)*(35*z**3 + 10*z + 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: -1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (29 - 50*z**2)*(35*z**3 + 10*z + 11)
Expanding the part (29 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(35*z**3 + 10*z + 11) + 29*(35*z**3 + 10*z + 11)
<replace-#Step 1>#Step 2:
Current expression: (-50*z**2)*(35*z**3 + 10*z + 11) + 29*(35*z**3 + 10*z + 11)</replace>
Simplifying the partial expression: 29*(35*z**3 + 10*z + 11)
Expanding the part (35*z**3 + 10*z + 11) using the distributive property, and we got: (10*z)*29 + (35*z**3)*29 + 11*29
Replacing 29*(35*z**3 + 10*z + 11) with (10*z)*29 + (35*z**3)*29 + 11*29 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*z)*29 + (-50*z**2)*(35*z**3 + 10*z + 11) + (35*z**3)*29 + 319</replace>
Simplifying the partial expression: (-50*z**2)*(35*z**3 + 10*z + 11)
Expanding the part (35*z**3 + 10*z + 11) using the distributive property, and we got: 11*(-50*z**2) + (10*z)*(-50*z**2) + (-50*z**2)*(35*z**3)
Replacing (-50*z**2)*(35*z**3 + 10*z + 11) with 11*(-50*z**2) + (10*z)*(-50*z**2) + (-50*z**2)*(35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 11*(-50)*z**2 + (10*z)*(-50*z**2) + (10*z)*29 + (-50*z**2)*(35*z**3) + (35*z**3)*29 + 319</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (10*z)*29 = 290*z
  (10*z)*(-50*z**2) = -500*z**3
  (35*z**3)*29 = 1015*z**3
  (35*z**3)*(-50*z**2) = -1750*z**5
  11*-50*z**2 = -550*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1750*z**5 - 500*z**3 + 1015*z**3 - 550*z**2 + 290*z + 319</replace>
Combining like terms, got -1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319
<replace-#Step 5>#Step 6:
Current expression: -1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319</replace>
No more calculations needed.
<answer>-1750*z**5 + 515*z**3 - 550*z**2 + 290*z + 319</answer>


Question:
Simplify this expression: (16*x**2 + 3)*(26*x**3 - 4*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 416*x**5 - 64*x**4 + 78*x**3 - 12*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: (16*x**2 + 3)*(26*x**3 - 4*x**2)
Expanding the part (16*x**2 + 3) using the distributive property, and we got: (16*x**2)*(26*x**3 - 4*x**2) + 3*(26*x**3 - 4*x**2)
<replace-#Step 1>#Step 2:
Current expression: (16*x**2)*(26*x**3 - 4*x**2) + 3*(26*x**3 - 4*x**2)</replace>
Simplifying the partial expression: 3*(26*x**3 - 4*x**2)
Expanding the part (26*x**3 - 4*x**2) using the distributive property, and we got: -4*x**2*3 + (26*x**3)*3
Replacing 3*(26*x**3 - 4*x**2) with -4*x**2*3 + (26*x**3)*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -4*x**2*3 + (16*x**2)*(26*x**3 - 4*x**2) + (26*x**3)*3</replace>
Simplifying the partial expression: (16*x**2)*(26*x**3 - 4*x**2)
Expanding the part (26*x**3 - 4*x**2) using the distributive property, and we got: (-4*x**2)*(16*x**2) + (16*x**2)*(26*x**3)
Replacing (16*x**2)*(26*x**3 - 4*x**2) with (-4*x**2)*(16*x**2) + (16*x**2)*(26*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-4*x**2)*(16*x**2) - 4*x**2*3 + (16*x**2)*(26*x**3) + (26*x**3)*3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-4*x**2)*3 = -12*x**2
  (-4*x**2)*(16*x**2) = -64*x**4
  (26*x**3)*3 = 78*x**3
  (26*x**3)*(16*x**2) = 416*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 416*x**5 - 64*x**4 + 78*x**3 - 12*x**2</replace>
No more calculations needed.
<answer>416*x**5 - 64*x**4 + 78*x**3 - 12*x**2</answer>


Question:
Simplify this expression: (-24*y**3 + 85*y**2 + 23)*(3*y**3 + 64*y - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -72*y**6 + 255*y**5 - 1536*y**4 + 6685*y**3 - 4165*y**2 + 1472*y - 1127


Question:
Simplify this expression: (-12*x**3 - 10)*(31*x**3 + 38)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -372*x**6 - 766*x**3 - 380

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 - 10)*(31*x**3 + 38)
Expanding the part (-12*x**3 - 10) using the distributive property, and we got: (-12*x**3)*(31*x**3 + 38) - 10*(31*x**3 + 38)
<replace-#Step 1>#Step 2:
Current expression: (-12*x**3)*(31*x**3 + 38) - 10*(31*x**3 + 38)</replace>
Simplifying the partial expression: -10*(31*x**3 + 38)
Expanding the part (31*x**3 + 38) using the distributive property, and we got: (31*x**3)*(-10) + 38*(-10)
Replacing -10*(31*x**3 + 38) with (31*x**3)*(-10) + 38*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-12*x**3)*(31*x**3 + 38) + (31*x**3)*(-10) - 380</replace>
Simplifying the partial expression: (-12*x**3)*(31*x**3 + 38)
Expanding the part (31*x**3 + 38) using the distributive property, and we got: 38*(-12*x**3) + (-12*x**3)*(31*x**3)
Replacing (-12*x**3)*(31*x**3 + 38) with 38*(-12*x**3) + (-12*x**3)*(31*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 38*(-12)*x**3 + (-12*x**3)*(31*x**3) + (31*x**3)*(-10) - 380</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*x**3)*-10 = -310*x**3
  (31*x**3)*(-12*x**3) = -372*x**6
  38*-12*x**3 = -456*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -372*x**6 - 456*x**3 - 310*x**3 - 380</replace>
Combining like terms, got -372*x**6 - 766*x**3 - 380
<replace-#Step 5>#Step 6:
Current expression: -372*x**6 - 766*x**3 - 380</replace>
No more calculations needed.
<answer>-372*x**6 - 766*x**3 - 380</answer>


Question:
Calculate the following: (38*z**2 - 11*z)*(71*z**2 + 78)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2698*z**4 - 781*z**3 + 2964*z**2 - 858*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: (38*z**2 - 11*z)*(71*z**2 + 78)
Expanding the part (71*z**2 + 78) using the distributive property, and we got: (71*z**2)*(38*z**2 - 11*z) + 78*(38*z**2 - 11*z)
<replace-#Step 1>#Step 2:
Current expression: (71*z**2)*(38*z**2 - 11*z) + 78*(38*z**2 - 11*z)</replace>
Simplifying the partial expression: 78*(38*z**2 - 11*z)
Expanding the part (38*z**2 - 11*z) using the distributive property, and we got: -11*z*78 + (38*z**2)*78
Replacing 78*(38*z**2 - 11*z) with -11*z*78 + (38*z**2)*78 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -11*z*78 + (38*z**2)*78 + (71*z**2)*(38*z**2 - 11*z)</replace>
Simplifying the partial expression: (71*z**2)*(38*z**2 - 11*z)
Expanding the part (38*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(71*z**2) + (38*z**2)*(71*z**2)
Replacing (71*z**2)*(38*z**2 - 11*z) with (-11*z)*(71*z**2) + (38*z**2)*(71*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(71*z**2) - 11*z*78 + (38*z**2)*(71*z**2) + (38*z**2)*78</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z)*78 = -858*z
  (-11*z)*(71*z**2) = -781*z**3
  (38*z**2)*78 = 2964*z**2
  (38*z**2)*(71*z**2) = 2698*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2698*z**4 - 781*z**3 + 2964*z**2 - 858*z</replace>
No more calculations needed.
<answer>2698*z**4 - 781*z**3 + 2964*z**2 - 858*z</answer>


Question:
Simplify this expression: (11*y**2 - 53*y)*(32*y**3 + 41*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: 352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (11*y**2 - 53*y)*(32*y**3 + 41*y + 11)
Expanding the part (11*y**2 - 53*y) using the distributive property, and we got: (-53*y)*(32*y**3 + 41*y + 11) + (11*y**2)*(32*y**3 + 41*y + 11)
<replace-#Step 1>#Step 2:
Current expression: (-53*y)*(32*y**3 + 41*y + 11) + (11*y**2)*(32*y**3 + 41*y + 11)</replace>
Simplifying the partial expression: (-53*y)*(32*y**3 + 41*y + 11)
Expanding the part (32*y**3 + 41*y + 11) using the distributive property, and we got: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53*y)
Replacing (-53*y)*(32*y**3 + 41*y + 11) with (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*(-53)*y + (11*y**2)*(32*y**3 + 41*y + 11)</replace>
Simplifying the partial expression: (11*y**2)*(32*y**3 + 41*y + 11)
Expanding the part (32*y**3 + 41*y + 11) using the distributive property, and we got: 11*(11*y**2) + (41*y)*(11*y**2) + (11*y**2)*(32*y**3)
Replacing (11*y**2)*(32*y**3 + 41*y + 11) with 11*(11*y**2) + (41*y)*(11*y**2) + (11*y**2)*(32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-53*y)*(41*y) + (-53*y)*(32*y**3) + 11*11*y**2 + 11*(-53)*y + (41*y)*(11*y**2) + (11*y**2)*(32*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (32*y**3)*(-53*y) = -1696*y**4
  (32*y**3)*(11*y**2) = 352*y**5
  (41*y)*(-53*y) = -2173*y**2
  (41*y)*(11*y**2) = 451*y**3
  11*-53*y = -583*y
  11*11*y**2 = 121*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 352*y**5 - 1696*y**4 + 451*y**3 - 2173*y**2 + 121*y**2 - 583*y</replace>
Combining like terms, got 352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y
<replace-#Step 5>#Step 6:
Current expression: 352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y</replace>
No more calculations needed.
<answer>352*y**5 - 1696*y**4 + 451*y**3 - 2052*y**2 - 583*y</answer>


Question:
Calculate the following: (-44*z**3 - 37*z - 40)*(-3*z**3 + 26*z**2 - 45*z + 10)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 132*z**6 - 1144*z**5 + 2091*z**4 - 1282*z**3 + 625*z**2 + 1430*z - 400


Question:
Calculate the following: (23*x**2 - 12)*(32*x**2 - 42*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 736*x**4 - 966*x**3 - 384*x**2 + 504*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: (23*x**2 - 12)*(32*x**2 - 42*x)
Expanding the part (23*x**2 - 12) using the distributive property, and we got: (23*x**2)*(32*x**2 - 42*x) - 12*(32*x**2 - 42*x)
<replace-#Step 1>#Step 2:
Current expression: (23*x**2)*(32*x**2 - 42*x) - 12*(32*x**2 - 42*x)</replace>
Simplifying the partial expression: -12*(32*x**2 - 42*x)
Expanding the part (32*x**2 - 42*x) using the distributive property, and we got: -42*x*(-12) + (32*x**2)*(-12)
Replacing -12*(32*x**2 - 42*x) with -42*x*(-12) + (32*x**2)*(-12) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*x*(-12) + (23*x**2)*(32*x**2 - 42*x) + (32*x**2)*(-12)</replace>
Simplifying the partial expression: (23*x**2)*(32*x**2 - 42*x)
Expanding the part (32*x**2 - 42*x) using the distributive property, and we got: (-42*x)*(23*x**2) + (23*x**2)*(32*x**2)
Replacing (23*x**2)*(32*x**2 - 42*x) with (-42*x)*(23*x**2) + (23*x**2)*(32*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*x)*(23*x**2) - 42*x*(-12) + (23*x**2)*(32*x**2) + (32*x**2)*(-12)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*x)*-12 = 504*x
  (-42*x)*(23*x**2) = -966*x**3
  (32*x**2)*-12 = -384*x**2
  (32*x**2)*(23*x**2) = 736*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 736*x**4 - 966*x**3 - 384*x**2 + 504*x</replace>
No more calculations needed.
<answer>736*x**4 - 966*x**3 - 384*x**2 + 504*x</answer>


Question:
Calculate the following: (33 - 20*y**3)*(-52*y**3 + 24*y + 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (33 - 20*y**3)*(-52*y**3 + 24*y + 19)
Expanding the part (33 - 20*y**3) using the distributive property, and we got: (-20*y**3)*(-52*y**3 + 24*y + 19) + 33*(-52*y**3 + 24*y + 19)
<replace-#Step 1>#Step 2:
Current expression: (-20*y**3)*(-52*y**3 + 24*y + 19) + 33*(-52*y**3 + 24*y + 19)</replace>
Simplifying the partial expression: 33*(-52*y**3 + 24*y + 19)
Expanding the part (-52*y**3 + 24*y + 19) using the distributive property, and we got: (24*y)*33 - 52*y**3*33 + 19*33
Replacing 33*(-52*y**3 + 24*y + 19) with (24*y)*33 - 52*y**3*33 + 19*33 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (24*y)*33 - 52*y**3*33 + (-20*y**3)*(-52*y**3 + 24*y + 19) + 627</replace>
Simplifying the partial expression: (-20*y**3)*(-52*y**3 + 24*y + 19)
Expanding the part (-52*y**3 + 24*y + 19) using the distributive property, and we got: 19*(-20*y**3) + (24*y)*(-20*y**3) + (-52*y**3)*(-20*y**3)
Replacing (-20*y**3)*(-52*y**3 + 24*y + 19) with 19*(-20*y**3) + (24*y)*(-20*y**3) + (-52*y**3)*(-20*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 19*(-20)*y**3 + (24*y)*(-20*y**3) + (24*y)*33 + (-52*y**3)*(-20*y**3) - 52*y**3*33 + 627</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-52*y**3)*33 = -1716*y**3
  (-52*y**3)*(-20*y**3) = 1040*y**6
  (24*y)*33 = 792*y
  (24*y)*(-20*y**3) = -480*y**4
  19*-20*y**3 = -380*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1040*y**6 - 480*y**4 - 1716*y**3 - 380*y**3 + 792*y + 627</replace>
Combining like terms, got 1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627
<replace-#Step 5>#Step 6:
Current expression: 1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627</replace>
No more calculations needed.
<answer>1040*y**6 - 480*y**4 - 2096*y**3 + 792*y + 627</answer>


Question:
Simplify this expression: (-6*y**2 - 12*y)*(-28*y**3 - 12*y - 34)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 168*y**5 + 336*y**4 + 72*y**3 + 348*y**2 + 408*y


Question:
Calculate the following: (-34*x**3 + 15*x)*(12*x**3 + 45*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: -408*x**6 - 1350*x**4 + 675*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 + 15*x)*(12*x**3 + 45*x)
Expanding the part (-34*x**3 + 15*x) using the distributive property, and we got: (15*x)*(12*x**3 + 45*x) + (-34*x**3)*(12*x**3 + 45*x)
<replace-#Step 1>#Step 2:
Current expression: (15*x)*(12*x**3 + 45*x) + (-34*x**3)*(12*x**3 + 45*x)</replace>
Simplifying the partial expression: (-34*x**3)*(12*x**3 + 45*x)
Expanding the part (12*x**3 + 45*x) using the distributive property, and we got: (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3)
Replacing (-34*x**3)*(12*x**3 + 45*x) with (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (15*x)*(12*x**3 + 45*x) + (45*x)*(-34*x**3) + (-34*x**3)*(12*x**3)</replace>
Simplifying the partial expression: (15*x)*(12*x**3 + 45*x)
Expanding the part (12*x**3 + 45*x) using the distributive property, and we got: (15*x)*(45*x) + (15*x)*(12*x**3)
Replacing (15*x)*(12*x**3 + 45*x) with (15*x)*(45*x) + (15*x)*(12*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (15*x)*(45*x) + (15*x)*(12*x**3) + (45*x)*(-34*x**3) + (-34*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:
  (12*x**3)*(-34*x**3) = -408*x**6
  (12*x**3)*(15*x) = 180*x**4
  (45*x)*(-34*x**3) = -1530*x**4
  (45*x)*(15*x) = 675*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -408*x**6 - 1530*x**4 + 180*x**4 + 675*x**2</replace>
Combining like terms, got -408*x**6 - 1350*x**4 + 675*x**2
<replace-#Step 5>#Step 6:
Current expression: -408*x**6 - 1350*x**4 + 675*x**2</replace>
No more calculations needed.
<answer>-408*x**6 - 1350*x**4 + 675*x**2</answer>


Question:
Simplify this expression: (35*z**3 - 44*z**2)*(-25*z**3 + 36*z**2 - 50*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -875*z**6 + 2360*z**5 - 3334*z**4 + 2200*z**3


Question:
Simplify this expression: (-15*z**3 - 46*z**2)*(3*z**3 - 27*z**2 + 18*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: -45*z**6 + 267*z**5 + 972*z**4 - 828*z**3


Question:
Calculate the following: -5*y**3*(27*y**2 - 10*y - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -135*y**5 + 50*y**4 + 250*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: -5*y**3*(27*y**2 - 10*y - 50)
Expanding the part (27*y**2 - 10*y - 50) using the distributive property, and we got: (-10*y)*(-5*y**3) - (-1)*250*y**3 + (27*y**2)*(-5*y**3)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(-5*y**3) - (-1)*250*y**3 + (27*y**2)*(-5*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -50*(-5*y**3) = 250*y**3
  (-10*y)*(-5*y**3) = 50*y**4
  (27*y**2)*(-5*y**3) = -135*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -135*y**5 + 50*y**4 + 250*y**3</replace>
No more calculations needed.
<answer>-135*y**5 + 50*y**4 + 250*y**3</answer>


Question:
Calculate the following: (-49*y**3 + 43*y**2)*(12*y**3 - 45*y - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -588*y**6 + 516*y**5 + 2205*y**4 - 1690*y**3 - 215*y**2


Question:
Calculate the following: (37 - 34*z**3)*(-38*z**2 + 30*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (37 - 34*z**3)*(-38*z**2 + 30*z)
Expanding the part (37 - 34*z**3) using the distributive property, and we got: (-34*z**3)*(-38*z**2 + 30*z) + 37*(-38*z**2 + 30*z)
<replace-#Step 1>#Step 2:
Current expression: (-34*z**3)*(-38*z**2 + 30*z) + 37*(-38*z**2 + 30*z)</replace>
Simplifying the partial expression: 37*(-38*z**2 + 30*z)
Expanding the part (-38*z**2 + 30*z) using the distributive property, and we got: (30*z)*37 - 38*z**2*37
Replacing 37*(-38*z**2 + 30*z) with (30*z)*37 - 38*z**2*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (30*z)*37 - 38*z**2*37 + (-34*z**3)*(-38*z**2 + 30*z)</replace>
Simplifying the partial expression: (-34*z**3)*(-38*z**2 + 30*z)
Expanding the part (-38*z**2 + 30*z) using the distributive property, and we got: (30*z)*(-34*z**3) + (-38*z**2)*(-34*z**3)
Replacing (-34*z**3)*(-38*z**2 + 30*z) with (30*z)*(-34*z**3) + (-38*z**2)*(-34*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (30*z)*(-34*z**3) + (30*z)*37 + (-38*z**2)*(-34*z**3) - 38*z**2*37</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*z**2)*37 = -1406*z**2
  (-38*z**2)*(-34*z**3) = 1292*z**5
  (30*z)*37 = 1110*z
  (30*z)*(-34*z**3) = -1020*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z</replace>
No more calculations needed.
<answer>1292*z**5 - 1020*z**4 - 1406*z**2 + 1110*z</answer>


Question:
Calculate the following: (49*y**3 - 35*y + 25)*(-39*y**3 - 47*y**2 + y + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1911*y**6 - 2303*y**5 + 1414*y**4 + 2973*y**3 - 1210*y**2 - 1620*y + 1175


Question:
Simplify this expression: (-40*y - 27)*(25*y**3 - 46)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1000*y**4 - 675*y**3 + 1840*y + 1242

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-40*y - 27)*(25*y**3 - 46)
Expanding the part (25*y**3 - 46) using the distributive property, and we got: (25*y**3)*(-40*y - 27) - 46*(-40*y - 27)
<replace-#Step 1>#Step 2:
Current expression: (25*y**3)*(-40*y - 27) - 46*(-40*y - 27)</replace>
Simplifying the partial expression: -46*(-40*y - 27)
Expanding the part (-40*y - 27) using the distributive property, and we got: -40*y*(-46) - 27*(-46)
Replacing -46*(-40*y - 27) with -40*y*(-46) - 27*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -40*y*(-46) + (25*y**3)*(-40*y - 27) + 1242</replace>
Simplifying the partial expression: (25*y**3)*(-40*y - 27)
Expanding the part (-40*y - 27) using the distributive property, and we got: (-40*y)*(25*y**3) - 675*y**3
Replacing (25*y**3)*(-40*y - 27) with (-40*y)*(25*y**3) - 675*y**3 in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-40*y)*(25*y**3) - 40*y*(-46) - 27*25*y**3 + 1242</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*y)*-46 = 1840*y
  (-40*y)*(25*y**3) = -1000*y**4
  -27*25*y**3 = -675*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1000*y**4 - 675*y**3 + 1840*y + 1242</replace>
No more calculations needed.
<answer>-1000*y**4 - 675*y**3 + 1840*y + 1242</answer>


Question:
Calculate the following: (40*z**2 + 3*z)*(6*z**3 + 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: 240*z**5 + 18*z**4 + 1200*z**2 + 90*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: (40*z**2 + 3*z)*(6*z**3 + 30)
Expanding the part (6*z**3 + 30) using the distributive property, and we got: (6*z**3)*(40*z**2 + 3*z) + 30*(40*z**2 + 3*z)
<replace-#Step 1>#Step 2:
Current expression: (6*z**3)*(40*z**2 + 3*z) + 30*(40*z**2 + 3*z)</replace>
Simplifying the partial expression: 30*(40*z**2 + 3*z)
Expanding the part (40*z**2 + 3*z) using the distributive property, and we got: (3*z)*30 + (40*z**2)*30
Replacing 30*(40*z**2 + 3*z) with (3*z)*30 + (40*z**2)*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*z)*30 + (40*z**2)*30 + (6*z**3)*(40*z**2 + 3*z)</replace>
Simplifying the partial expression: (6*z**3)*(40*z**2 + 3*z)
Expanding the part (40*z**2 + 3*z) using the distributive property, and we got: (3*z)*(6*z**3) + (40*z**2)*(6*z**3)
Replacing (6*z**3)*(40*z**2 + 3*z) with (3*z)*(6*z**3) + (40*z**2)*(6*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*z)*(6*z**3) + (3*z)*30 + (40*z**2)*(6*z**3) + (40*z**2)*30</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*z)*30 = 90*z
  (3*z)*(6*z**3) = 18*z**4
  (40*z**2)*30 = 1200*z**2
  (40*z**2)*(6*z**3) = 240*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 240*z**5 + 18*z**4 + 1200*z**2 + 90*z</replace>
No more calculations needed.
<answer>240*z**5 + 18*z**4 + 1200*z**2 + 90*z</answer>


Question:
Simplify this expression: -30*z**2*(45*z**3 + 20*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: -1350*z**5 - 600*z**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -30*z**2*(45*z**3 + 20*z)
Expanding the part (45*z**3 + 20*z) using the distributive property, and we got: (20*z)*(-30*z**2) + (-30*z**2)*(45*z**3)
<replace-#Step 1>#Step 2:
Current expression: (20*z)*(-30*z**2) + (-30*z**2)*(45*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (20*z)*(-30*z**2) = -600*z**3
  (45*z**3)*(-30*z**2) = -1350*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1350*z**5 - 600*z**3</replace>
No more calculations needed.
<answer>-1350*z**5 - 600*z**3</answer>


Question:
Simplify this expression: -54*x*(-5*x**3 - 8*x**2 + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 270*x**4 + 432*x**3 - 432*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -54*x*(-5*x**3 - 8*x**2 + 8)
Expanding the part (-5*x**3 - 8*x**2 + 8) using the distributive property, and we got: (-54*x)*(-8*x**2) + (-54*x)*(-5*x**3) + 8*(-54*x)
<replace-#Step 1>#Step 2:
Current expression: (-54*x)*(-8*x**2) + (-54*x)*(-5*x**3) + 8*(-54*x)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  8*(-54*x) = -432*x
  (-8*x**2)*(-54*x) = 432*x**3
  (-5*x**3)*(-54*x) = 270*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 270*x**4 + 432*x**3 - 432*x</replace>
No more calculations needed.
<answer>270*x**4 + 432*x**3 - 432*x</answer>


Question:
Simplify this expression: (21*x**2 + 4*x)*(14*x**2 + 26*x - 25)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 294*x**4 + 602*x**3 - 421*x**2 - 100*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: (21*x**2 + 4*x)*(14*x**2 + 26*x - 25)
Expanding the part (21*x**2 + 4*x) using the distributive property, and we got: (4*x)*(14*x**2 + 26*x - 25) + (21*x**2)*(14*x**2 + 26*x - 25)
<replace-#Step 1>#Step 2:
Current expression: (4*x)*(14*x**2 + 26*x - 25) + (21*x**2)*(14*x**2 + 26*x - 25)</replace>
Simplifying the partial expression: (4*x)*(14*x**2 + 26*x - 25)
Expanding the part (14*x**2 + 26*x - 25) using the distributive property, and we got: -100*x + (4*x)*(26*x) + (4*x)*(14*x**2)
Replacing (4*x)*(14*x**2 + 26*x - 25) with -100*x + (4*x)*(26*x) + (4*x)*(14*x**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -25*4*x + (4*x)*(26*x) + (4*x)*(14*x**2) + (21*x**2)*(14*x**2 + 26*x - 25)</replace>
Simplifying the partial expression: (21*x**2)*(14*x**2 + 26*x - 25)
Expanding the part (14*x**2 + 26*x - 25) using the distributive property, and we got: -525*x**2 + (26*x)*(21*x**2) + (14*x**2)*(21*x**2)
Replacing (21*x**2)*(14*x**2 + 26*x - 25) with -525*x**2 + (26*x)*(21*x**2) + (14*x**2)*(21*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -25*21*x**2 - 25*4*x + (4*x)*(26*x) + (4*x)*(14*x**2) + (26*x)*(21*x**2) + (14*x**2)*(21*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*x**2)*(4*x) = 56*x**3
  (14*x**2)*(21*x**2) = 294*x**4
  (26*x)*(4*x) = 104*x**2
  (26*x)*(21*x**2) = 546*x**3
  -25*4*x = -100*x
  -25*21*x**2 = -525*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 294*x**4 + 56*x**3 + 546*x**3 - 525*x**2 + 104*x**2 - 100*x</replace>
Combining like terms, got 294*x**4 + 602*x**3 - 421*x**2 - 100*x
<replace-#Step 5>#Step 6:
Current expression: 294*x**4 + 602*x**3 - 421*x**2 - 100*x</replace>
No more calculations needed.
<answer>294*x**4 + 602*x**3 - 421*x**2 - 100*x</answer>


Question:
Simplify this expression: (5*x**3 + 18*x**2)*(39*x**3 - 37*x**2 - 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 195*x**6 + 517*x**5 - 666*x**4 - 65*x**3 - 234*x**2


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

Answer: -46*x**5 + 1804*x**4 - 351*x**3 - 1521*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: (x**3 - 39*x**2)*(-46*x**2 + 10*x + 39)
Expanding the part (x**3 - 39*x**2) using the distributive property, and we got: x**3*(-46*x**2 + 10*x + 39) + (-39*x**2)*(-46*x**2 + 10*x + 39)
<replace-#Step 1>#Step 2:
Current expression: x**3*(-46*x**2 + 10*x + 39) + (-39*x**2)*(-46*x**2 + 10*x + 39)</replace>
Simplifying the partial expression: x**3*(-46*x**2 + 10*x + 39)
Expanding the part (-46*x**2 + 10*x + 39) using the distributive property, and we got: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3
Replacing x**3*(-46*x**2 + 10*x + 39) with (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 + (-39*x**2)*(-46*x**2 + 10*x + 39)</replace>
Simplifying the partial expression: (-39*x**2)*(-46*x**2 + 10*x + 39)
Expanding the part (-46*x**2 + 10*x + 39) using the distributive property, and we got: 39*(-39*x**2) + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2)
Replacing (-39*x**2)*(-46*x**2 + 10*x + 39) with 39*(-39*x**2) + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*x)*x**3 + (-46*x**2)*x**3 + 39*x**3 + 39*(-39)*x**2 + (10*x)*(-39*x**2) + (-46*x**2)*(-39*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*x**2)*x**3 = -46*x**5
  (-46*x**2)*(-39*x**2) = 1794*x**4
  (10*x)*x**3 = 10*x**4
  (10*x)*(-39*x**2) = -390*x**3
  39*-39*x**2 = -1521*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -46*x**5 + 10*x**4 + 1794*x**4 - 390*x**3 + 39*x**3 - 1521*x**2</replace>
Combining like terms, got -46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2
<replace-#Step 5>#Step 6:
Current expression: -46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2</replace>
No more calculations needed.
<answer>-46*x**5 + 1804*x**4 - 351*x**3 - 1521*x**2</answer>


Question:
Simplify this expression: (14 - 33*z**3)*(25*z**3 - 11*z**2 + 21*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (14 - 33*z**3)*(25*z**3 - 11*z**2 + 21*z)
Expanding the part (14 - 33*z**3) using the distributive property, and we got: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + 14*(25*z**3 - 11*z**2 + 21*z)
<replace-#Step 1>#Step 2:
Current expression: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + 14*(25*z**3 - 11*z**2 + 21*z)</replace>
Simplifying the partial expression: 14*(25*z**3 - 11*z**2 + 21*z)
Expanding the part (25*z**3 - 11*z**2 + 21*z) using the distributive property, and we got: (21*z)*14 - 11*z**2*14 + (25*z**3)*14
Replacing 14*(25*z**3 - 11*z**2 + 21*z) with (21*z)*14 - 11*z**2*14 + (25*z**3)*14 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (21*z)*14 - 11*z**2*14 + (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) + (25*z**3)*14</replace>
Simplifying the partial expression: (-33*z**3)*(25*z**3 - 11*z**2 + 21*z)
Expanding the part (25*z**3 - 11*z**2 + 21*z) using the distributive property, and we got: (21*z)*(-33*z**3) + (-11*z**2)*(-33*z**3) + (-33*z**3)*(25*z**3)
Replacing (-33*z**3)*(25*z**3 - 11*z**2 + 21*z) with (21*z)*(-33*z**3) + (-11*z**2)*(-33*z**3) + (-33*z**3)*(25*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (21*z)*(-33*z**3) + (21*z)*14 + (-11*z**2)*(-33*z**3) - 11*z**2*14 + (-33*z**3)*(25*z**3) + (25*z**3)*14</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z**2)*14 = -154*z**2
  (-11*z**2)*(-33*z**3) = 363*z**5
  (21*z)*14 = 294*z
  (21*z)*(-33*z**3) = -693*z**4
  (25*z**3)*14 = 350*z**3
  (25*z**3)*(-33*z**3) = -825*z**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z</replace>
No more calculations needed.
<answer>-825*z**6 + 363*z**5 - 693*z**4 + 350*z**3 - 154*z**2 + 294*z</answer>


Question:
Calculate the following: (7*y**2 - 46*y)*(-54*y**3 - 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: -378*y**5 + 2484*y**4 - 231*y**2 + 1518*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: (7*y**2 - 46*y)*(-54*y**3 - 33)
Expanding the part (-54*y**3 - 33) using the distributive property, and we got: (-54*y**3)*(7*y**2 - 46*y) - 33*(7*y**2 - 46*y)
<replace-#Step 1>#Step 2:
Current expression: (-54*y**3)*(7*y**2 - 46*y) - 33*(7*y**2 - 46*y)</replace>
Simplifying the partial expression: -33*(7*y**2 - 46*y)
Expanding the part (7*y**2 - 46*y) using the distributive property, and we got: -46*y*(-33) + (7*y**2)*(-33)
Replacing -33*(7*y**2 - 46*y) with -46*y*(-33) + (7*y**2)*(-33) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*y*(-33) + (7*y**2)*(-33) + (-54*y**3)*(7*y**2 - 46*y)</replace>
Simplifying the partial expression: (-54*y**3)*(7*y**2 - 46*y)
Expanding the part (7*y**2 - 46*y) using the distributive property, and we got: (-46*y)*(-54*y**3) + (7*y**2)*(-54*y**3)
Replacing (-54*y**3)*(7*y**2 - 46*y) with (-46*y)*(-54*y**3) + (7*y**2)*(-54*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*y)*(-54*y**3) - 46*y*(-33) + (7*y**2)*(-54*y**3) + (7*y**2)*(-33)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*y)*-33 = 1518*y
  (-46*y)*(-54*y**3) = 2484*y**4
  (7*y**2)*-33 = -231*y**2
  (7*y**2)*(-54*y**3) = -378*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -378*y**5 + 2484*y**4 - 231*y**2 + 1518*y</replace>
No more calculations needed.
<answer>-378*y**5 + 2484*y**4 - 231*y**2 + 1518*y</answer>


Question:
Calculate the following: (27*z**2 - 14)*(-28*z**3 + 17*z - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27*z**2 - 14)*(-28*z**3 + 17*z - 31)
Expanding the part (27*z**2 - 14) using the distributive property, and we got: (27*z**2)*(-28*z**3 + 17*z - 31) - 14*(-28*z**3 + 17*z - 31)
<replace-#Step 1>#Step 2:
Current expression: (27*z**2)*(-28*z**3 + 17*z - 31) - 14*(-28*z**3 + 17*z - 31)</replace>
Simplifying the partial expression: -14*(-28*z**3 + 17*z - 31)
Expanding the part (-28*z**3 + 17*z - 31) using the distributive property, and we got: (17*z)*(-14) - 28*z**3*(-14) - 31*(-14)
Replacing -14*(-28*z**3 + 17*z - 31) with (17*z)*(-14) - 28*z**3*(-14) - 31*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*z)*(-14) + (27*z**2)*(-28*z**3 + 17*z - 31) - 28*z**3*(-14) + 434</replace>
Simplifying the partial expression: (27*z**2)*(-28*z**3 + 17*z - 31)
Expanding the part (-28*z**3 + 17*z - 31) using the distributive property, and we got: -837*z**2 + (17*z)*(27*z**2) + (27*z**2)*(-28*z**3)
Replacing (27*z**2)*(-28*z**3 + 17*z - 31) with -837*z**2 + (17*z)*(27*z**2) + (27*z**2)*(-28*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -31*27*z**2 + (17*z)*(27*z**2) + (17*z)*(-14) + (27*z**2)*(-28*z**3) - 28*z**3*(-14) + 434</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-28*z**3)*-14 = 392*z**3
  (-28*z**3)*(27*z**2) = -756*z**5
  (17*z)*-14 = -238*z
  (17*z)*(27*z**2) = 459*z**3
  -31*27*z**2 = -837*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -756*z**5 + 392*z**3 + 459*z**3 - 837*z**2 - 238*z + 434</replace>
Combining like terms, got -756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434
<replace-#Step 5>#Step 6:
Current expression: -756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434</replace>
No more calculations needed.
<answer>-756*z**5 + 851*z**3 - 837*z**2 - 238*z + 434</answer>


Question:
Simplify this expression: (70*x**3 + 52)*(49*x**3 + 24*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: 3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*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: (70*x**3 + 52)*(49*x**3 + 24*x**2 - 56*x)
Expanding the part (70*x**3 + 52) using the distributive property, and we got: (70*x**3)*(49*x**3 + 24*x**2 - 56*x) + 52*(49*x**3 + 24*x**2 - 56*x)
<replace-#Step 1>#Step 2:
Current expression: (70*x**3)*(49*x**3 + 24*x**2 - 56*x) + 52*(49*x**3 + 24*x**2 - 56*x)</replace>
Simplifying the partial expression: 52*(49*x**3 + 24*x**2 - 56*x)
Expanding the part (49*x**3 + 24*x**2 - 56*x) using the distributive property, and we got: -56*x*52 + (24*x**2)*52 + (49*x**3)*52
Replacing 52*(49*x**3 + 24*x**2 - 56*x) with -56*x*52 + (24*x**2)*52 + (49*x**3)*52 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -56*x*52 + (24*x**2)*52 + (49*x**3)*52 + (70*x**3)*(49*x**3 + 24*x**2 - 56*x)</replace>
Simplifying the partial expression: (70*x**3)*(49*x**3 + 24*x**2 - 56*x)
Expanding the part (49*x**3 + 24*x**2 - 56*x) using the distributive property, and we got: (-56*x)*(70*x**3) + (24*x**2)*(70*x**3) + (49*x**3)*(70*x**3)
Replacing (70*x**3)*(49*x**3 + 24*x**2 - 56*x) with (-56*x)*(70*x**3) + (24*x**2)*(70*x**3) + (49*x**3)*(70*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-56*x)*(70*x**3) - 56*x*52 + (24*x**2)*(70*x**3) + (24*x**2)*52 + (49*x**3)*(70*x**3) + (49*x**3)*52</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-56*x)*52 = -2912*x
  (-56*x)*(70*x**3) = -3920*x**4
  (24*x**2)*52 = 1248*x**2
  (24*x**2)*(70*x**3) = 1680*x**5
  (49*x**3)*52 = 2548*x**3
  (49*x**3)*(70*x**3) = 3430*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x</replace>
No more calculations needed.
<answer>3430*x**6 + 1680*x**5 - 3920*x**4 + 2548*x**3 + 1248*x**2 - 2912*x</answer>


Question:
Calculate the following: (-30*y**3 - 34*y**2)*(-44*y**2 + y - 27)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1320*y**5 + 1466*y**4 + 776*y**3 + 918*y**2


Question:
Simplify this expression: -1300*z**3 + 1235*z - 260
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1300*z**3 + 1235*z - 260

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: -1300*z**3 + 1235*z - 260
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: -1300*z**3 + 1235*z - 260</replace>
No more calculations needed.
<answer>-1300*z**3 + 1235*z - 260</answer>


Question:
Simplify this expression: (27 - 9*x)*(-39*x**3 - 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 351*x**4 - 1053*x**3 + 180*x**2 - 540*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: (27 - 9*x)*(-39*x**3 - 20*x)
Expanding the part (27 - 9*x) using the distributive property, and we got: (-9*x)*(-39*x**3 - 20*x) + 27*(-39*x**3 - 20*x)
<replace-#Step 1>#Step 2:
Current expression: (-9*x)*(-39*x**3 - 20*x) + 27*(-39*x**3 - 20*x)</replace>
Simplifying the partial expression: 27*(-39*x**3 - 20*x)
Expanding the part (-39*x**3 - 20*x) using the distributive property, and we got: -20*x*27 - 39*x**3*27
Replacing 27*(-39*x**3 - 20*x) with -20*x*27 - 39*x**3*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*x*27 + (-9*x)*(-39*x**3 - 20*x) - 39*x**3*27</replace>
Simplifying the partial expression: (-9*x)*(-39*x**3 - 20*x)
Expanding the part (-39*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(-9*x) + (-9*x)*(-39*x**3)
Replacing (-9*x)*(-39*x**3 - 20*x) with (-20*x)*(-9*x) + (-9*x)*(-39*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*x)*(-9*x) - 20*x*27 + (-9*x)*(-39*x**3) - 39*x**3*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*27 = -1053*x**3
  (-39*x**3)*(-9*x) = 351*x**4
  (-20*x)*27 = -540*x
  (-20*x)*(-9*x) = 180*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 351*x**4 - 1053*x**3 + 180*x**2 - 540*x</replace>
No more calculations needed.
<answer>351*x**4 - 1053*x**3 + 180*x**2 - 540*x</answer>


Question:
Calculate the following: (41*z**2 - 46*z)*(12*z**3 + 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 492*z**5 - 552*z**4 + 1066*z**2 - 1196*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (41*z**2 - 46*z)*(12*z**3 + 26)
Expanding the part (12*z**3 + 26) using the distributive property, and we got: (12*z**3)*(41*z**2 - 46*z) + 26*(41*z**2 - 46*z)
<replace-#Step 1>#Step 2:
Current expression: (12*z**3)*(41*z**2 - 46*z) + 26*(41*z**2 - 46*z)</replace>
Simplifying the partial expression: 26*(41*z**2 - 46*z)
Expanding the part (41*z**2 - 46*z) using the distributive property, and we got: -46*z*26 + (41*z**2)*26
Replacing 26*(41*z**2 - 46*z) with -46*z*26 + (41*z**2)*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*z*26 + (41*z**2)*26 + (12*z**3)*(41*z**2 - 46*z)</replace>
Simplifying the partial expression: (12*z**3)*(41*z**2 - 46*z)
Expanding the part (41*z**2 - 46*z) using the distributive property, and we got: (-46*z)*(12*z**3) + (41*z**2)*(12*z**3)
Replacing (12*z**3)*(41*z**2 - 46*z) with (-46*z)*(12*z**3) + (41*z**2)*(12*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*z)*(12*z**3) - 46*z*26 + (41*z**2)*(12*z**3) + (41*z**2)*26</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*z)*26 = -1196*z
  (-46*z)*(12*z**3) = -552*z**4
  (41*z**2)*26 = 1066*z**2
  (41*z**2)*(12*z**3) = 492*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 492*z**5 - 552*z**4 + 1066*z**2 - 1196*z</replace>
No more calculations needed.
<answer>492*z**5 - 552*z**4 + 1066*z**2 - 1196*z</answer>


Question:
Calculate the following: (16 - 2*x**3)*(-36*x**2 + 9*x - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80

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 - 2*x**3)*(-36*x**2 + 9*x - 5)
Expanding the part (16 - 2*x**3) using the distributive property, and we got: (-2*x**3)*(-36*x**2 + 9*x - 5) + 16*(-36*x**2 + 9*x - 5)
<replace-#Step 1>#Step 2:
Current expression: (-2*x**3)*(-36*x**2 + 9*x - 5) + 16*(-36*x**2 + 9*x - 5)</replace>
Simplifying the partial expression: 16*(-36*x**2 + 9*x - 5)
Expanding the part (-36*x**2 + 9*x - 5) using the distributive property, and we got: (9*x)*16 - 36*x**2*16 - 5*16
Replacing 16*(-36*x**2 + 9*x - 5) with (9*x)*16 - 36*x**2*16 - 5*16 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*x)*16 - 36*x**2*16 + (-2*x**3)*(-36*x**2 + 9*x - 5) - 80</replace>
Simplifying the partial expression: (-2*x**3)*(-36*x**2 + 9*x - 5)
Expanding the part (-36*x**2 + 9*x - 5) using the distributive property, and we got: -(-1)*10*x**3 + (9*x)*(-2*x**3) + (-36*x**2)*(-2*x**3)
Replacing (-2*x**3)*(-36*x**2 + 9*x - 5) with -(-1)*10*x**3 + (9*x)*(-2*x**3) + (-36*x**2)*(-2*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -5*(-2)*x**3 + (9*x)*(-2*x**3) + (9*x)*16 + (-36*x**2)*(-2*x**3) - 36*x**2*16 - 80</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*x**2)*16 = -576*x**2
  (-36*x**2)*(-2*x**3) = 72*x**5
  (9*x)*16 = 144*x
  (9*x)*(-2*x**3) = -18*x**4
  -5*-2*x**3 = 10*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80</replace>
No more calculations needed.
<answer>72*x**5 - 18*x**4 + 10*x**3 - 576*x**2 + 144*x - 80</answer>


Question:
Calculate the following: (49 - 34*y)*(14*y**3 + 12*y**2 + 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: -476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862

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 - 34*y)*(14*y**3 + 12*y**2 + 38)
Expanding the part (49 - 34*y) using the distributive property, and we got: (-34*y)*(14*y**3 + 12*y**2 + 38) + 49*(14*y**3 + 12*y**2 + 38)
<replace-#Step 1>#Step 2:
Current expression: (-34*y)*(14*y**3 + 12*y**2 + 38) + 49*(14*y**3 + 12*y**2 + 38)</replace>
Simplifying the partial expression: 49*(14*y**3 + 12*y**2 + 38)
Expanding the part (14*y**3 + 12*y**2 + 38) using the distributive property, and we got: (12*y**2)*49 + (14*y**3)*49 + 38*49
Replacing 49*(14*y**3 + 12*y**2 + 38) with (12*y**2)*49 + (14*y**3)*49 + 38*49 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-34*y)*(14*y**3 + 12*y**2 + 38) + (12*y**2)*49 + (14*y**3)*49 + 1862</replace>
Simplifying the partial expression: (-34*y)*(14*y**3 + 12*y**2 + 38)
Expanding the part (14*y**3 + 12*y**2 + 38) using the distributive property, and we got: (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34*y)
Replacing (-34*y)*(14*y**3 + 12*y**2 + 38) with (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-34*y)*(12*y**2) + (-34*y)*(14*y**3) + 38*(-34)*y + (12*y**2)*49 + (14*y**3)*49 + 1862</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (12*y**2)*49 = 588*y**2
  (12*y**2)*(-34*y) = -408*y**3
  (14*y**3)*49 = 686*y**3
  (14*y**3)*(-34*y) = -476*y**4
  38*-34*y = -1292*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -476*y**4 - 408*y**3 + 686*y**3 + 588*y**2 - 1292*y + 1862</replace>
Combining like terms, got -476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862
<replace-#Step 5>#Step 6:
Current expression: -476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862</replace>
No more calculations needed.
<answer>-476*y**4 + 278*y**3 + 588*y**2 - 1292*y + 1862</answer>


Question:
Calculate the following: (17*x**3 - 46)*(34*x**3 - 17*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: 578*x**6 - 289*x**4 - 1564*x**3 + 782*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: (17*x**3 - 46)*(34*x**3 - 17*x)
Expanding the part (17*x**3 - 46) using the distributive property, and we got: (17*x**3)*(34*x**3 - 17*x) - 46*(34*x**3 - 17*x)
<replace-#Step 1>#Step 2:
Current expression: (17*x**3)*(34*x**3 - 17*x) - 46*(34*x**3 - 17*x)</replace>
Simplifying the partial expression: -46*(34*x**3 - 17*x)
Expanding the part (34*x**3 - 17*x) using the distributive property, and we got: -17*x*(-46) + (34*x**3)*(-46)
Replacing -46*(34*x**3 - 17*x) with -17*x*(-46) + (34*x**3)*(-46) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -17*x*(-46) + (17*x**3)*(34*x**3 - 17*x) + (34*x**3)*(-46)</replace>
Simplifying the partial expression: (17*x**3)*(34*x**3 - 17*x)
Expanding the part (34*x**3 - 17*x) using the distributive property, and we got: (-17*x)*(17*x**3) + (17*x**3)*(34*x**3)
Replacing (17*x**3)*(34*x**3 - 17*x) with (-17*x)*(17*x**3) + (17*x**3)*(34*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-17*x)*(17*x**3) - 17*x*(-46) + (17*x**3)*(34*x**3) + (34*x**3)*(-46)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-17*x)*-46 = 782*x
  (-17*x)*(17*x**3) = -289*x**4
  (34*x**3)*-46 = -1564*x**3
  (34*x**3)*(17*x**3) = 578*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 578*x**6 - 289*x**4 - 1564*x**3 + 782*x</replace>
No more calculations needed.
<answer>578*x**6 - 289*x**4 - 1564*x**3 + 782*x</answer>


Question:
Calculate the following: -210*z**2 - 336
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -210*z**2 - 336

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: -210*z**2 - 336
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: -210*z**2 - 336</replace>
No more calculations needed.
<answer>-210*z**2 - 336</answer>


Question:
Simplify this expression: -21*z*(54*z**2 - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1134*z**3 + 105*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: -21*z*(54*z**2 - 5)
Expanding the part (54*z**2 - 5) using the distributive property, and we got: (-21*z)*(54*z**2) - (-1)*105*z
<replace-#Step 1>#Step 2:
Current expression: (-21*z)*(54*z**2) - (-1)*105*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -5*(-21*z) = 105*z
  (54*z**2)*(-21*z) = -1134*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1134*z**3 + 105*z</replace>
No more calculations needed.
<answer>-1134*z**3 + 105*z</answer>


Question:
Simplify this expression: (6*z**3 + 35*z**2)*(-79*z**3 + 8*z**2 - 12*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: -474*z**6 - 2717*z**5 + 208*z**4 - 420*z**3


Question:
Simplify this expression: 30*z**2*(31 - 44*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: -1320*z**3 + 930*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: 30*z**2*(31 - 44*z)
Expanding the part (31 - 44*z) using the distributive property, and we got: (-44*z)*(30*z**2) + 31*(30*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-44*z)*(30*z**2) + 31*(30*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  31*(30*z**2) = 930*z**2
  (-44*z)*(30*z**2) = -1320*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1320*z**3 + 930*z**2</replace>
No more calculations needed.
<answer>-1320*z**3 + 930*z**2</answer>


Question:
Calculate the following: (45 - 33*y)*(-34*y**3 - 46*y - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (45 - 33*y)*(-34*y**3 - 46*y - 31)
Expanding the part (45 - 33*y) using the distributive property, and we got: (-33*y)*(-34*y**3 - 46*y - 31) + 45*(-34*y**3 - 46*y - 31)
<replace-#Step 1>#Step 2:
Current expression: (-33*y)*(-34*y**3 - 46*y - 31) + 45*(-34*y**3 - 46*y - 31)</replace>
Simplifying the partial expression: 45*(-34*y**3 - 46*y - 31)
Expanding the part (-34*y**3 - 46*y - 31) using the distributive property, and we got: -46*y*45 - 34*y**3*45 - 31*45
Replacing 45*(-34*y**3 - 46*y - 31) with -46*y*45 - 34*y**3*45 - 31*45 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -46*y*45 + (-33*y)*(-34*y**3 - 46*y - 31) - 34*y**3*45 - 1395</replace>
Simplifying the partial expression: (-33*y)*(-34*y**3 - 46*y - 31)
Expanding the part (-34*y**3 - 46*y - 31) using the distributive property, and we got: (-46*y)*(-33*y) + (-33*y)*(-34*y**3) - (-1)*1023*y
Replacing (-33*y)*(-34*y**3 - 46*y - 31) with (-46*y)*(-33*y) + (-33*y)*(-34*y**3) - (-1)*1023*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-46*y)*(-33*y) - 46*y*45 + (-33*y)*(-34*y**3) - 31*(-33)*y - 34*y**3*45 - 1395</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-46*y)*45 = -2070*y
  (-46*y)*(-33*y) = 1518*y**2
  (-34*y**3)*45 = -1530*y**3
  (-34*y**3)*(-33*y) = 1122*y**4
  -31*-33*y = 1023*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1122*y**4 - 1530*y**3 + 1518*y**2 - 2070*y + 1023*y - 1395</replace>
Combining like terms, got 1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395
<replace-#Step 5>#Step 6:
Current expression: 1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395</replace>
No more calculations needed.
<answer>1122*y**4 - 1530*y**3 + 1518*y**2 - 1047*y - 1395</answer>


Question:
Calculate the following: (-33*z - 45)*(-10*z**3 - 25*z**2 - 44*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: 330*z**4 + 1275*z**3 + 2577*z**2 + 1980*z


Question:
Simplify this expression: (8*y + 24)*(-28*y**3 - 33*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: -224*y**4 - 672*y**3 - 264*y**2 - 792*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: (8*y + 24)*(-28*y**3 - 33*y)
Expanding the part (8*y + 24) using the distributive property, and we got: (8*y)*(-28*y**3 - 33*y) + 24*(-28*y**3 - 33*y)
<replace-#Step 1>#Step 2:
Current expression: (8*y)*(-28*y**3 - 33*y) + 24*(-28*y**3 - 33*y)</replace>
Simplifying the partial expression: 24*(-28*y**3 - 33*y)
Expanding the part (-28*y**3 - 33*y) using the distributive property, and we got: -33*y*24 - 28*y**3*24
Replacing 24*(-28*y**3 - 33*y) with -33*y*24 - 28*y**3*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -33*y*24 + (8*y)*(-28*y**3 - 33*y) - 28*y**3*24</replace>
Simplifying the partial expression: (8*y)*(-28*y**3 - 33*y)
Expanding the part (-28*y**3 - 33*y) using the distributive property, and we got: (-33*y)*(8*y) + (8*y)*(-28*y**3)
Replacing (8*y)*(-28*y**3 - 33*y) with (-33*y)*(8*y) + (8*y)*(-28*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-33*y)*(8*y) - 33*y*24 + (8*y)*(-28*y**3) - 28*y**3*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-33*y)*24 = -792*y
  (-33*y)*(8*y) = -264*y**2
  (-28*y**3)*24 = -672*y**3
  (-28*y**3)*(8*y) = -224*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -224*y**4 - 672*y**3 - 264*y**2 - 792*y</replace>
No more calculations needed.
<answer>-224*y**4 - 672*y**3 - 264*y**2 - 792*y</answer>


Question:
Simplify this expression: (15*x**2 + 48*x)*(77*x**3 + 26)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1155*x**5 + 3696*x**4 + 390*x**2 + 1248*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: (15*x**2 + 48*x)*(77*x**3 + 26)
Expanding the part (77*x**3 + 26) using the distributive property, and we got: (77*x**3)*(15*x**2 + 48*x) + 26*(15*x**2 + 48*x)
<replace-#Step 1>#Step 2:
Current expression: (77*x**3)*(15*x**2 + 48*x) + 26*(15*x**2 + 48*x)</replace>
Simplifying the partial expression: 26*(15*x**2 + 48*x)
Expanding the part (15*x**2 + 48*x) using the distributive property, and we got: (48*x)*26 + (15*x**2)*26
Replacing 26*(15*x**2 + 48*x) with (48*x)*26 + (15*x**2)*26 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*x)*26 + (15*x**2)*26 + (77*x**3)*(15*x**2 + 48*x)</replace>
Simplifying the partial expression: (77*x**3)*(15*x**2 + 48*x)
Expanding the part (15*x**2 + 48*x) using the distributive property, and we got: (48*x)*(77*x**3) + (15*x**2)*(77*x**3)
Replacing (77*x**3)*(15*x**2 + 48*x) with (48*x)*(77*x**3) + (15*x**2)*(77*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (48*x)*(77*x**3) + (48*x)*26 + (15*x**2)*(77*x**3) + (15*x**2)*26</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (15*x**2)*26 = 390*x**2
  (15*x**2)*(77*x**3) = 1155*x**5
  (48*x)*26 = 1248*x
  (48*x)*(77*x**3) = 3696*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x</replace>
No more calculations needed.
<answer>1155*x**5 + 3696*x**4 + 390*x**2 + 1248*x</answer>


Question:
Calculate the following: (-4*x**2 - 68*x)*(-x**2 - 30)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 4*x**4 + 68*x**3 + 120*x**2 + 2040*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**2 - 68*x)*(-x**2 - 30)
Expanding the part (-x**2 - 30) using the distributive property, and we got: (-x**2)*(-4*x**2 - 68*x) - 30*(-4*x**2 - 68*x)
<replace-#Step 1>#Step 2:
Current expression: (-x**2)*(-4*x**2 - 68*x) - 30*(-4*x**2 - 68*x)</replace>
Simplifying the partial expression: -30*(-4*x**2 - 68*x)
Expanding the part (-4*x**2 - 68*x) using the distributive property, and we got: -68*x*(-30) - 4*x**2*(-30)
Replacing -30*(-4*x**2 - 68*x) with -68*x*(-30) - 4*x**2*(-30) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -68*x*(-30) - 4*x**2*(-30) + (-x**2)*(-4*x**2 - 68*x)</replace>
Simplifying the partial expression: (-x**2)*(-4*x**2 - 68*x)
Expanding the part (-4*x**2 - 68*x) using the distributive property, and we got: (-68*x)*(-x**2) + (-4*x**2)*(-x**2)
Replacing (-x**2)*(-4*x**2 - 68*x) with (-68*x)*(-x**2) + (-4*x**2)*(-x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-68*x)*(-x**2) - 68*x*(-30) + (-4*x**2)*(-x**2) - 4*x**2*(-30)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-68*x)*-30 = 2040*x
  (-68*x)*(-x**2) = 68*x**3
  (-4*x**2)*-30 = 120*x**2
  (-4*x**2)*(-x**2) = 4*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 4*x**4 + 68*x**3 + 120*x**2 + 2040*x</replace>
No more calculations needed.
<answer>4*x**4 + 68*x**3 + 120*x**2 + 2040*x</answer>


Question:
Simplify this expression: (43*z**2 + 39*z)*(9*z**2 - 22*z + 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 387*z**4 - 595*z**3 + 647*z**2 + 1365*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: (43*z**2 + 39*z)*(9*z**2 - 22*z + 35)
Expanding the part (43*z**2 + 39*z) using the distributive property, and we got: (39*z)*(9*z**2 - 22*z + 35) + (43*z**2)*(9*z**2 - 22*z + 35)
<replace-#Step 1>#Step 2:
Current expression: (39*z)*(9*z**2 - 22*z + 35) + (43*z**2)*(9*z**2 - 22*z + 35)</replace>
Simplifying the partial expression: (39*z)*(9*z**2 - 22*z + 35)
Expanding the part (9*z**2 - 22*z + 35) using the distributive property, and we got: (-22*z)*(39*z) + 35*(39*z) + (39*z)*(9*z**2)
Replacing (39*z)*(9*z**2 - 22*z + 35) with (-22*z)*(39*z) + 35*(39*z) + (39*z)*(9*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-22*z)*(39*z) + 35*39*z + (39*z)*(9*z**2) + (43*z**2)*(9*z**2 - 22*z + 35)</replace>
Simplifying the partial expression: (43*z**2)*(9*z**2 - 22*z + 35)
Expanding the part (9*z**2 - 22*z + 35) using the distributive property, and we got: (-22*z)*(43*z**2) + 35*(43*z**2) + (9*z**2)*(43*z**2)
Replacing (43*z**2)*(9*z**2 - 22*z + 35) with (-22*z)*(43*z**2) + 35*(43*z**2) + (9*z**2)*(43*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*z)*(39*z) + (-22*z)*(43*z**2) + 35*43*z**2 + 35*39*z + (39*z)*(9*z**2) + (9*z**2)*(43*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*z)*(39*z) = -858*z**2
  (-22*z)*(43*z**2) = -946*z**3
  (9*z**2)*(39*z) = 351*z**3
  (9*z**2)*(43*z**2) = 387*z**4
  35*39*z = 1365*z
  35*43*z**2 = 1505*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 387*z**4 - 946*z**3 + 351*z**3 - 858*z**2 + 1505*z**2 + 1365*z</replace>
Combining like terms, got 387*z**4 - 595*z**3 + 647*z**2 + 1365*z
<replace-#Step 5>#Step 6:
Current expression: 387*z**4 - 595*z**3 + 647*z**2 + 1365*z</replace>
No more calculations needed.
<answer>387*z**4 - 595*z**3 + 647*z**2 + 1365*z</answer>


Question:
Calculate the following: (17*x**2 - 22*x)*(2*x**3 - 15*x**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 34*x**5 - 299*x**4 + 330*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: (17*x**2 - 22*x)*(2*x**3 - 15*x**2)
Expanding the part (17*x**2 - 22*x) using the distributive property, and we got: (-22*x)*(2*x**3 - 15*x**2) + (17*x**2)*(2*x**3 - 15*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(2*x**3 - 15*x**2) + (17*x**2)*(2*x**3 - 15*x**2)</replace>
Simplifying the partial expression: (-22*x)*(2*x**3 - 15*x**2)
Expanding the part (2*x**3 - 15*x**2) using the distributive property, and we got: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3)
Replacing (-22*x)*(2*x**3 - 15*x**2) with (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) + (17*x**2)*(2*x**3 - 15*x**2)</replace>
Simplifying the partial expression: (17*x**2)*(2*x**3 - 15*x**2)
Expanding the part (2*x**3 - 15*x**2) using the distributive property, and we got: (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3)
Replacing (17*x**2)*(2*x**3 - 15*x**2) with (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-22*x)*(-15*x**2) + (-22*x)*(2*x**3) + (-15*x**2)*(17*x**2) + (17*x**2)*(2*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-15*x**2)*(-22*x) = 330*x**3
  (-15*x**2)*(17*x**2) = -255*x**4
  (2*x**3)*(-22*x) = -44*x**4
  (2*x**3)*(17*x**2) = 34*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 34*x**5 - 255*x**4 - 44*x**4 + 330*x**3</replace>
Combining like terms, got 34*x**5 - 299*x**4 + 330*x**3
<replace-#Step 5>#Step 6:
Current expression: 34*x**5 - 299*x**4 + 330*x**3</replace>
No more calculations needed.
<answer>34*x**5 - 299*x**4 + 330*x**3</answer>


Question:
Calculate the following: (35*x - 34)*(-40*x**3 + 9*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: -1400*x**4 + 1360*x**3 + 315*x**2 - 306*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: (35*x - 34)*(-40*x**3 + 9*x)
Expanding the part (35*x - 34) using the distributive property, and we got: (35*x)*(-40*x**3 + 9*x) - 34*(-40*x**3 + 9*x)
<replace-#Step 1>#Step 2:
Current expression: (35*x)*(-40*x**3 + 9*x) - 34*(-40*x**3 + 9*x)</replace>
Simplifying the partial expression: -34*(-40*x**3 + 9*x)
Expanding the part (-40*x**3 + 9*x) using the distributive property, and we got: (9*x)*(-34) - 40*x**3*(-34)
Replacing -34*(-40*x**3 + 9*x) with (9*x)*(-34) - 40*x**3*(-34) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*x)*(-34) + (35*x)*(-40*x**3 + 9*x) - 40*x**3*(-34)</replace>
Simplifying the partial expression: (35*x)*(-40*x**3 + 9*x)
Expanding the part (-40*x**3 + 9*x) using the distributive property, and we got: (9*x)*(35*x) + (35*x)*(-40*x**3)
Replacing (35*x)*(-40*x**3 + 9*x) with (9*x)*(35*x) + (35*x)*(-40*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (9*x)*(35*x) + (9*x)*(-34) + (35*x)*(-40*x**3) - 40*x**3*(-34)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-40*x**3)*-34 = 1360*x**3
  (-40*x**3)*(35*x) = -1400*x**4
  (9*x)*-34 = -306*x
  (9*x)*(35*x) = 315*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1400*x**4 + 1360*x**3 + 315*x**2 - 306*x</replace>
No more calculations needed.
<answer>-1400*x**4 + 1360*x**3 + 315*x**2 - 306*x</answer>


Question:
Simplify this expression: (-29*x**2 - 15)*(18*x**2 - 48*x - 50)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-29*x**2 - 15)*(18*x**2 - 48*x - 50)
Expanding the part (-29*x**2 - 15) using the distributive property, and we got: (-29*x**2)*(18*x**2 - 48*x - 50) - 15*(18*x**2 - 48*x - 50)
<replace-#Step 1>#Step 2:
Current expression: (-29*x**2)*(18*x**2 - 48*x - 50) - 15*(18*x**2 - 48*x - 50)</replace>
Simplifying the partial expression: -15*(18*x**2 - 48*x - 50)
Expanding the part (18*x**2 - 48*x - 50) using the distributive property, and we got: -48*x*(-15) + (18*x**2)*(-15) - 50*(-15)
Replacing -15*(18*x**2 - 48*x - 50) with -48*x*(-15) + (18*x**2)*(-15) - 50*(-15) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -48*x*(-15) + (-29*x**2)*(18*x**2 - 48*x - 50) + (18*x**2)*(-15) + 750</replace>
Simplifying the partial expression: (-29*x**2)*(18*x**2 - 48*x - 50)
Expanding the part (18*x**2 - 48*x - 50) using the distributive property, and we got: (-48*x)*(-29*x**2) - (-1)*1450*x**2 + (-29*x**2)*(18*x**2)
Replacing (-29*x**2)*(18*x**2 - 48*x - 50) with (-48*x)*(-29*x**2) - (-1)*1450*x**2 + (-29*x**2)*(18*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-48*x)*(-29*x**2) - 48*x*(-15) - 50*(-29)*x**2 + (-29*x**2)*(18*x**2) + (18*x**2)*(-15) + 750</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-48*x)*-15 = 720*x
  (-48*x)*(-29*x**2) = 1392*x**3
  (18*x**2)*-15 = -270*x**2
  (18*x**2)*(-29*x**2) = -522*x**4
  -50*-29*x**2 = 1450*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -522*x**4 + 1392*x**3 - 270*x**2 + 1450*x**2 + 720*x + 750</replace>
Combining like terms, got -522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750
<replace-#Step 5>#Step 6:
Current expression: -522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750</replace>
No more calculations needed.
<answer>-522*x**4 + 1392*x**3 + 1180*x**2 + 720*x + 750</answer>


Question:
Calculate the following: 38*z**2*(40*z**3 - 18*z**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1520*z**5 - 684*z**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 38*z**2*(40*z**3 - 18*z**2)
Expanding the part (40*z**3 - 18*z**2) using the distributive property, and we got: (-18*z**2)*(38*z**2) + (38*z**2)*(40*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-18*z**2)*(38*z**2) + (38*z**2)*(40*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*z**2)*(38*z**2) = -684*z**4
  (40*z**3)*(38*z**2) = 1520*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1520*z**5 - 684*z**4</replace>
No more calculations needed.
<answer>1520*z**5 - 684*z**4</answer>


Question:
Simplify this expression: (-10*y**2 - 44)*(-34*y**3 - 3*y**2 - 37*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 340*y**5 + 30*y**4 + 1866*y**3 + 132*y**2 + 1628*y


Question:
Calculate the following: (-8*y**2 - 42*y + 29)*(2*y**2 + 47*y + 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-8*y**2 - 42*y + 29)*(2*y**2 + 47*y + 3)
Expanding the part (2*y**2 + 47*y + 3) using the distributive property, and we got: (47*y)*(-8*y**2 - 42*y + 29) + (2*y**2)*(-8*y**2 - 42*y + 29) + 3*(-8*y**2 - 42*y + 29)
<replace-#Step 1>#Step 2:
Current expression: (47*y)*(-8*y**2 - 42*y + 29) + (2*y**2)*(-8*y**2 - 42*y + 29) + 3*(-8*y**2 - 42*y + 29)</replace>
Simplifying the partial expression: 3*(-8*y**2 - 42*y + 29)
Expanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: -42*y*3 - 8*y**2*3 + 29*3
Replacing 3*(-8*y**2 - 42*y + 29) with -42*y*3 - 8*y**2*3 + 29*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*y*3 + (47*y)*(-8*y**2 - 42*y + 29) - 8*y**2*3 + (2*y**2)*(-8*y**2 - 42*y + 29) + 87</replace>
Simplifying the partial expression: (2*y**2)*(-8*y**2 - 42*y + 29)
Expanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: (-42*y)*(2*y**2) + 29*(2*y**2) + (-8*y**2)*(2*y**2)
Replacing (2*y**2)*(-8*y**2 - 42*y + 29) with (-42*y)*(2*y**2) + 29*(2*y**2) + (-8*y**2)*(2*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*y)*(2*y**2) - 42*y*3 + 29*2*y**2 + (47*y)*(-8*y**2 - 42*y + 29) + (-8*y**2)*(2*y**2) - 8*y**2*3 + 87</replace>
Simplifying the partial expression: (47*y)*(-8*y**2 - 42*y + 29)
Expanding the part (-8*y**2 - 42*y + 29) using the distributive property, and we got: (-42*y)*(47*y) + 29*(47*y) + (47*y)*(-8*y**2)
Replacing (47*y)*(-8*y**2 - 42*y + 29) with (-42*y)*(47*y) + 29*(47*y) + (47*y)*(-8*y**2) in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: (-42*y)*(47*y) + (-42*y)*(2*y**2) - 42*y*3 + 29*2*y**2 + 29*47*y + (47*y)*(-8*y**2) + (-8*y**2)*(2*y**2) - 8*y**2*3 + 87</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y)*3 = -126*y
  (-42*y)*(2*y**2) = -84*y**3
  (-42*y)*(47*y) = -1974*y**2
  (-8*y**2)*3 = -24*y**2
  (-8*y**2)*(2*y**2) = -16*y**4
  (-8*y**2)*(47*y) = -376*y**3
  29*2*y**2 = 58*y**2
  29*47*y = 1363*y
Replacing them in the overall expression.
<replace-#Step 5>#Step 6:
Current expression: -16*y**4 - 376*y**3 - 84*y**3 - 1974*y**2 - 24*y**2 + 58*y**2 - 126*y + 1363*y + 87</replace>
Combining like terms, got -16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87
<replace-#Step 6>#Step 7:
Current expression: -16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87</replace>
No more calculations needed.
<answer>-16*y**4 - 460*y**3 - 1940*y**2 + 1237*y + 87</answer>


Question:
Calculate the following: (6 - z)*(43*z**2 + 45*z - 19)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -43*z**3 + 213*z**2 + 289*z - 114

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 - z)*(43*z**2 + 45*z - 19)
Expanding the part (6 - z) using the distributive property, and we got: (-z)*(43*z**2 + 45*z - 19) + 6*(43*z**2 + 45*z - 19)
<replace-#Step 1>#Step 2:
Current expression: (-z)*(43*z**2 + 45*z - 19) + 6*(43*z**2 + 45*z - 19)</replace>
Simplifying the partial expression: 6*(43*z**2 + 45*z - 19)
Expanding the part (43*z**2 + 45*z - 19) using the distributive property, and we got: (45*z)*6 + (43*z**2)*6 - 19*6
Replacing 6*(43*z**2 + 45*z - 19) with (45*z)*6 + (43*z**2)*6 - 19*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-z)*(43*z**2 + 45*z - 19) + (45*z)*6 + (43*z**2)*6 - 114</replace>
Simplifying the partial expression: (-z)*(43*z**2 + 45*z - 19)
Expanding the part (43*z**2 + 45*z - 19) using the distributive property, and we got: (-z)*(45*z) + (-z)*(43*z**2) - (-1)*19*z
Replacing (-z)*(43*z**2 + 45*z - 19) with (-z)*(45*z) + (-z)*(43*z**2) - (-1)*19*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-z)*(45*z) + (-z)*(43*z**2) - 19*(-1)*z + (45*z)*6 + (43*z**2)*6 - 114</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (43*z**2)*6 = 258*z**2
  (43*z**2)*(-z) = -43*z**3
  (45*z)*6 = 270*z
  (45*z)*(-z) = -45*z**2
  -19*-1*z = 19*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -43*z**3 - 45*z**2 + 258*z**2 + 19*z + 270*z - 114</replace>
Combining like terms, got -43*z**3 + 213*z**2 + 289*z - 114
<replace-#Step 5>#Step 6:
Current expression: -43*z**3 + 213*z**2 + 289*z - 114</replace>
No more calculations needed.
<answer>-43*z**3 + 213*z**2 + 289*z - 114</answer>


Question:
Simplify this expression: (-16*y**2 - 13*y - 8)*(y**3 + 9*y**2 - 6*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -16*y**5 - 157*y**4 - 29*y**3 + 6*y**2 + 48*y


Question:
Simplify this expression: (-41*y**3 - 5*y**2 + 2*y)*(50*y**3 - 37*y**2 + 11*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2050*y**6 + 1267*y**5 - 166*y**4 - 129*y**3 + 22*y**2


Question:
Calculate the following: (30*y**2 + 46*y - 14)*(49*y**2 - 3*y + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1470*y**4 + 2164*y**3 + 586*y**2 + 2204*y - 658


Question:
Calculate the following: 16*z*(48*z - 43)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 768*z**2 - 688*z

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 16*z*(48*z - 43)
Expanding the part (48*z - 43) using the distributive property, and we got: -688*z + (16*z)*(48*z)
<replace-#Step 1>#Step 2:
Current expression: -688*z + (16*z)*(48*z)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -43*(16*z) = -688*z
  (48*z)*(16*z) = 768*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 768*z**2 - 688*z</replace>
No more calculations needed.
<answer>768*z**2 - 688*z</answer>


Question:
Simplify this expression: (47*z**3 + 19*z)*(30*z**3 - 37*z**2 - 20*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: 1410*z**6 - 1739*z**5 - 370*z**4 - 703*z**3 - 380*z**2