Question:
Simplify this expression: (31 - 32*x)*(-67*x**2 - 44*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: 2144*x**3 - 669*x**2 - 1364*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: (31 - 32*x)*(-67*x**2 - 44*x)
Expanding the part (31 - 32*x) using the distributive property, and we got: (-32*x)*(-67*x**2 - 44*x) + 31*(-67*x**2 - 44*x)
<replace-#Step 1>#Step 2:
Current expression: (-32*x)*(-67*x**2 - 44*x) + 31*(-67*x**2 - 44*x)</replace>
Simplifying the partial expression: 31*(-67*x**2 - 44*x)
Expanding the part (-67*x**2 - 44*x) using the distributive property, and we got: -44*x*31 - 67*x**2*31
Replacing 31*(-67*x**2 - 44*x) with -44*x*31 - 67*x**2*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -44*x*31 + (-32*x)*(-67*x**2 - 44*x) - 67*x**2*31</replace>
Simplifying the partial expression: (-32*x)*(-67*x**2 - 44*x)
Expanding the part (-67*x**2 - 44*x) using the distributive property, and we got: (-44*x)*(-32*x) + (-32*x)*(-67*x**2)
Replacing (-32*x)*(-67*x**2 - 44*x) with (-44*x)*(-32*x) + (-32*x)*(-67*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-44*x)*(-32*x) - 44*x*31 + (-32*x)*(-67*x**2) - 67*x**2*31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-67*x**2)*31 = -2077*x**2
  (-67*x**2)*(-32*x) = 2144*x**3
  (-44*x)*31 = -1364*x
  (-44*x)*(-32*x) = 1408*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2144*x**3 - 2077*x**2 + 1408*x**2 - 1364*x</replace>
Combining like terms, got 2144*x**3 - 669*x**2 - 1364*x
<replace-#Step 5>#Step 6:
Current expression: 2144*x**3 - 669*x**2 - 1364*x</replace>
No more calculations needed.
<answer>2144*x**3 - 669*x**2 - 1364*x</answer>


Question:
Simplify this expression: (11*z**2 - 36*z + 34)*(18*z**3 + 18*z**2 - 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: 198*z**5 - 450*z**4 - 36*z**3 + 62*z**2 + 1800*z - 1700


Question:
Calculate the following: (-22*z**3 - 5*z**2 + z)*(-17*z**3 + 7*z**2 + 11*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: 374*z**6 - 69*z**5 - 294*z**4 - 48*z**3 + 11*z**2


Question:
Simplify this expression: (-9*z**3 + 27*z)*(-7*z**3 + 37*z**2 - 46*z - 21)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 63*z**6 - 333*z**5 + 225*z**4 + 1188*z**3 - 1242*z**2 - 567*z


Question:
Calculate the following: (10*y**3 + 19*y**2)*(-28*y**3 + 20*y - 17)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -280*y**6 - 532*y**5 + 200*y**4 + 210*y**3 - 323*y**2


Question:
Simplify this expression: (29*y**2 + 4)*(-38*y**3 - 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: -1102*y**5 - 152*y**3 - 290*y**2 - 40

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*y**2 + 4)*(-38*y**3 - 10)
Expanding the part (-38*y**3 - 10) using the distributive property, and we got: (-38*y**3)*(29*y**2 + 4) - 10*(29*y**2 + 4)
<replace-#Step 1>#Step 2:
Current expression: (-38*y**3)*(29*y**2 + 4) - 10*(29*y**2 + 4)</replace>
Simplifying the partial expression: -10*(29*y**2 + 4)
Expanding the part (29*y**2 + 4) using the distributive property, and we got: (29*y**2)*(-10) + 4*(-10)
Replacing -10*(29*y**2 + 4) with (29*y**2)*(-10) + 4*(-10) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (29*y**2)*(-10) + (-38*y**3)*(29*y**2 + 4) - 40</replace>
Simplifying the partial expression: (-38*y**3)*(29*y**2 + 4)
Expanding the part (29*y**2 + 4) using the distributive property, and we got: 4*(-38*y**3) + (29*y**2)*(-38*y**3)
Replacing (-38*y**3)*(29*y**2 + 4) with 4*(-38*y**3) + (29*y**2)*(-38*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 4*(-38)*y**3 + (29*y**2)*(-38*y**3) + (29*y**2)*(-10) - 40</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (29*y**2)*-10 = -290*y**2
  (29*y**2)*(-38*y**3) = -1102*y**5
  4*-38*y**3 = -152*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1102*y**5 - 152*y**3 - 290*y**2 - 40</replace>
No more calculations needed.
<answer>-1102*y**5 - 152*y**3 - 290*y**2 - 40</answer>


Question:
Simplify this expression: (53*x + 19)*(6*x**3 + 23*x**2 + 10*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 318*x**4 + 1333*x**3 + 967*x**2 + 190*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: (53*x + 19)*(6*x**3 + 23*x**2 + 10*x)
Expanding the part (53*x + 19) using the distributive property, and we got: (53*x)*(6*x**3 + 23*x**2 + 10*x) + 19*(6*x**3 + 23*x**2 + 10*x)
<replace-#Step 1>#Step 2:
Current expression: (53*x)*(6*x**3 + 23*x**2 + 10*x) + 19*(6*x**3 + 23*x**2 + 10*x)</replace>
Simplifying the partial expression: 19*(6*x**3 + 23*x**2 + 10*x)
Expanding the part (6*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*19 + (23*x**2)*19 + (6*x**3)*19
Replacing 19*(6*x**3 + 23*x**2 + 10*x) with (10*x)*19 + (23*x**2)*19 + (6*x**3)*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (10*x)*19 + (53*x)*(6*x**3 + 23*x**2 + 10*x) + (23*x**2)*19 + (6*x**3)*19</replace>
Simplifying the partial expression: (53*x)*(6*x**3 + 23*x**2 + 10*x)
Expanding the part (6*x**3 + 23*x**2 + 10*x) using the distributive property, and we got: (10*x)*(53*x) + (53*x)*(23*x**2) + (53*x)*(6*x**3)
Replacing (53*x)*(6*x**3 + 23*x**2 + 10*x) with (10*x)*(53*x) + (53*x)*(23*x**2) + (53*x)*(6*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (10*x)*(53*x) + (10*x)*19 + (53*x)*(23*x**2) + (53*x)*(6*x**3) + (23*x**2)*19 + (6*x**3)*19</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (6*x**3)*19 = 114*x**3
  (6*x**3)*(53*x) = 318*x**4
  (10*x)*19 = 190*x
  (10*x)*(53*x) = 530*x**2
  (23*x**2)*19 = 437*x**2
  (23*x**2)*(53*x) = 1219*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 318*x**4 + 114*x**3 + 1219*x**3 + 437*x**2 + 530*x**2 + 190*x</replace>
Combining like terms, got 318*x**4 + 1333*x**3 + 967*x**2 + 190*x
<replace-#Step 5>#Step 6:
Current expression: 318*x**4 + 1333*x**3 + 967*x**2 + 190*x</replace>
No more calculations needed.
<answer>318*x**4 + 1333*x**3 + 967*x**2 + 190*x</answer>


Question:
Calculate the following: (-49*x**3 - 4*x**2 - 46*x)*(-43*x**3 + 29*x**2 - 23*x - 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: 2107*x**6 - 1249*x**5 + 2989*x**4 + 1012*x**3 + 1242*x**2 + 2116*x


Question:
Calculate the following: (-29*z**3 + 25*z**2)*(25*z**3 + 18*z**2 - 42*z + 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -725*z**6 + 103*z**5 + 1668*z**4 - 1253*z**3 + 175*z**2


Question:
Calculate the following: (40*z**3 + 62*z)*(-47*z**3 - 21*z**2 - 9*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1880*z**6 - 840*z**5 - 3274*z**4 - 1302*z**3 - 558*z**2


Question:
Calculate the following: 14*x*(35*x**2 + 30*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 490*x**3 + 420*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: 14*x*(35*x**2 + 30*x)
Expanding the part (35*x**2 + 30*x) using the distributive property, and we got: (14*x)*(30*x) + (14*x)*(35*x**2)
<replace-#Step 1>#Step 2:
Current expression: (14*x)*(30*x) + (14*x)*(35*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (30*x)*(14*x) = 420*x**2
  (35*x**2)*(14*x) = 490*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 490*x**3 + 420*x**2</replace>
No more calculations needed.
<answer>490*x**3 + 420*x**2</answer>


Question:
Simplify this expression: (2*z**3 + 42)*(37*z**3 - 41)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 74*z**6 + 1472*z**3 - 1722

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (2*z**3 + 42)*(37*z**3 - 41)
Expanding the part (37*z**3 - 41) using the distributive property, and we got: (37*z**3)*(2*z**3 + 42) - 41*(2*z**3 + 42)
<replace-#Step 1>#Step 2:
Current expression: (37*z**3)*(2*z**3 + 42) - 41*(2*z**3 + 42)</replace>
Simplifying the partial expression: -41*(2*z**3 + 42)
Expanding the part (2*z**3 + 42) using the distributive property, and we got: (2*z**3)*(-41) + 42*(-41)
Replacing -41*(2*z**3 + 42) with (2*z**3)*(-41) + 42*(-41) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (2*z**3)*(-41) + (37*z**3)*(2*z**3 + 42) - 1722</replace>
Simplifying the partial expression: (37*z**3)*(2*z**3 + 42)
Expanding the part (2*z**3 + 42) using the distributive property, and we got: 42*(37*z**3) + (2*z**3)*(37*z**3)
Replacing (37*z**3)*(2*z**3 + 42) with 42*(37*z**3) + (2*z**3)*(37*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 42*37*z**3 + (2*z**3)*(37*z**3) + (2*z**3)*(-41) - 1722</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*z**3)*-41 = -82*z**3
  (2*z**3)*(37*z**3) = 74*z**6
  42*37*z**3 = 1554*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 74*z**6 - 82*z**3 + 1554*z**3 - 1722</replace>
Combining like terms, got 74*z**6 + 1472*z**3 - 1722
<replace-#Step 5>#Step 6:
Current expression: 74*z**6 + 1472*z**3 - 1722</replace>
No more calculations needed.
<answer>74*z**6 + 1472*z**3 - 1722</answer>


Question:
Calculate the following: 33*z**3*(28*z**3 - 47*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: 924*z**6 - 1551*z**5 + 693*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: 33*z**3*(28*z**3 - 47*z**2 + 21*z)
Expanding the part (28*z**3 - 47*z**2 + 21*z) using the distributive property, and we got: (21*z)*(33*z**3) + (-47*z**2)*(33*z**3) + (28*z**3)*(33*z**3)
<replace-#Step 1>#Step 2:
Current expression: (21*z)*(33*z**3) + (-47*z**2)*(33*z**3) + (28*z**3)*(33*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*z**2)*(33*z**3) = -1551*z**5
  (21*z)*(33*z**3) = 693*z**4
  (28*z**3)*(33*z**3) = 924*z**6
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 924*z**6 - 1551*z**5 + 693*z**4</replace>
No more calculations needed.
<answer>924*z**6 - 1551*z**5 + 693*z**4</answer>


Question:
Simplify this expression: 2120*x**4
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2120*x**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 2120*x**4
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: 2120*x**4</replace>
No more calculations needed.
<answer>2120*x**4</answer>


Question:
Simplify this expression: (13*z**3 - 36*z)*(13*z**3 - 30*z + 42)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*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: (13*z**3 - 36*z)*(13*z**3 - 30*z + 42)
Expanding the part (13*z**3 - 36*z) using the distributive property, and we got: (-36*z)*(13*z**3 - 30*z + 42) + (13*z**3)*(13*z**3 - 30*z + 42)
<replace-#Step 1>#Step 2:
Current expression: (-36*z)*(13*z**3 - 30*z + 42) + (13*z**3)*(13*z**3 - 30*z + 42)</replace>
Simplifying the partial expression: (-36*z)*(13*z**3 - 30*z + 42)
Expanding the part (13*z**3 - 30*z + 42) using the distributive property, and we got: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36*z)
Replacing (-36*z)*(13*z**3 - 30*z + 42) with (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36*z) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + 42*(-36)*z + (13*z**3)*(13*z**3 - 30*z + 42)</replace>
Simplifying the partial expression: (13*z**3)*(13*z**3 - 30*z + 42)
Expanding the part (13*z**3 - 30*z + 42) using the distributive property, and we got: (-30*z)*(13*z**3) + 42*(13*z**3) + (13*z**3)*(13*z**3)
Replacing (13*z**3)*(13*z**3 - 30*z + 42) with (-30*z)*(13*z**3) + 42*(13*z**3) + (13*z**3)*(13*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*z)*(-30*z) + (-36*z)*(13*z**3) + (-30*z)*(13*z**3) + 42*13*z**3 + 42*(-36)*z + (13*z**3)*(13*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z)*(-36*z) = 1080*z**2
  (-30*z)*(13*z**3) = -390*z**4
  (13*z**3)*(-36*z) = -468*z**4
  (13*z**3)*(13*z**3) = 169*z**6
  42*-36*z = -1512*z
  42*13*z**3 = 546*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 169*z**6 - 468*z**4 - 390*z**4 + 546*z**3 + 1080*z**2 - 1512*z</replace>
Combining like terms, got 169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z
<replace-#Step 5>#Step 6:
Current expression: 169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z</replace>
No more calculations needed.
<answer>169*z**6 - 858*z**4 + 546*z**3 + 1080*z**2 - 1512*z</answer>


Question:
Calculate the following: (68*x + 6)*(47*x**2 - 37*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3196*x**3 - 2234*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: (68*x + 6)*(47*x**2 - 37*x)
Expanding the part (68*x + 6) using the distributive property, and we got: (68*x)*(47*x**2 - 37*x) + 6*(47*x**2 - 37*x)
<replace-#Step 1>#Step 2:
Current expression: (68*x)*(47*x**2 - 37*x) + 6*(47*x**2 - 37*x)</replace>
Simplifying the partial expression: 6*(47*x**2 - 37*x)
Expanding the part (47*x**2 - 37*x) using the distributive property, and we got: -37*x*6 + (47*x**2)*6
Replacing 6*(47*x**2 - 37*x) with -37*x*6 + (47*x**2)*6 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -37*x*6 + (68*x)*(47*x**2 - 37*x) + (47*x**2)*6</replace>
Simplifying the partial expression: (68*x)*(47*x**2 - 37*x)
Expanding the part (47*x**2 - 37*x) using the distributive property, and we got: (-37*x)*(68*x) + (68*x)*(47*x**2)
Replacing (68*x)*(47*x**2 - 37*x) with (-37*x)*(68*x) + (68*x)*(47*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*x)*(68*x) - 37*x*6 + (68*x)*(47*x**2) + (47*x**2)*6</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*x)*6 = -222*x
  (-37*x)*(68*x) = -2516*x**2
  (47*x**2)*6 = 282*x**2
  (47*x**2)*(68*x) = 3196*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 3196*x**3 - 2516*x**2 + 282*x**2 - 222*x</replace>
Combining like terms, got 3196*x**3 - 2234*x**2 - 222*x
<replace-#Step 5>#Step 6:
Current expression: 3196*x**3 - 2234*x**2 - 222*x</replace>
No more calculations needed.
<answer>3196*x**3 - 2234*x**2 - 222*x</answer>


Question:
Calculate the following: (34*x**3 - 5*x**2 - 23*x)*(40*x**3 + 29*x - 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1360*x**6 - 200*x**5 + 66*x**4 - 349*x**3 - 637*x**2 + 138*x


Question:
Calculate the following: (18*z**2 - 16*z)*(-33*z**3 + 52*z**2 - 23*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: -594*z**5 + 1464*z**4 - 1246*z**3 + 368*z**2


Question:
Simplify this expression: (-11*z**3 + 38*z)*(42*z**2 - 7*z + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*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: (-11*z**3 + 38*z)*(42*z**2 - 7*z + 45)
Expanding the part (-11*z**3 + 38*z) using the distributive property, and we got: (38*z)*(42*z**2 - 7*z + 45) + (-11*z**3)*(42*z**2 - 7*z + 45)
<replace-#Step 1>#Step 2:
Current expression: (38*z)*(42*z**2 - 7*z + 45) + (-11*z**3)*(42*z**2 - 7*z + 45)</replace>
Simplifying the partial expression: (-11*z**3)*(42*z**2 - 7*z + 45)
Expanding the part (42*z**2 - 7*z + 45) using the distributive property, and we got: (-7*z)*(-11*z**3) + 45*(-11*z**3) + (42*z**2)*(-11*z**3)
Replacing (-11*z**3)*(42*z**2 - 7*z + 45) with (-7*z)*(-11*z**3) + 45*(-11*z**3) + (42*z**2)*(-11*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-7*z)*(-11*z**3) + 45*(-11)*z**3 + (38*z)*(42*z**2 - 7*z + 45) + (42*z**2)*(-11*z**3)</replace>
Simplifying the partial expression: (38*z)*(42*z**2 - 7*z + 45)
Expanding the part (42*z**2 - 7*z + 45) using the distributive property, and we got: (-7*z)*(38*z) + 45*(38*z) + (38*z)*(42*z**2)
Replacing (38*z)*(42*z**2 - 7*z + 45) with (-7*z)*(38*z) + 45*(38*z) + (38*z)*(42*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-7*z)*(38*z) + (-7*z)*(-11*z**3) + 45*(-11)*z**3 + 45*38*z + (38*z)*(42*z**2) + (42*z**2)*(-11*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-7*z)*(-11*z**3) = 77*z**4
  (-7*z)*(38*z) = -266*z**2
  (42*z**2)*(-11*z**3) = -462*z**5
  (42*z**2)*(38*z) = 1596*z**3
  45*-11*z**3 = -495*z**3
  45*38*z = 1710*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -462*z**5 + 77*z**4 - 495*z**3 + 1596*z**3 - 266*z**2 + 1710*z</replace>
Combining like terms, got -462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z
<replace-#Step 5>#Step 6:
Current expression: -462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z</replace>
No more calculations needed.
<answer>-462*z**5 + 77*z**4 + 1101*z**3 - 266*z**2 + 1710*z</answer>


Question:
Calculate the following: (41*z**2 + 59)*(15*z**2 - 37*z - 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832

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 + 59)*(15*z**2 - 37*z - 48)
Expanding the part (41*z**2 + 59) using the distributive property, and we got: (41*z**2)*(15*z**2 - 37*z - 48) + 59*(15*z**2 - 37*z - 48)
<replace-#Step 1>#Step 2:
Current expression: (41*z**2)*(15*z**2 - 37*z - 48) + 59*(15*z**2 - 37*z - 48)</replace>
Simplifying the partial expression: 59*(15*z**2 - 37*z - 48)
Expanding the part (15*z**2 - 37*z - 48) using the distributive property, and we got: -37*z*59 + (15*z**2)*59 - 48*59
Replacing 59*(15*z**2 - 37*z - 48) with -37*z*59 + (15*z**2)*59 - 48*59 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -37*z*59 + (15*z**2)*59 + (41*z**2)*(15*z**2 - 37*z - 48) - 2832</replace>
Simplifying the partial expression: (41*z**2)*(15*z**2 - 37*z - 48)
Expanding the part (15*z**2 - 37*z - 48) using the distributive property, and we got: (-37*z)*(41*z**2) - 1968*z**2 + (15*z**2)*(41*z**2)
Replacing (41*z**2)*(15*z**2 - 37*z - 48) with (-37*z)*(41*z**2) - 1968*z**2 + (15*z**2)*(41*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*z)*(41*z**2) - 37*z*59 - 48*41*z**2 + (15*z**2)*(41*z**2) + (15*z**2)*59 - 2832</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*z)*59 = -2183*z
  (-37*z)*(41*z**2) = -1517*z**3
  (15*z**2)*59 = 885*z**2
  (15*z**2)*(41*z**2) = 615*z**4
  -48*41*z**2 = -1968*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 615*z**4 - 1517*z**3 - 1968*z**2 + 885*z**2 - 2183*z - 2832</replace>
Combining like terms, got 615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832
<replace-#Step 5>#Step 6:
Current expression: 615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832</replace>
No more calculations needed.
<answer>615*z**4 - 1517*z**3 - 1083*z**2 - 2183*z - 2832</answer>


Question:
Simplify this expression: -87*z**2*(31*z**3 - 70*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: -2697*z**5 + 6090*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: -87*z**2*(31*z**3 - 70*z)
Expanding the part (31*z**3 - 70*z) using the distributive property, and we got: (-70*z)*(-87*z**2) + (-87*z**2)*(31*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-70*z)*(-87*z**2) + (-87*z**2)*(31*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-70*z)*(-87*z**2) = 6090*z**3
  (31*z**3)*(-87*z**2) = -2697*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2697*z**5 + 6090*z**3</replace>
No more calculations needed.
<answer>-2697*z**5 + 6090*z**3</answer>


Question:
Calculate the following: (-18*y**3 - 48)*(19*y**3 + 10*y**2 - 36*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -342*y**6 - 180*y**5 + 648*y**4 - 912*y**3 - 480*y**2 + 1728*y


Question:
Simplify this expression: (-47*x**3 + 47*x - 4)*(44*x**3 - 59*x**2 - 11*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2068*x**6 + 2773*x**5 + 2585*x**4 - 2949*x**3 - 281*x**2 + 44*x


Question:
Simplify this expression: (12*y**3 - 28)*(48*y**3 + 45*y**2 + 46*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: 576*y**6 + 540*y**5 + 552*y**4 - 1020*y**3 - 1260*y**2 - 1288*y - 756


Question:
Calculate the following: (28*y**2 - 34*y)*(41*y**2 - 37*y + 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: 1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*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: (28*y**2 - 34*y)*(41*y**2 - 37*y + 46)
Expanding the part (28*y**2 - 34*y) using the distributive property, and we got: (-34*y)*(41*y**2 - 37*y + 46) + (28*y**2)*(41*y**2 - 37*y + 46)
<replace-#Step 1>#Step 2:
Current expression: (-34*y)*(41*y**2 - 37*y + 46) + (28*y**2)*(41*y**2 - 37*y + 46)</replace>
Simplifying the partial expression: (-34*y)*(41*y**2 - 37*y + 46)
Expanding the part (41*y**2 - 37*y + 46) using the distributive property, and we got: (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34*y)
Replacing (-34*y)*(41*y**2 - 37*y + 46) with (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34*y) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*y)*(-34*y) + (-34*y)*(41*y**2) + 46*(-34)*y + (28*y**2)*(41*y**2 - 37*y + 46)</replace>
Simplifying the partial expression: (28*y**2)*(41*y**2 - 37*y + 46)
Expanding the part (41*y**2 - 37*y + 46) using the distributive property, and we got: (-37*y)*(28*y**2) + 46*(28*y**2) + (28*y**2)*(41*y**2)
Replacing (28*y**2)*(41*y**2 - 37*y + 46) with (-37*y)*(28*y**2) + 46*(28*y**2) + (28*y**2)*(41*y**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*y)*(-34*y) + (-37*y)*(28*y**2) + (-34*y)*(41*y**2) + 46*28*y**2 + 46*(-34)*y + (28*y**2)*(41*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-37*y)*(-34*y) = 1258*y**2
  (-37*y)*(28*y**2) = -1036*y**3
  (41*y**2)*(-34*y) = -1394*y**3
  (41*y**2)*(28*y**2) = 1148*y**4
  46*-34*y = -1564*y
  46*28*y**2 = 1288*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1148*y**4 - 1394*y**3 - 1036*y**3 + 1258*y**2 + 1288*y**2 - 1564*y</replace>
Combining like terms, got 1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y
<replace-#Step 5>#Step 6:
Current expression: 1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y</replace>
No more calculations needed.
<answer>1148*y**4 - 2430*y**3 + 2546*y**2 - 1564*y</answer>


Question:
Simplify this expression: (-36*z**2 - 30*z)*(-31*z**2 + 26*z + 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: 1116*z**4 - 6*z**3 - 1068*z**2 - 240*z


Question:
Calculate the following: (-46*z**2 + 2*z)*(41*z**2 - 36*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: -1886*z**4 + 1738*z**3 - 72*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-46*z**2 + 2*z)*(41*z**2 - 36*z)
Expanding the part (-46*z**2 + 2*z) using the distributive property, and we got: (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2 - 36*z)
<replace-#Step 1>#Step 2:
Current expression: (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2 - 36*z)</replace>
Simplifying the partial expression: (-46*z**2)*(41*z**2 - 36*z)
Expanding the part (41*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(-46*z**2) + (-46*z**2)*(41*z**2)
Replacing (-46*z**2)*(41*z**2 - 36*z) with (-36*z)*(-46*z**2) + (-46*z**2)*(41*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-36*z)*(-46*z**2) + (2*z)*(41*z**2 - 36*z) + (-46*z**2)*(41*z**2)</replace>
Simplifying the partial expression: (2*z)*(41*z**2 - 36*z)
Expanding the part (41*z**2 - 36*z) using the distributive property, and we got: (-36*z)*(2*z) + (2*z)*(41*z**2)
Replacing (2*z)*(41*z**2 - 36*z) with (-36*z)*(2*z) + (2*z)*(41*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*z)*(2*z) + (-36*z)*(-46*z**2) + (2*z)*(41*z**2) + (-46*z**2)*(41*z**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*z)*(-46*z**2) = 1656*z**3
  (-36*z)*(2*z) = -72*z**2
  (41*z**2)*(-46*z**2) = -1886*z**4
  (41*z**2)*(2*z) = 82*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1886*z**4 + 82*z**3 + 1656*z**3 - 72*z**2</replace>
Combining like terms, got -1886*z**4 + 1738*z**3 - 72*z**2
<replace-#Step 5>#Step 6:
Current expression: -1886*z**4 + 1738*z**3 - 72*z**2</replace>
No more calculations needed.
<answer>-1886*z**4 + 1738*z**3 - 72*z**2</answer>


Question:
Simplify this expression: (42 - 38*x**2)*(-12*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: 456*x**5 - 1150*x**3 + 714*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: (42 - 38*x**2)*(-12*x**3 + 17*x)
Expanding the part (42 - 38*x**2) using the distributive property, and we got: (-38*x**2)*(-12*x**3 + 17*x) + 42*(-12*x**3 + 17*x)
<replace-#Step 1>#Step 2:
Current expression: (-38*x**2)*(-12*x**3 + 17*x) + 42*(-12*x**3 + 17*x)</replace>
Simplifying the partial expression: 42*(-12*x**3 + 17*x)
Expanding the part (-12*x**3 + 17*x) using the distributive property, and we got: (17*x)*42 - 12*x**3*42
Replacing 42*(-12*x**3 + 17*x) with (17*x)*42 - 12*x**3*42 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (17*x)*42 + (-38*x**2)*(-12*x**3 + 17*x) - 12*x**3*42</replace>
Simplifying the partial expression: (-38*x**2)*(-12*x**3 + 17*x)
Expanding the part (-12*x**3 + 17*x) using the distributive property, and we got: (17*x)*(-38*x**2) + (-38*x**2)*(-12*x**3)
Replacing (-38*x**2)*(-12*x**3 + 17*x) with (17*x)*(-38*x**2) + (-38*x**2)*(-12*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (17*x)*(-38*x**2) + (17*x)*42 + (-38*x**2)*(-12*x**3) - 12*x**3*42</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-12*x**3)*42 = -504*x**3
  (-12*x**3)*(-38*x**2) = 456*x**5
  (17*x)*42 = 714*x
  (17*x)*(-38*x**2) = -646*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 456*x**5 - 646*x**3 - 504*x**3 + 714*x</replace>
Combining like terms, got 456*x**5 - 1150*x**3 + 714*x
<replace-#Step 5>#Step 6:
Current expression: 456*x**5 - 1150*x**3 + 714*x</replace>
No more calculations needed.
<answer>456*x**5 - 1150*x**3 + 714*x</answer>


Question:
Simplify this expression: (-24*z - 40)*(14*z**3 + 49*z**2 - 23*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: -336*z**4 - 1736*z**3 - 1408*z**2 + 920*z


Question:
Simplify this expression: 355 - 85*y**2
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 355 - 85*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 355 - 85*y**2
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:

Replacing them in the overall expression.
<replace-#Step 1>#Step 2:
Current expression: 355 - 85*y**2</replace>
No more calculations needed.
<answer>355 - 85*y**2</answer>


Question:
Calculate the following: (15*x + 25)*(17*x**2 + 25*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 255*x**3 + 800*x**2 + 625*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 + 25)*(17*x**2 + 25*x)
Expanding the part (15*x + 25) using the distributive property, and we got: (15*x)*(17*x**2 + 25*x) + 25*(17*x**2 + 25*x)
<replace-#Step 1>#Step 2:
Current expression: (15*x)*(17*x**2 + 25*x) + 25*(17*x**2 + 25*x)</replace>
Simplifying the partial expression: 25*(17*x**2 + 25*x)
Expanding the part (17*x**2 + 25*x) using the distributive property, and we got: (25*x)*25 + (17*x**2)*25
Replacing 25*(17*x**2 + 25*x) with (25*x)*25 + (17*x**2)*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (15*x)*(17*x**2 + 25*x) + (25*x)*25 + (17*x**2)*25</replace>
Simplifying the partial expression: (15*x)*(17*x**2 + 25*x)
Expanding the part (17*x**2 + 25*x) using the distributive property, and we got: (15*x)*(25*x) + (15*x)*(17*x**2)
Replacing (15*x)*(17*x**2 + 25*x) with (15*x)*(25*x) + (15*x)*(17*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (15*x)*(25*x) + (15*x)*(17*x**2) + (25*x)*25 + (17*x**2)*25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (17*x**2)*25 = 425*x**2
  (17*x**2)*(15*x) = 255*x**3
  (25*x)*25 = 625*x
  (25*x)*(15*x) = 375*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 255*x**3 + 375*x**2 + 425*x**2 + 625*x</replace>
Combining like terms, got 255*x**3 + 800*x**2 + 625*x
<replace-#Step 5>#Step 6:
Current expression: 255*x**3 + 800*x**2 + 625*x</replace>
No more calculations needed.
<answer>255*x**3 + 800*x**2 + 625*x</answer>


Question:
Calculate the following: -10*x**2*(15*x**3 + 46*x**2 - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -150*x**5 - 460*x**4 + 310*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: -10*x**2*(15*x**3 + 46*x**2 - 31)
Expanding the part (15*x**3 + 46*x**2 - 31) using the distributive property, and we got: -(-1)*310*x**2 + (-10*x**2)*(46*x**2) + (-10*x**2)*(15*x**3)
<replace-#Step 1>#Step 2:
Current expression: -(-1)*310*x**2 + (-10*x**2)*(46*x**2) + (-10*x**2)*(15*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -31*(-10*x**2) = 310*x**2
  (15*x**3)*(-10*x**2) = -150*x**5
  (46*x**2)*(-10*x**2) = -460*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -150*x**5 - 460*x**4 + 310*x**2</replace>
No more calculations needed.
<answer>-150*x**5 - 460*x**4 + 310*x**2</answer>


Question:
Calculate the following: (6*z + 40)*(-30*z**3 + 26*z + 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760

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 + 40)*(-30*z**3 + 26*z + 44)
Expanding the part (6*z + 40) using the distributive property, and we got: (6*z)*(-30*z**3 + 26*z + 44) + 40*(-30*z**3 + 26*z + 44)
<replace-#Step 1>#Step 2:
Current expression: (6*z)*(-30*z**3 + 26*z + 44) + 40*(-30*z**3 + 26*z + 44)</replace>
Simplifying the partial expression: 40*(-30*z**3 + 26*z + 44)
Expanding the part (-30*z**3 + 26*z + 44) using the distributive property, and we got: (26*z)*40 - 30*z**3*40 + 44*40
Replacing 40*(-30*z**3 + 26*z + 44) with (26*z)*40 - 30*z**3*40 + 44*40 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (6*z)*(-30*z**3 + 26*z + 44) + (26*z)*40 - 30*z**3*40 + 1760</replace>
Simplifying the partial expression: (6*z)*(-30*z**3 + 26*z + 44)
Expanding the part (-30*z**3 + 26*z + 44) using the distributive property, and we got: 44*(6*z) + (6*z)*(26*z) + (6*z)*(-30*z**3)
Replacing (6*z)*(-30*z**3 + 26*z + 44) with 44*(6*z) + (6*z)*(26*z) + (6*z)*(-30*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 44*6*z + (6*z)*(26*z) + (6*z)*(-30*z**3) + (26*z)*40 - 30*z**3*40 + 1760</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-30*z**3)*40 = -1200*z**3
  (-30*z**3)*(6*z) = -180*z**4
  (26*z)*40 = 1040*z
  (26*z)*(6*z) = 156*z**2
  44*6*z = 264*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -180*z**4 - 1200*z**3 + 156*z**2 + 264*z + 1040*z + 1760</replace>
Combining like terms, got -180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760
<replace-#Step 5>#Step 6:
Current expression: -180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760</replace>
No more calculations needed.
<answer>-180*z**4 - 1200*z**3 + 156*z**2 + 1304*z + 1760</answer>


Question:
Calculate the following: 26*x*(3*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: 78*x**4 + 234*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: 26*x*(3*x**3 + 9*x)
Expanding the part (3*x**3 + 9*x) using the distributive property, and we got: (9*x)*(26*x) + (26*x)*(3*x**3)
<replace-#Step 1>#Step 2:
Current expression: (9*x)*(26*x) + (26*x)*(3*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*x**3)*(26*x) = 78*x**4
  (9*x)*(26*x) = 234*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 78*x**4 + 234*x**2</replace>
No more calculations needed.
<answer>78*x**4 + 234*x**2</answer>


Question:
Simplify this expression: (-3*z**2 - 23*z)*(6*z**3 - 14*z**2 - 45*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: -18*z**5 - 96*z**4 + 457*z**3 + 1035*z**2


Question:
Simplify this expression: (50*z**2 + 9*z)*(9*z**3 + 40*z**2 - 11*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: 450*z**5 + 2081*z**4 - 190*z**3 - 99*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: (50*z**2 + 9*z)*(9*z**3 + 40*z**2 - 11*z)
Expanding the part (50*z**2 + 9*z) using the distributive property, and we got: (9*z)*(9*z**3 + 40*z**2 - 11*z) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)
<replace-#Step 1>#Step 2:
Current expression: (9*z)*(9*z**3 + 40*z**2 - 11*z) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)</replace>
Simplifying the partial expression: (9*z)*(9*z**3 + 40*z**2 - 11*z)
Expanding the part (9*z**3 + 40*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3)
Replacing (9*z)*(9*z**3 + 40*z**2 - 11*z) with (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-11*z)*(9*z) + (9*z)*(40*z**2) + (9*z)*(9*z**3) + (50*z**2)*(9*z**3 + 40*z**2 - 11*z)</replace>
Simplifying the partial expression: (50*z**2)*(9*z**3 + 40*z**2 - 11*z)
Expanding the part (9*z**3 + 40*z**2 - 11*z) using the distributive property, and we got: (-11*z)*(50*z**2) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3)
Replacing (50*z**2)*(9*z**3 + 40*z**2 - 11*z) with (-11*z)*(50*z**2) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-11*z)*(9*z) + (-11*z)*(50*z**2) + (9*z)*(40*z**2) + (9*z)*(9*z**3) + (40*z**2)*(50*z**2) + (50*z**2)*(9*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-11*z)*(9*z) = -99*z**2
  (-11*z)*(50*z**2) = -550*z**3
  (9*z**3)*(9*z) = 81*z**4
  (9*z**3)*(50*z**2) = 450*z**5
  (40*z**2)*(9*z) = 360*z**3
  (40*z**2)*(50*z**2) = 2000*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 450*z**5 + 81*z**4 + 2000*z**4 - 550*z**3 + 360*z**3 - 99*z**2</replace>
Combining like terms, got 450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2
<replace-#Step 5>#Step 6:
Current expression: 450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2</replace>
No more calculations needed.
<answer>450*z**5 + 2081*z**4 - 190*z**3 - 99*z**2</answer>


Question:
Calculate the following: -2190*y**2 + 2263*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: -2190*y**2 + 2263*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: -2190*y**2 + 2263*y
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: -2190*y**2 + 2263*y</replace>
No more calculations needed.
<answer>-2190*y**2 + 2263*y</answer>


Question:
Simplify this expression: (13*z**2 + 11*z)*(-38*z**3 - 50*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: -494*z**5 - 1068*z**4 - 550*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: (13*z**2 + 11*z)*(-38*z**3 - 50*z**2)
Expanding the part (-38*z**3 - 50*z**2) using the distributive property, and we got: (-50*z**2)*(13*z**2 + 11*z) + (-38*z**3)*(13*z**2 + 11*z)
<replace-#Step 1>#Step 2:
Current expression: (-50*z**2)*(13*z**2 + 11*z) + (-38*z**3)*(13*z**2 + 11*z)</replace>
Simplifying the partial expression: (-50*z**2)*(13*z**2 + 11*z)
Expanding the part (13*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2)
Replacing (-50*z**2)*(13*z**2 + 11*z) with (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (11*z)*(-50*z**2) + (-50*z**2)*(13*z**2) + (-38*z**3)*(13*z**2 + 11*z)</replace>
Simplifying the partial expression: (-38*z**3)*(13*z**2 + 11*z)
Expanding the part (13*z**2 + 11*z) using the distributive property, and we got: (11*z)*(-38*z**3) + (13*z**2)*(-38*z**3)
Replacing (-38*z**3)*(13*z**2 + 11*z) with (11*z)*(-38*z**3) + (13*z**2)*(-38*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (11*z)*(-50*z**2) + (11*z)*(-38*z**3) + (-50*z**2)*(13*z**2) + (13*z**2)*(-38*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (11*z)*(-50*z**2) = -550*z**3
  (11*z)*(-38*z**3) = -418*z**4
  (13*z**2)*(-50*z**2) = -650*z**4
  (13*z**2)*(-38*z**3) = -494*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -494*z**5 - 650*z**4 - 418*z**4 - 550*z**3</replace>
Combining like terms, got -494*z**5 - 1068*z**4 - 550*z**3
<replace-#Step 5>#Step 6:
Current expression: -494*z**5 - 1068*z**4 - 550*z**3</replace>
No more calculations needed.
<answer>-494*z**5 - 1068*z**4 - 550*z**3</answer>


Question:
Calculate the following: (50*y**2 - 9)*(27*y**3 + 9*y**2 + 37)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (50*y**2 - 9)*(27*y**3 + 9*y**2 + 37)
Expanding the part (50*y**2 - 9) using the distributive property, and we got: (50*y**2)*(27*y**3 + 9*y**2 + 37) - 9*(27*y**3 + 9*y**2 + 37)
<replace-#Step 1>#Step 2:
Current expression: (50*y**2)*(27*y**3 + 9*y**2 + 37) - 9*(27*y**3 + 9*y**2 + 37)</replace>
Simplifying the partial expression: -9*(27*y**3 + 9*y**2 + 37)
Expanding the part (27*y**3 + 9*y**2 + 37) using the distributive property, and we got: (9*y**2)*(-9) + (27*y**3)*(-9) + 37*(-9)
Replacing -9*(27*y**3 + 9*y**2 + 37) with (9*y**2)*(-9) + (27*y**3)*(-9) + 37*(-9) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (9*y**2)*(-9) + (50*y**2)*(27*y**3 + 9*y**2 + 37) + (27*y**3)*(-9) - 333</replace>
Simplifying the partial expression: (50*y**2)*(27*y**3 + 9*y**2 + 37)
Expanding the part (27*y**3 + 9*y**2 + 37) using the distributive property, and we got: 37*(50*y**2) + (9*y**2)*(50*y**2) + (50*y**2)*(27*y**3)
Replacing (50*y**2)*(27*y**3 + 9*y**2 + 37) with 37*(50*y**2) + (9*y**2)*(50*y**2) + (50*y**2)*(27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 37*50*y**2 + (9*y**2)*(50*y**2) + (9*y**2)*(-9) + (50*y**2)*(27*y**3) + (27*y**3)*(-9) - 333</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (9*y**2)*-9 = -81*y**2
  (9*y**2)*(50*y**2) = 450*y**4
  (27*y**3)*-9 = -243*y**3
  (27*y**3)*(50*y**2) = 1350*y**5
  37*50*y**2 = 1850*y**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1350*y**5 + 450*y**4 - 243*y**3 - 81*y**2 + 1850*y**2 - 333</replace>
Combining like terms, got 1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333
<replace-#Step 5>#Step 6:
Current expression: 1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333</replace>
No more calculations needed.
<answer>1350*y**5 + 450*y**4 - 243*y**3 + 1769*y**2 - 333</answer>


Question:
Calculate the following: (67*y**2 - 13)*(-26*y**3 - 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: -1742*y**5 + 338*y**3 - 3283*y**2 + 637

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: (67*y**2 - 13)*(-26*y**3 - 49)
Expanding the part (-26*y**3 - 49) using the distributive property, and we got: (-26*y**3)*(67*y**2 - 13) - 49*(67*y**2 - 13)
<replace-#Step 1>#Step 2:
Current expression: (-26*y**3)*(67*y**2 - 13) - 49*(67*y**2 - 13)</replace>
Simplifying the partial expression: -49*(67*y**2 - 13)
Expanding the part (67*y**2 - 13) using the distributive property, and we got: (67*y**2)*(-49) - 13*(-49)
Replacing -49*(67*y**2 - 13) with (67*y**2)*(-49) - 13*(-49) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (67*y**2)*(-49) + (-26*y**3)*(67*y**2 - 13) + 637</replace>
Simplifying the partial expression: (-26*y**3)*(67*y**2 - 13)
Expanding the part (67*y**2 - 13) using the distributive property, and we got: -(-1)*338*y**3 + (67*y**2)*(-26*y**3)
Replacing (-26*y**3)*(67*y**2 - 13) with -(-1)*338*y**3 + (67*y**2)*(-26*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -13*(-26)*y**3 + (67*y**2)*(-26*y**3) + (67*y**2)*(-49) + 637</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (67*y**2)*-49 = -3283*y**2
  (67*y**2)*(-26*y**3) = -1742*y**5
  -13*-26*y**3 = 338*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1742*y**5 + 338*y**3 - 3283*y**2 + 637</replace>
No more calculations needed.
<answer>-1742*y**5 + 338*y**3 - 3283*y**2 + 637</answer>


Question:
Simplify this expression: (y + 10)*(-38*y**3 - 11*y**2 - 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: -38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (y + 10)*(-38*y**3 - 11*y**2 - 46)
Expanding the part (y + 10) using the distributive property, and we got: y*(-38*y**3 - 11*y**2 - 46) + 10*(-38*y**3 - 11*y**2 - 46)
<replace-#Step 1>#Step 2:
Current expression: y*(-38*y**3 - 11*y**2 - 46) + 10*(-38*y**3 - 11*y**2 - 46)</replace>
Simplifying the partial expression: 10*(-38*y**3 - 11*y**2 - 46)
Expanding the part (-38*y**3 - 11*y**2 - 46) using the distributive property, and we got: -11*y**2*10 - 38*y**3*10 - 46*10
Replacing 10*(-38*y**3 - 11*y**2 - 46) with -11*y**2*10 - 38*y**3*10 - 46*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: y*(-38*y**3 - 11*y**2 - 46) - 11*y**2*10 - 38*y**3*10 - 460</replace>
Simplifying the partial expression: y*(-38*y**3 - 11*y**2 - 46)
Expanding the part (-38*y**3 - 11*y**2 - 46) using the distributive property, and we got: y*(-11*y**2) + y*(-38*y**3) - 46*y
Replacing y*(-38*y**3 - 11*y**2 - 46) with y*(-11*y**2) + y*(-38*y**3) - 46*y in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: y*(-11*y**2) + y*(-38*y**3) - 46*y - 11*y**2*10 - 38*y**3*10 - 460</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-38*y**3)*10 = -380*y**3
  (-38*y**3)*y = -38*y**4
  (-11*y**2)*10 = -110*y**2
  (-11*y**2)*y = -11*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -38*y**4 - 380*y**3 - 11*y**3 - 110*y**2 - 46*y - 460</replace>
Combining like terms, got -38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460
<replace-#Step 5>#Step 6:
Current expression: -38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460</replace>
No more calculations needed.
<answer>-38*y**4 - 391*y**3 - 110*y**2 - 46*y - 460</answer>


Question:
Simplify this expression: -64*z*(-52*z**3 - 43*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: 3328*z**4 + 2752*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: -64*z*(-52*z**3 - 43*z**2)
Expanding the part (-52*z**3 - 43*z**2) using the distributive property, and we got: (-64*z)*(-43*z**2) + (-64*z)*(-52*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-64*z)*(-43*z**2) + (-64*z)*(-52*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-52*z**3)*(-64*z) = 3328*z**4
  (-43*z**2)*(-64*z) = 2752*z**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 3328*z**4 + 2752*z**3</replace>
No more calculations needed.
<answer>3328*z**4 + 2752*z**3</answer>


Question:
Calculate the following: (-47*y**3 + 49*y**2)*(-22*y**3 - 18*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1034*y**6 - 1078*y**5 + 846*y**4 - 882*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: (-47*y**3 + 49*y**2)*(-22*y**3 - 18*y)
Expanding the part (-47*y**3 + 49*y**2) using the distributive property, and we got: (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3 - 18*y)
<replace-#Step 1>#Step 2:
Current expression: (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3 - 18*y)</replace>
Simplifying the partial expression: (-47*y**3)*(-22*y**3 - 18*y)
Expanding the part (-22*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(-47*y**3) + (-47*y**3)*(-22*y**3)
Replacing (-47*y**3)*(-22*y**3 - 18*y) with (-18*y)*(-47*y**3) + (-47*y**3)*(-22*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-18*y)*(-47*y**3) + (49*y**2)*(-22*y**3 - 18*y) + (-47*y**3)*(-22*y**3)</replace>
Simplifying the partial expression: (49*y**2)*(-22*y**3 - 18*y)
Expanding the part (-22*y**3 - 18*y) using the distributive property, and we got: (-18*y)*(49*y**2) + (49*y**2)*(-22*y**3)
Replacing (49*y**2)*(-22*y**3 - 18*y) with (-18*y)*(49*y**2) + (49*y**2)*(-22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*y)*(49*y**2) + (-18*y)*(-47*y**3) + (49*y**2)*(-22*y**3) + (-47*y**3)*(-22*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y**3)*(-47*y**3) = 1034*y**6
  (-22*y**3)*(49*y**2) = -1078*y**5
  (-18*y)*(-47*y**3) = 846*y**4
  (-18*y)*(49*y**2) = -882*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3</replace>
No more calculations needed.
<answer>1034*y**6 - 1078*y**5 + 846*y**4 - 882*y**3</answer>


Question:
Calculate the following: z**2*(-5*z**3 - 24)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -5*z**5 - 24*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: z**2*(-5*z**3 - 24)
Expanding the part (-5*z**3 - 24) using the distributive property, and we got: z**2*(-5*z**3) - 24*z**2
<replace-#Step 1>#Step 2:
Current expression: z**2*(-5*z**3) - 24*z**2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-5*z**3)*z**2 = -5*z**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -5*z**5 - 24*z**2</replace>
No more calculations needed.
<answer>-5*z**5 - 24*z**2</answer>


Question:
Calculate the following: (81*z**3 + 26*z**2)*(14*z**3 + z**2 + 38*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: 1134*z**6 + 445*z**5 + 3104*z**4 + 988*z**3


Question:
Simplify this expression: (-7*y**3 - 51*y**2)*(31*y**3 + 38*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: -217*y**6 - 1581*y**5 - 266*y**4 - 1938*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: (-7*y**3 - 51*y**2)*(31*y**3 + 38*y)
Expanding the part (-7*y**3 - 51*y**2) using the distributive property, and we got: (-51*y**2)*(31*y**3 + 38*y) + (-7*y**3)*(31*y**3 + 38*y)
<replace-#Step 1>#Step 2:
Current expression: (-51*y**2)*(31*y**3 + 38*y) + (-7*y**3)*(31*y**3 + 38*y)</replace>
Simplifying the partial expression: (-51*y**2)*(31*y**3 + 38*y)
Expanding the part (31*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3)
Replacing (-51*y**2)*(31*y**3 + 38*y) with (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (38*y)*(-51*y**2) + (-51*y**2)*(31*y**3) + (-7*y**3)*(31*y**3 + 38*y)</replace>
Simplifying the partial expression: (-7*y**3)*(31*y**3 + 38*y)
Expanding the part (31*y**3 + 38*y) using the distributive property, and we got: (38*y)*(-7*y**3) + (-7*y**3)*(31*y**3)
Replacing (-7*y**3)*(31*y**3 + 38*y) with (38*y)*(-7*y**3) + (-7*y**3)*(31*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (38*y)*(-51*y**2) + (38*y)*(-7*y**3) + (-51*y**2)*(31*y**3) + (-7*y**3)*(31*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*y**3)*(-51*y**2) = -1581*y**5
  (31*y**3)*(-7*y**3) = -217*y**6
  (38*y)*(-51*y**2) = -1938*y**3
  (38*y)*(-7*y**3) = -266*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3</replace>
No more calculations needed.
<answer>-217*y**6 - 1581*y**5 - 266*y**4 - 1938*y**3</answer>


Question:
Calculate the following: (7*z**2 + 21)*(42*z**3 - 23*z**2 - 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: 294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (7*z**2 + 21)*(42*z**3 - 23*z**2 - 3)
Expanding the part (7*z**2 + 21) using the distributive property, and we got: (7*z**2)*(42*z**3 - 23*z**2 - 3) + 21*(42*z**3 - 23*z**2 - 3)
<replace-#Step 1>#Step 2:
Current expression: (7*z**2)*(42*z**3 - 23*z**2 - 3) + 21*(42*z**3 - 23*z**2 - 3)</replace>
Simplifying the partial expression: 21*(42*z**3 - 23*z**2 - 3)
Expanding the part (42*z**3 - 23*z**2 - 3) using the distributive property, and we got: -23*z**2*21 + (42*z**3)*21 - 3*21
Replacing 21*(42*z**3 - 23*z**2 - 3) with -23*z**2*21 + (42*z**3)*21 - 3*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -23*z**2*21 + (7*z**2)*(42*z**3 - 23*z**2 - 3) + (42*z**3)*21 - 63</replace>
Simplifying the partial expression: (7*z**2)*(42*z**3 - 23*z**2 - 3)
Expanding the part (42*z**3 - 23*z**2 - 3) using the distributive property, and we got: -21*z**2 + (-23*z**2)*(7*z**2) + (7*z**2)*(42*z**3)
Replacing (7*z**2)*(42*z**3 - 23*z**2 - 3) with -21*z**2 + (-23*z**2)*(7*z**2) + (7*z**2)*(42*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -3*7*z**2 + (-23*z**2)*(7*z**2) - 23*z**2*21 + (7*z**2)*(42*z**3) + (42*z**3)*21 - 63</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*z**2)*21 = -483*z**2
  (-23*z**2)*(7*z**2) = -161*z**4
  (42*z**3)*21 = 882*z**3
  (42*z**3)*(7*z**2) = 294*z**5
  -3*7*z**2 = -21*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 294*z**5 - 161*z**4 + 882*z**3 - 483*z**2 - 21*z**2 - 63</replace>
Combining like terms, got 294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63
<replace-#Step 5>#Step 6:
Current expression: 294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63</replace>
No more calculations needed.
<answer>294*z**5 - 161*z**4 + 882*z**3 - 504*z**2 - 63</answer>


Question:
Calculate the following: (-14*x**3 - 7*x**2)*(15*x**2 - 3*x + 9)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -210*x**5 - 63*x**4 - 105*x**3 - 63*x**2


Question:
Calculate the following: (6 - 88*y**2)*(-27*y**3 + 47*y**2 - 43*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 2376*y**5 - 4136*y**4 + 3622*y**3 + 282*y**2 - 258*y


Question:
Calculate the following: (-46*z**3 - 28*z)*(32*z**3 - 24*z**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: -1472*z**6 + 1104*z**5 - 896*z**4 + 2420*z**3 + 1064*z


Question:
Simplify this expression: (23*y**2 - 17)*(-18*y**3 - 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: -414*y**5 + 306*y**3 - 1081*y**2 + 799

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*y**2 - 17)*(-18*y**3 - 47)
Expanding the part (-18*y**3 - 47) using the distributive property, and we got: (-18*y**3)*(23*y**2 - 17) - 47*(23*y**2 - 17)
<replace-#Step 1>#Step 2:
Current expression: (-18*y**3)*(23*y**2 - 17) - 47*(23*y**2 - 17)</replace>
Simplifying the partial expression: -47*(23*y**2 - 17)
Expanding the part (23*y**2 - 17) using the distributive property, and we got: (23*y**2)*(-47) - 17*(-47)
Replacing -47*(23*y**2 - 17) with (23*y**2)*(-47) - 17*(-47) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (23*y**2)*(-47) + (-18*y**3)*(23*y**2 - 17) + 799</replace>
Simplifying the partial expression: (-18*y**3)*(23*y**2 - 17)
Expanding the part (23*y**2 - 17) using the distributive property, and we got: -(-1)*306*y**3 + (23*y**2)*(-18*y**3)
Replacing (-18*y**3)*(23*y**2 - 17) with -(-1)*306*y**3 + (23*y**2)*(-18*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -17*(-18)*y**3 + (23*y**2)*(-18*y**3) + (23*y**2)*(-47) + 799</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (23*y**2)*-47 = -1081*y**2
  (23*y**2)*(-18*y**3) = -414*y**5
  -17*-18*y**3 = 306*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -414*y**5 + 306*y**3 - 1081*y**2 + 799</replace>
No more calculations needed.
<answer>-414*y**5 + 306*y**3 - 1081*y**2 + 799</answer>


Question:
Simplify this expression: (-6*x**3 - 24*x)*(-41*x**3 + 21*x**2 - 29)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 246*x**6 - 126*x**5 + 984*x**4 - 330*x**3 + 696*x


Question:
Calculate the following: (-74*x - 17)*(-19*x**3 - 2*x**2 - 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: 1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731

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: (-74*x - 17)*(-19*x**3 - 2*x**2 - 43)
Expanding the part (-74*x - 17) using the distributive property, and we got: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 17*(-19*x**3 - 2*x**2 - 43)
<replace-#Step 1>#Step 2:
Current expression: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 17*(-19*x**3 - 2*x**2 - 43)</replace>
Simplifying the partial expression: -17*(-19*x**3 - 2*x**2 - 43)
Expanding the part (-19*x**3 - 2*x**2 - 43) using the distributive property, and we got: -2*x**2*(-17) - 19*x**3*(-17) - 43*(-17)
Replacing -17*(-19*x**3 - 2*x**2 - 43) with -2*x**2*(-17) - 19*x**3*(-17) - 43*(-17) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-74*x)*(-19*x**3 - 2*x**2 - 43) - 2*x**2*(-17) - 19*x**3*(-17) + 731</replace>
Simplifying the partial expression: (-74*x)*(-19*x**3 - 2*x**2 - 43)
Expanding the part (-19*x**3 - 2*x**2 - 43) using the distributive property, and we got: (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - (-1)*3182*x
Replacing (-74*x)*(-19*x**3 - 2*x**2 - 43) with (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - (-1)*3182*x in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-74*x)*(-2*x**2) + (-74*x)*(-19*x**3) - 43*(-74)*x - 2*x**2*(-17) - 19*x**3*(-17) + 731</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-19*x**3)*-17 = 323*x**3
  (-19*x**3)*(-74*x) = 1406*x**4
  (-2*x**2)*-17 = 34*x**2
  (-2*x**2)*(-74*x) = 148*x**3
  -43*-74*x = 3182*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1406*x**4 + 148*x**3 + 323*x**3 + 34*x**2 + 3182*x + 731</replace>
Combining like terms, got 1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731
<replace-#Step 5>#Step 6:
Current expression: 1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731</replace>
No more calculations needed.
<answer>1406*x**4 + 471*x**3 + 34*x**2 + 3182*x + 731</answer>


Question:
Calculate the following: -924*y - 880
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -924*y - 880

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: -924*y - 880
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: -924*y - 880</replace>
No more calculations needed.
<answer>-924*y - 880</answer>


Question:
Calculate the following: (-49*y**3 + 40*y**2)*(-38*y**3 - 47*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1862*y**6 + 783*y**5 - 1880*y**4

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-49*y**3 + 40*y**2)*(-38*y**3 - 47*y**2)
Expanding the part (-49*y**3 + 40*y**2) using the distributive property, and we got: (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3 - 47*y**2)
<replace-#Step 1>#Step 2:
Current expression: (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3 - 47*y**2)</replace>
Simplifying the partial expression: (-49*y**3)*(-38*y**3 - 47*y**2)
Expanding the part (-38*y**3 - 47*y**2) using the distributive property, and we got: (-47*y**2)*(-49*y**3) + (-49*y**3)*(-38*y**3)
Replacing (-49*y**3)*(-38*y**3 - 47*y**2) with (-47*y**2)*(-49*y**3) + (-49*y**3)*(-38*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-47*y**2)*(-49*y**3) + (40*y**2)*(-38*y**3 - 47*y**2) + (-49*y**3)*(-38*y**3)</replace>
Simplifying the partial expression: (40*y**2)*(-38*y**3 - 47*y**2)
Expanding the part (-38*y**3 - 47*y**2) using the distributive property, and we got: (-47*y**2)*(40*y**2) + (40*y**2)*(-38*y**3)
Replacing (40*y**2)*(-38*y**3 - 47*y**2) with (-47*y**2)*(40*y**2) + (40*y**2)*(-38*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-47*y**2)*(40*y**2) + (-47*y**2)*(-49*y**3) + (40*y**2)*(-38*y**3) + (-49*y**3)*(-38*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y**2)*(-49*y**3) = 2303*y**5
  (-47*y**2)*(40*y**2) = -1880*y**4
  (-38*y**3)*(-49*y**3) = 1862*y**6
  (-38*y**3)*(40*y**2) = -1520*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1862*y**6 - 1520*y**5 + 2303*y**5 - 1880*y**4</replace>
Combining like terms, got 1862*y**6 + 783*y**5 - 1880*y**4
<replace-#Step 5>#Step 6:
Current expression: 1862*y**6 + 783*y**5 - 1880*y**4</replace>
No more calculations needed.
<answer>1862*y**6 + 783*y**5 - 1880*y**4</answer>


Question:
Calculate the following: -62*x**2*(40*x**2 + 39*x + 45)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2480*x**4 - 2418*x**3 - 2790*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: -62*x**2*(40*x**2 + 39*x + 45)
Expanding the part (40*x**2 + 39*x + 45) using the distributive property, and we got: 45*(-62*x**2) + (39*x)*(-62*x**2) + (-62*x**2)*(40*x**2)
<replace-#Step 1>#Step 2:
Current expression: 45*(-62*x**2) + (39*x)*(-62*x**2) + (-62*x**2)*(40*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  45*(-62*x**2) = -2790*x**2
  (39*x)*(-62*x**2) = -2418*x**3
  (40*x**2)*(-62*x**2) = -2480*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2480*x**4 - 2418*x**3 - 2790*x**2</replace>
No more calculations needed.
<answer>-2480*x**4 - 2418*x**3 - 2790*x**2</answer>


Question:
Simplify this expression: 189*z**3 + 405*z**2 + 1026
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 189*z**3 + 405*z**2 + 1026

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: 189*z**3 + 405*z**2 + 1026
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: 189*z**3 + 405*z**2 + 1026</replace>
No more calculations needed.
<answer>189*z**3 + 405*z**2 + 1026</answer>


Question:
Simplify this expression: 96*x**2*(-25*x**3 - 37*x + 16)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -2400*x**5 - 3552*x**3 + 1536*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: 96*x**2*(-25*x**3 - 37*x + 16)
Expanding the part (-25*x**3 - 37*x + 16) using the distributive property, and we got: (-37*x)*(96*x**2) + 16*(96*x**2) + (96*x**2)*(-25*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-37*x)*(96*x**2) + 16*(96*x**2) + (96*x**2)*(-25*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  16*(96*x**2) = 1536*x**2
  (-37*x)*(96*x**2) = -3552*x**3
  (-25*x**3)*(96*x**2) = -2400*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -2400*x**5 - 3552*x**3 + 1536*x**2</replace>
No more calculations needed.
<answer>-2400*x**5 - 3552*x**3 + 1536*x**2</answer>


Question:
Simplify this expression: 5*x**2*(-22*x - 31)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -110*x**3 - 155*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: 5*x**2*(-22*x - 31)
Expanding the part (-22*x - 31) using the distributive property, and we got: (-22*x)*(5*x**2) - 155*x**2
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(5*x**2) - 155*x**2</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -31*(5*x**2) = -155*x**2
  (-22*x)*(5*x**2) = -110*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -110*x**3 - 155*x**2</replace>
No more calculations needed.
<answer>-110*x**3 - 155*x**2</answer>


Question:
Calculate the following: (-43*z**2 + 14*z)*(2*z**3 + 48*z - 51)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*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 + 14*z)*(2*z**3 + 48*z - 51)
Expanding the part (-43*z**2 + 14*z) using the distributive property, and we got: (14*z)*(2*z**3 + 48*z - 51) + (-43*z**2)*(2*z**3 + 48*z - 51)
<replace-#Step 1>#Step 2:
Current expression: (14*z)*(2*z**3 + 48*z - 51) + (-43*z**2)*(2*z**3 + 48*z - 51)</replace>
Simplifying the partial expression: (-43*z**2)*(2*z**3 + 48*z - 51)
Expanding the part (2*z**3 + 48*z - 51) using the distributive property, and we got: -(-1)*2193*z**2 + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)
Replacing (-43*z**2)*(2*z**3 + 48*z - 51) with -(-1)*2193*z**2 + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -51*(-43)*z**2 + (14*z)*(2*z**3 + 48*z - 51) + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)</replace>
Simplifying the partial expression: (14*z)*(2*z**3 + 48*z - 51)
Expanding the part (2*z**3 + 48*z - 51) using the distributive property, and we got: -714*z + (14*z)*(48*z) + (14*z)*(2*z**3)
Replacing (14*z)*(2*z**3 + 48*z - 51) with -714*z + (14*z)*(48*z) + (14*z)*(2*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -51*(-43)*z**2 - 51*14*z + (14*z)*(48*z) + (14*z)*(2*z**3) + (48*z)*(-43*z**2) + (-43*z**2)*(2*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (2*z**3)*(-43*z**2) = -86*z**5
  (2*z**3)*(14*z) = 28*z**4
  (48*z)*(-43*z**2) = -2064*z**3
  (48*z)*(14*z) = 672*z**2
  -51*-43*z**2 = 2193*z**2
  -51*14*z = -714*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -86*z**5 + 28*z**4 - 2064*z**3 + 672*z**2 + 2193*z**2 - 714*z</replace>
Combining like terms, got -86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z
<replace-#Step 5>#Step 6:
Current expression: -86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z</replace>
No more calculations needed.
<answer>-86*z**5 + 28*z**4 - 2064*z**3 + 2865*z**2 - 714*z</answer>


Question:
Calculate the following: (10*y**2 + 21)*(-22*y**3 - 20*y**2)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -220*y**5 - 200*y**4 - 462*y**3 - 420*y**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (10*y**2 + 21)*(-22*y**3 - 20*y**2)
Expanding the part (10*y**2 + 21) using the distributive property, and we got: (10*y**2)*(-22*y**3 - 20*y**2) + 21*(-22*y**3 - 20*y**2)
<replace-#Step 1>#Step 2:
Current expression: (10*y**2)*(-22*y**3 - 20*y**2) + 21*(-22*y**3 - 20*y**2)</replace>
Simplifying the partial expression: 21*(-22*y**3 - 20*y**2)
Expanding the part (-22*y**3 - 20*y**2) using the distributive property, and we got: -20*y**2*21 - 22*y**3*21
Replacing 21*(-22*y**3 - 20*y**2) with -20*y**2*21 - 22*y**3*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -20*y**2*21 + (10*y**2)*(-22*y**3 - 20*y**2) - 22*y**3*21</replace>
Simplifying the partial expression: (10*y**2)*(-22*y**3 - 20*y**2)
Expanding the part (-22*y**3 - 20*y**2) using the distributive property, and we got: (-20*y**2)*(10*y**2) + (10*y**2)*(-22*y**3)
Replacing (10*y**2)*(-22*y**3 - 20*y**2) with (-20*y**2)*(10*y**2) + (10*y**2)*(-22*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-20*y**2)*(10*y**2) - 20*y**2*21 + (10*y**2)*(-22*y**3) - 22*y**3*21</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*y**3)*21 = -462*y**3
  (-22*y**3)*(10*y**2) = -220*y**5
  (-20*y**2)*21 = -420*y**2
  (-20*y**2)*(10*y**2) = -200*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -220*y**5 - 200*y**4 - 462*y**3 - 420*y**2</replace>
No more calculations needed.
<answer>-220*y**5 - 200*y**4 - 462*y**3 - 420*y**2</answer>


Question:
Simplify this expression: (45 - 38*z**2)*(-16*z**3 - 79*z**2 - 24*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: 608*z**5 + 3002*z**4 + 192*z**3 - 3555*z**2 - 1080*z


Question:
Calculate the following: (-30*x**3 + 99*x**2)*(30*x**3 - 33*x**2 + 30*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -900*x**6 + 3960*x**5 - 4167*x**4 + 2970*x**3


Question:
Simplify this expression: (3 - 28*x**3)*(-39*x**3 + 48*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: 1092*x**6 - 1344*x**5 - 117*x**3 + 144*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: (3 - 28*x**3)*(-39*x**3 + 48*x**2)
Expanding the part (3 - 28*x**3) using the distributive property, and we got: (-28*x**3)*(-39*x**3 + 48*x**2) + 3*(-39*x**3 + 48*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-28*x**3)*(-39*x**3 + 48*x**2) + 3*(-39*x**3 + 48*x**2)</replace>
Simplifying the partial expression: 3*(-39*x**3 + 48*x**2)
Expanding the part (-39*x**3 + 48*x**2) using the distributive property, and we got: (48*x**2)*3 - 39*x**3*3
Replacing 3*(-39*x**3 + 48*x**2) with (48*x**2)*3 - 39*x**3*3 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (48*x**2)*3 - 39*x**3*3 + (-28*x**3)*(-39*x**3 + 48*x**2)</replace>
Simplifying the partial expression: (-28*x**3)*(-39*x**3 + 48*x**2)
Expanding the part (-39*x**3 + 48*x**2) using the distributive property, and we got: (48*x**2)*(-28*x**3) + (-39*x**3)*(-28*x**3)
Replacing (-28*x**3)*(-39*x**3 + 48*x**2) with (48*x**2)*(-28*x**3) + (-39*x**3)*(-28*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (48*x**2)*(-28*x**3) + (48*x**2)*3 + (-39*x**3)*(-28*x**3) - 39*x**3*3</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*3 = -117*x**3
  (-39*x**3)*(-28*x**3) = 1092*x**6
  (48*x**2)*3 = 144*x**2
  (48*x**2)*(-28*x**3) = -1344*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2</replace>
No more calculations needed.
<answer>1092*x**6 - 1344*x**5 - 117*x**3 + 144*x**2</answer>


Question:
Simplify this expression: (5*z + 27)*(-16*z**3 + 32*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: -80*z**4 - 272*z**3 + 864*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: (5*z + 27)*(-16*z**3 + 32*z**2)
Expanding the part (5*z + 27) using the distributive property, and we got: (5*z)*(-16*z**3 + 32*z**2) + 27*(-16*z**3 + 32*z**2)
<replace-#Step 1>#Step 2:
Current expression: (5*z)*(-16*z**3 + 32*z**2) + 27*(-16*z**3 + 32*z**2)</replace>
Simplifying the partial expression: 27*(-16*z**3 + 32*z**2)
Expanding the part (-16*z**3 + 32*z**2) using the distributive property, and we got: (32*z**2)*27 - 16*z**3*27
Replacing 27*(-16*z**3 + 32*z**2) with (32*z**2)*27 - 16*z**3*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (5*z)*(-16*z**3 + 32*z**2) + (32*z**2)*27 - 16*z**3*27</replace>
Simplifying the partial expression: (5*z)*(-16*z**3 + 32*z**2)
Expanding the part (-16*z**3 + 32*z**2) using the distributive property, and we got: (5*z)*(32*z**2) + (5*z)*(-16*z**3)
Replacing (5*z)*(-16*z**3 + 32*z**2) with (5*z)*(32*z**2) + (5*z)*(-16*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (5*z)*(32*z**2) + (5*z)*(-16*z**3) + (32*z**2)*27 - 16*z**3*27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-16*z**3)*27 = -432*z**3
  (-16*z**3)*(5*z) = -80*z**4
  (32*z**2)*27 = 864*z**2
  (32*z**2)*(5*z) = 160*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -80*z**4 - 432*z**3 + 160*z**3 + 864*z**2</replace>
Combining like terms, got -80*z**4 - 272*z**3 + 864*z**2
<replace-#Step 5>#Step 6:
Current expression: -80*z**4 - 272*z**3 + 864*z**2</replace>
No more calculations needed.
<answer>-80*z**4 - 272*z**3 + 864*z**2</answer>