Question:
Simplify this expression: -18*x**2*(-5*x**3 + 43*x**2 + 8)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 90*x**5 - 774*x**4 - 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: -18*x**2*(-5*x**3 + 43*x**2 + 8)
Expanding the part (-5*x**3 + 43*x**2 + 8) using the distributive property, and we got: 8*(-18*x**2) + (-18*x**2)*(43*x**2) + (-18*x**2)*(-5*x**3)
<replace-#Step 1>#Step 2:
Current expression: 8*(-18*x**2) + (-18*x**2)*(43*x**2) + (-18*x**2)*(-5*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  8*(-18*x**2) = -144*x**2
  (-5*x**3)*(-18*x**2) = 90*x**5
  (43*x**2)*(-18*x**2) = -774*x**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 90*x**5 - 774*x**4 - 144*x**2</replace>
No more calculations needed.
<answer>90*x**5 - 774*x**4 - 144*x**2</answer>


Question:
Simplify this expression: (52*x**2 - 13*x)*(-30*x**3 + 13*x**2 - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1560*x**5 + 1066*x**4 - 169*x**3 - 52*x**2 + 13*x


Question:
Simplify this expression: (43*y**2 + 40*y + 40)*(29*y**3 - 46*y**2 + 24*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: 1247*y**5 - 818*y**4 + 352*y**3 - 880*y**2 + 960*y


Question:
Calculate the following: -89*y**2*(41*y**2 - 41*y + 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: -3649*y**4 + 3649*y**3 - 3382*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: -89*y**2*(41*y**2 - 41*y + 38)
Expanding the part (41*y**2 - 41*y + 38) using the distributive property, and we got: (-41*y)*(-89*y**2) + 38*(-89*y**2) + (-89*y**2)*(41*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-41*y)*(-89*y**2) + 38*(-89*y**2) + (-89*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:
  38*(-89*y**2) = -3382*y**2
  (-41*y)*(-89*y**2) = 3649*y**3
  (41*y**2)*(-89*y**2) = -3649*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3649*y**4 + 3649*y**3 - 3382*y**2</replace>
No more calculations needed.
<answer>-3649*y**4 + 3649*y**3 - 3382*y**2</answer>


Question:
Simplify this expression: (25*y**2 + 39)*(7*y**3 - 5*y**2 - 7*y + 11)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 175*y**5 - 125*y**4 + 98*y**3 + 80*y**2 - 273*y + 429


Question:
Simplify this expression: (11*z**2 - 37*z)*(47*z**3 - 19*z**2 + 61*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: 517*z**5 - 1948*z**4 + 1374*z**3 - 2257*z**2


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

Answer: 147*z**6 - 9*z**5 - 686*z**4 + 42*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: (-49*z**3 + 3*z**2)*(-3*z**3 + 14*z)
Expanding the part (-49*z**3 + 3*z**2) using the distributive property, and we got: (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3 + 14*z)
<replace-#Step 1>#Step 2:
Current expression: (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3 + 14*z)</replace>
Simplifying the partial expression: (-49*z**3)*(-3*z**3 + 14*z)
Expanding the part (-3*z**3 + 14*z) using the distributive property, and we got: (14*z)*(-49*z**3) + (-49*z**3)*(-3*z**3)
Replacing (-49*z**3)*(-3*z**3 + 14*z) with (14*z)*(-49*z**3) + (-49*z**3)*(-3*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (14*z)*(-49*z**3) + (3*z**2)*(-3*z**3 + 14*z) + (-49*z**3)*(-3*z**3)</replace>
Simplifying the partial expression: (3*z**2)*(-3*z**3 + 14*z)
Expanding the part (-3*z**3 + 14*z) using the distributive property, and we got: (14*z)*(3*z**2) + (3*z**2)*(-3*z**3)
Replacing (3*z**2)*(-3*z**3 + 14*z) with (14*z)*(3*z**2) + (3*z**2)*(-3*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (14*z)*(3*z**2) + (14*z)*(-49*z**3) + (3*z**2)*(-3*z**3) + (-49*z**3)*(-3*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*z**3)*(-49*z**3) = 147*z**6
  (-3*z**3)*(3*z**2) = -9*z**5
  (14*z)*(-49*z**3) = -686*z**4
  (14*z)*(3*z**2) = 42*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 147*z**6 - 9*z**5 - 686*z**4 + 42*z**3</replace>
No more calculations needed.
<answer>147*z**6 - 9*z**5 - 686*z**4 + 42*z**3</answer>


Question:
Calculate the following: (43 - 10*x)*(-59*x**2 - 14*x + 32)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 590*x**3 - 2397*x**2 - 922*x + 1376

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 - 10*x)*(-59*x**2 - 14*x + 32)
Expanding the part (43 - 10*x) using the distributive property, and we got: (-10*x)*(-59*x**2 - 14*x + 32) + 43*(-59*x**2 - 14*x + 32)
<replace-#Step 1>#Step 2:
Current expression: (-10*x)*(-59*x**2 - 14*x + 32) + 43*(-59*x**2 - 14*x + 32)</replace>
Simplifying the partial expression: 43*(-59*x**2 - 14*x + 32)
Expanding the part (-59*x**2 - 14*x + 32) using the distributive property, and we got: -14*x*43 - 59*x**2*43 + 32*43
Replacing 43*(-59*x**2 - 14*x + 32) with -14*x*43 - 59*x**2*43 + 32*43 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -14*x*43 + (-10*x)*(-59*x**2 - 14*x + 32) - 59*x**2*43 + 1376</replace>
Simplifying the partial expression: (-10*x)*(-59*x**2 - 14*x + 32)
Expanding the part (-59*x**2 - 14*x + 32) using the distributive property, and we got: (-14*x)*(-10*x) + (-10*x)*(-59*x**2) + 32*(-10*x)
Replacing (-10*x)*(-59*x**2 - 14*x + 32) with (-14*x)*(-10*x) + (-10*x)*(-59*x**2) + 32*(-10*x) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-14*x)*(-10*x) - 14*x*43 + (-10*x)*(-59*x**2) + 32*(-10)*x - 59*x**2*43 + 1376</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-59*x**2)*43 = -2537*x**2
  (-59*x**2)*(-10*x) = 590*x**3
  (-14*x)*43 = -602*x
  (-14*x)*(-10*x) = 140*x**2
  32*-10*x = -320*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 590*x**3 - 2537*x**2 + 140*x**2 - 602*x - 320*x + 1376</replace>
Combining like terms, got 590*x**3 - 2397*x**2 - 922*x + 1376
<replace-#Step 5>#Step 6:
Current expression: 590*x**3 - 2397*x**2 - 922*x + 1376</replace>
No more calculations needed.
<answer>590*x**3 - 2397*x**2 - 922*x + 1376</answer>


Question:
Calculate the following: (42*z**2 - 8*z)*(-25*z**3 + 32*z**2 + 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: -1050*z**5 + 1544*z**4 - 256*z**3 + 2058*z**2 - 392*z


Question:
Simplify this expression: (-33*z**3 - 48*z**2 + 45)*(-4*z**3 + 14*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: 132*z**6 - 270*z**5 + 516*z**4 + 1548*z**3 + 630*z**2 - 1620*z


Question:
Simplify this expression: 70*x**3 + 750*x - 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: 70*x**3 + 750*x - 10

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 70*x**3 + 750*x - 10
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: 70*x**3 + 750*x - 10</replace>
No more calculations needed.
<answer>70*x**3 + 750*x - 10</answer>


Question:
Calculate the following: (19 - 34*y**2)*(-42*y**3 + 33*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1428*y**5 - 1920*y**3 + 627*y

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (19 - 34*y**2)*(-42*y**3 + 33*y)
Expanding the part (19 - 34*y**2) using the distributive property, and we got: (-34*y**2)*(-42*y**3 + 33*y) + 19*(-42*y**3 + 33*y)
<replace-#Step 1>#Step 2:
Current expression: (-34*y**2)*(-42*y**3 + 33*y) + 19*(-42*y**3 + 33*y)</replace>
Simplifying the partial expression: 19*(-42*y**3 + 33*y)
Expanding the part (-42*y**3 + 33*y) using the distributive property, and we got: (33*y)*19 - 42*y**3*19
Replacing 19*(-42*y**3 + 33*y) with (33*y)*19 - 42*y**3*19 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (33*y)*19 + (-34*y**2)*(-42*y**3 + 33*y) - 42*y**3*19</replace>
Simplifying the partial expression: (-34*y**2)*(-42*y**3 + 33*y)
Expanding the part (-42*y**3 + 33*y) using the distributive property, and we got: (33*y)*(-34*y**2) + (-34*y**2)*(-42*y**3)
Replacing (-34*y**2)*(-42*y**3 + 33*y) with (33*y)*(-34*y**2) + (-34*y**2)*(-42*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (33*y)*(-34*y**2) + (33*y)*19 + (-34*y**2)*(-42*y**3) - 42*y**3*19</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y**3)*19 = -798*y**3
  (-42*y**3)*(-34*y**2) = 1428*y**5
  (33*y)*19 = 627*y
  (33*y)*(-34*y**2) = -1122*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1428*y**5 - 1122*y**3 - 798*y**3 + 627*y</replace>
Combining like terms, got 1428*y**5 - 1920*y**3 + 627*y
<replace-#Step 5>#Step 6:
Current expression: 1428*y**5 - 1920*y**3 + 627*y</replace>
No more calculations needed.
<answer>1428*y**5 - 1920*y**3 + 627*y</answer>


Question:
Calculate the following: (-78*y**3 - 10*y)*(14*y**3 + 83*y - 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: -1092*y**6 - 6614*y**4 + 3198*y**3 - 830*y**2 + 410*y


Question:
Calculate the following: 44*x**2*(44 - 16*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: -704*x**3 + 1936*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: 44*x**2*(44 - 16*x)
Expanding the part (44 - 16*x) using the distributive property, and we got: (-16*x)*(44*x**2) + 44*(44*x**2)
<replace-#Step 1>#Step 2:
Current expression: (-16*x)*(44*x**2) + 44*(44*x**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  44*(44*x**2) = 1936*x**2
  (-16*x)*(44*x**2) = -704*x**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -704*x**3 + 1936*x**2</replace>
No more calculations needed.
<answer>-704*x**3 + 1936*x**2</answer>


Question:
Calculate the following: -5*z*(26*z**3 + 17*z - 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: -130*z**4 - 85*z**2 + 20*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: -5*z*(26*z**3 + 17*z - 4)
Expanding the part (26*z**3 + 17*z - 4) using the distributive property, and we got: (-5*z)*(17*z) + (-5*z)*(26*z**3) - (-1)*20*z
<replace-#Step 1>#Step 2:
Current expression: (-5*z)*(17*z) + (-5*z)*(26*z**3) - (-1)*20*z</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -4*(-5*z) = 20*z
  (17*z)*(-5*z) = -85*z**2
  (26*z**3)*(-5*z) = -130*z**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -130*z**4 - 85*z**2 + 20*z</replace>
No more calculations needed.
<answer>-130*z**4 - 85*z**2 + 20*z</answer>


Question:
Calculate the following: (-22*z**2 - 17*z + 41)*(-41*z**3 - 41*z - 40)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 902*z**5 + 697*z**4 - 779*z**3 + 1577*z**2 - 1001*z - 1640


Question:
Calculate the following: 54*x**2*(-10*x**3 - 44*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: -540*x**5 - 2376*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: 54*x**2*(-10*x**3 - 44*x**2)
Expanding the part (-10*x**3 - 44*x**2) using the distributive property, and we got: (-44*x**2)*(54*x**2) + (54*x**2)*(-10*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-44*x**2)*(54*x**2) + (54*x**2)*(-10*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*x**2)*(54*x**2) = -2376*x**4
  (-10*x**3)*(54*x**2) = -540*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -540*x**5 - 2376*x**4</replace>
No more calculations needed.
<answer>-540*x**5 - 2376*x**4</answer>


Question:
Simplify this expression: (5 - 66*x**3)*(-14*x**2 - 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 924*x**5 + 330*x**3 - 70*x**2 - 25

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 - 66*x**3)*(-14*x**2 - 5)
Expanding the part (-14*x**2 - 5) using the distributive property, and we got: (-14*x**2)*(5 - 66*x**3) - 5*(5 - 66*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-14*x**2)*(5 - 66*x**3) - 5*(5 - 66*x**3)</replace>
Simplifying the partial expression: -5*(5 - 66*x**3)
Expanding the part (5 - 66*x**3) using the distributive property, and we got: -66*x**3*(-5) + 5*(-5)
Replacing -5*(5 - 66*x**3) with -66*x**3*(-5) + 5*(-5) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-14*x**2)*(5 - 66*x**3) - 66*x**3*(-5) - 25</replace>
Simplifying the partial expression: (-14*x**2)*(5 - 66*x**3)
Expanding the part (5 - 66*x**3) using the distributive property, and we got: 5*(-14*x**2) + (-14*x**2)*(-66*x**3)
Replacing (-14*x**2)*(5 - 66*x**3) with 5*(-14*x**2) + (-14*x**2)*(-66*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 5*(-14)*x**2 + (-14*x**2)*(-66*x**3) - 66*x**3*(-5) - 25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-66*x**3)*-5 = 330*x**3
  (-66*x**3)*(-14*x**2) = 924*x**5
  5*-14*x**2 = -70*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 924*x**5 + 330*x**3 - 70*x**2 - 25</replace>
No more calculations needed.
<answer>924*x**5 + 330*x**3 - 70*x**2 - 25</answer>


Question:
Simplify this expression: (40*z**3 + 27)*(74*z**3 - 41*z**2 - 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: 2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (40*z**3 + 27)*(74*z**3 - 41*z**2 - 41)
Expanding the part (40*z**3 + 27) using the distributive property, and we got: (40*z**3)*(74*z**3 - 41*z**2 - 41) + 27*(74*z**3 - 41*z**2 - 41)
<replace-#Step 1>#Step 2:
Current expression: (40*z**3)*(74*z**3 - 41*z**2 - 41) + 27*(74*z**3 - 41*z**2 - 41)</replace>
Simplifying the partial expression: 27*(74*z**3 - 41*z**2 - 41)
Expanding the part (74*z**3 - 41*z**2 - 41) using the distributive property, and we got: -41*z**2*27 + (74*z**3)*27 - 41*27
Replacing 27*(74*z**3 - 41*z**2 - 41) with -41*z**2*27 + (74*z**3)*27 - 41*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -41*z**2*27 + (40*z**3)*(74*z**3 - 41*z**2 - 41) + (74*z**3)*27 - 1107</replace>
Simplifying the partial expression: (40*z**3)*(74*z**3 - 41*z**2 - 41)
Expanding the part (74*z**3 - 41*z**2 - 41) using the distributive property, and we got: -1640*z**3 + (-41*z**2)*(40*z**3) + (40*z**3)*(74*z**3)
Replacing (40*z**3)*(74*z**3 - 41*z**2 - 41) with -1640*z**3 + (-41*z**2)*(40*z**3) + (40*z**3)*(74*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -41*40*z**3 + (-41*z**2)*(40*z**3) - 41*z**2*27 + (40*z**3)*(74*z**3) + (74*z**3)*27 - 1107</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-41*z**2)*27 = -1107*z**2
  (-41*z**2)*(40*z**3) = -1640*z**5
  (74*z**3)*27 = 1998*z**3
  (74*z**3)*(40*z**3) = 2960*z**6
  -41*40*z**3 = -1640*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 2960*z**6 - 1640*z**5 - 1640*z**3 + 1998*z**3 - 1107*z**2 - 1107</replace>
Combining like terms, got 2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107
<replace-#Step 5>#Step 6:
Current expression: 2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107</replace>
No more calculations needed.
<answer>2960*z**6 - 1640*z**5 + 358*z**3 - 1107*z**2 - 1107</answer>


Question:
Calculate the following: (-x**3 - 24*x**2)*(-35*x**3 + 12*x**2 + 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: 35*x**6 + 828*x**5 - 288*x**4 - 9*x**3 - 216*x**2


Question:
Simplify this expression: (-39*y**2 + 3*y)*(19*y**3 + 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: -741*y**5 + 57*y**4 - 1443*y**2 + 111*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: (-39*y**2 + 3*y)*(19*y**3 + 37)
Expanding the part (19*y**3 + 37) using the distributive property, and we got: (19*y**3)*(-39*y**2 + 3*y) + 37*(-39*y**2 + 3*y)
<replace-#Step 1>#Step 2:
Current expression: (19*y**3)*(-39*y**2 + 3*y) + 37*(-39*y**2 + 3*y)</replace>
Simplifying the partial expression: 37*(-39*y**2 + 3*y)
Expanding the part (-39*y**2 + 3*y) using the distributive property, and we got: (3*y)*37 - 39*y**2*37
Replacing 37*(-39*y**2 + 3*y) with (3*y)*37 - 39*y**2*37 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (3*y)*37 - 39*y**2*37 + (19*y**3)*(-39*y**2 + 3*y)</replace>
Simplifying the partial expression: (19*y**3)*(-39*y**2 + 3*y)
Expanding the part (-39*y**2 + 3*y) using the distributive property, and we got: (3*y)*(19*y**3) + (-39*y**2)*(19*y**3)
Replacing (19*y**3)*(-39*y**2 + 3*y) with (3*y)*(19*y**3) + (-39*y**2)*(19*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (3*y)*(19*y**3) + (3*y)*37 + (-39*y**2)*(19*y**3) - 39*y**2*37</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*y**2)*37 = -1443*y**2
  (-39*y**2)*(19*y**3) = -741*y**5
  (3*y)*37 = 111*y
  (3*y)*(19*y**3) = 57*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -741*y**5 + 57*y**4 - 1443*y**2 + 111*y</replace>
No more calculations needed.
<answer>-741*y**5 + 57*y**4 - 1443*y**2 + 111*y</answer>


Question:
Calculate the following: (27 - 14*z**2)*(17*z**3 - 49*z - 1)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (27 - 14*z**2)*(17*z**3 - 49*z - 1)
Expanding the part (27 - 14*z**2) using the distributive property, and we got: (-14*z**2)*(17*z**3 - 49*z - 1) + 27*(17*z**3 - 49*z - 1)
<replace-#Step 1>#Step 2:
Current expression: (-14*z**2)*(17*z**3 - 49*z - 1) + 27*(17*z**3 - 49*z - 1)</replace>
Simplifying the partial expression: 27*(17*z**3 - 49*z - 1)
Expanding the part (17*z**3 - 49*z - 1) using the distributive property, and we got: -49*z*27 + (17*z**3)*27 - 1*27
Replacing 27*(17*z**3 - 49*z - 1) with -49*z*27 + (17*z**3)*27 - 1*27 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -49*z*27 + (-14*z**2)*(17*z**3 - 49*z - 1) + (17*z**3)*27 - 27</replace>
Simplifying the partial expression: (-14*z**2)*(17*z**3 - 49*z - 1)
Expanding the part (17*z**3 - 49*z - 1) using the distributive property, and we got: (-49*z)*(-14*z**2) - (-1)*14*z**2 + (-14*z**2)*(17*z**3)
Replacing (-14*z**2)*(17*z**3 - 49*z - 1) with (-49*z)*(-14*z**2) - (-1)*14*z**2 + (-14*z**2)*(17*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-49*z)*(-14*z**2) - 49*z*27 - 1*(-14)*z**2 + (-14*z**2)*(17*z**3) + (17*z**3)*27 - 27</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-49*z)*27 = -1323*z
  (-49*z)*(-14*z**2) = 686*z**3
  (17*z**3)*27 = 459*z**3
  (17*z**3)*(-14*z**2) = -238*z**5
  -1*-14*z**2 = 14*z**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -238*z**5 + 459*z**3 + 686*z**3 + 14*z**2 - 1323*z - 27</replace>
Combining like terms, got -238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27
<replace-#Step 5>#Step 6:
Current expression: -238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27</replace>
No more calculations needed.
<answer>-238*z**5 + 1145*z**3 + 14*z**2 - 1323*z - 27</answer>


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

Answer: 336*x**5 - 140*x**3

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: 7*x**2*(48*x**3 - 20*x)
Expanding the part (48*x**3 - 20*x) using the distributive property, and we got: (-20*x)*(7*x**2) + (7*x**2)*(48*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-20*x)*(7*x**2) + (7*x**2)*(48*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-20*x)*(7*x**2) = -140*x**3
  (48*x**3)*(7*x**2) = 336*x**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 336*x**5 - 140*x**3</replace>
No more calculations needed.
<answer>336*x**5 - 140*x**3</answer>


Question:
Simplify this expression: (4*y**3 - 37*y)*(32*y**3 + 3*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: 128*y**6 - 1172*y**4 - 111*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: (4*y**3 - 37*y)*(32*y**3 + 3*y)
Expanding the part (4*y**3 - 37*y) using the distributive property, and we got: (-37*y)*(32*y**3 + 3*y) + (4*y**3)*(32*y**3 + 3*y)
<replace-#Step 1>#Step 2:
Current expression: (-37*y)*(32*y**3 + 3*y) + (4*y**3)*(32*y**3 + 3*y)</replace>
Simplifying the partial expression: (-37*y)*(32*y**3 + 3*y)
Expanding the part (32*y**3 + 3*y) using the distributive property, and we got: (-37*y)*(3*y) + (-37*y)*(32*y**3)
Replacing (-37*y)*(32*y**3 + 3*y) with (-37*y)*(3*y) + (-37*y)*(32*y**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-37*y)*(3*y) + (-37*y)*(32*y**3) + (4*y**3)*(32*y**3 + 3*y)</replace>
Simplifying the partial expression: (4*y**3)*(32*y**3 + 3*y)
Expanding the part (32*y**3 + 3*y) using the distributive property, and we got: (3*y)*(4*y**3) + (4*y**3)*(32*y**3)
Replacing (4*y**3)*(32*y**3 + 3*y) with (3*y)*(4*y**3) + (4*y**3)*(32*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-37*y)*(3*y) + (-37*y)*(32*y**3) + (3*y)*(4*y**3) + (4*y**3)*(32*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (3*y)*(-37*y) = -111*y**2
  (3*y)*(4*y**3) = 12*y**4
  (32*y**3)*(-37*y) = -1184*y**4
  (32*y**3)*(4*y**3) = 128*y**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 128*y**6 - 1184*y**4 + 12*y**4 - 111*y**2</replace>
Combining like terms, got 128*y**6 - 1172*y**4 - 111*y**2
<replace-#Step 5>#Step 6:
Current expression: 128*y**6 - 1172*y**4 - 111*y**2</replace>
No more calculations needed.
<answer>128*y**6 - 1172*y**4 - 111*y**2</answer>


Question:
Simplify this expression: 34*x*(-30*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: -1020*x**2 - 1564*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: 34*x*(-30*x - 46)
Expanding the part (-30*x - 46) using the distributive property, and we got: (-30*x)*(34*x) - 1564*x
<replace-#Step 1>#Step 2:
Current expression: (-30*x)*(34*x) - 1564*x</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -46*(34*x) = -1564*x
  (-30*x)*(34*x) = -1020*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -1020*x**2 - 1564*x</replace>
No more calculations needed.
<answer>-1020*x**2 - 1564*x</answer>


Question:
Calculate the following: (21*y**2 + 34)*(-11*y**3 - 42*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: -231*y**5 - 882*y**4 - 374*y**3 - 1428*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: (21*y**2 + 34)*(-11*y**3 - 42*y**2)
Expanding the part (21*y**2 + 34) using the distributive property, and we got: (21*y**2)*(-11*y**3 - 42*y**2) + 34*(-11*y**3 - 42*y**2)
<replace-#Step 1>#Step 2:
Current expression: (21*y**2)*(-11*y**3 - 42*y**2) + 34*(-11*y**3 - 42*y**2)</replace>
Simplifying the partial expression: 34*(-11*y**3 - 42*y**2)
Expanding the part (-11*y**3 - 42*y**2) using the distributive property, and we got: -42*y**2*34 - 11*y**3*34
Replacing 34*(-11*y**3 - 42*y**2) with -42*y**2*34 - 11*y**3*34 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -42*y**2*34 + (21*y**2)*(-11*y**3 - 42*y**2) - 11*y**3*34</replace>
Simplifying the partial expression: (21*y**2)*(-11*y**3 - 42*y**2)
Expanding the part (-11*y**3 - 42*y**2) using the distributive property, and we got: (-42*y**2)*(21*y**2) + (21*y**2)*(-11*y**3)
Replacing (21*y**2)*(-11*y**3 - 42*y**2) with (-42*y**2)*(21*y**2) + (21*y**2)*(-11*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-42*y**2)*(21*y**2) - 42*y**2*34 + (21*y**2)*(-11*y**3) - 11*y**3*34</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-42*y**2)*34 = -1428*y**2
  (-42*y**2)*(21*y**2) = -882*y**4
  (-11*y**3)*34 = -374*y**3
  (-11*y**3)*(21*y**2) = -231*y**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2</replace>
No more calculations needed.
<answer>-231*y**5 - 882*y**4 - 374*y**3 - 1428*y**2</answer>


Question:
Simplify this expression: (39*y**2 - 50)*(-27*y**3 - 25*y**2 + 45*y - 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: -1053*y**5 - 975*y**4 + 3105*y**3 + 860*y**2 - 2250*y + 500


Question:
Simplify this expression: (30 - 10*y)*(50*y**3 + 40*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: -500*y**4 + 1100*y**3 + 1200*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: (30 - 10*y)*(50*y**3 + 40*y**2)
Expanding the part (30 - 10*y) using the distributive property, and we got: (-10*y)*(50*y**3 + 40*y**2) + 30*(50*y**3 + 40*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-10*y)*(50*y**3 + 40*y**2) + 30*(50*y**3 + 40*y**2)</replace>
Simplifying the partial expression: 30*(50*y**3 + 40*y**2)
Expanding the part (50*y**3 + 40*y**2) using the distributive property, and we got: (40*y**2)*30 + (50*y**3)*30
Replacing 30*(50*y**3 + 40*y**2) with (40*y**2)*30 + (50*y**3)*30 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-10*y)*(50*y**3 + 40*y**2) + (40*y**2)*30 + (50*y**3)*30</replace>
Simplifying the partial expression: (-10*y)*(50*y**3 + 40*y**2)
Expanding the part (50*y**3 + 40*y**2) using the distributive property, and we got: (-10*y)*(40*y**2) + (-10*y)*(50*y**3)
Replacing (-10*y)*(50*y**3 + 40*y**2) with (-10*y)*(40*y**2) + (-10*y)*(50*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-10*y)*(40*y**2) + (-10*y)*(50*y**3) + (40*y**2)*30 + (50*y**3)*30</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (40*y**2)*30 = 1200*y**2
  (40*y**2)*(-10*y) = -400*y**3
  (50*y**3)*30 = 1500*y**3
  (50*y**3)*(-10*y) = -500*y**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -500*y**4 - 400*y**3 + 1500*y**3 + 1200*y**2</replace>
Combining like terms, got -500*y**4 + 1100*y**3 + 1200*y**2
<replace-#Step 5>#Step 6:
Current expression: -500*y**4 + 1100*y**3 + 1200*y**2</replace>
No more calculations needed.
<answer>-500*y**4 + 1100*y**3 + 1200*y**2</answer>


Question:
Simplify this expression: (4*x**2 - 50)*(-22*x**3 + 33*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: -88*x**5 + 132*x**4 + 1100*x**3 - 1650*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: (4*x**2 - 50)*(-22*x**3 + 33*x**2)
Expanding the part (4*x**2 - 50) using the distributive property, and we got: (4*x**2)*(-22*x**3 + 33*x**2) - 50*(-22*x**3 + 33*x**2)
<replace-#Step 1>#Step 2:
Current expression: (4*x**2)*(-22*x**3 + 33*x**2) - 50*(-22*x**3 + 33*x**2)</replace>
Simplifying the partial expression: -50*(-22*x**3 + 33*x**2)
Expanding the part (-22*x**3 + 33*x**2) using the distributive property, and we got: (33*x**2)*(-50) - 22*x**3*(-50)
Replacing -50*(-22*x**3 + 33*x**2) with (33*x**2)*(-50) - 22*x**3*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (4*x**2)*(-22*x**3 + 33*x**2) + (33*x**2)*(-50) - 22*x**3*(-50)</replace>
Simplifying the partial expression: (4*x**2)*(-22*x**3 + 33*x**2)
Expanding the part (-22*x**3 + 33*x**2) using the distributive property, and we got: (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3)
Replacing (4*x**2)*(-22*x**3 + 33*x**2) with (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (4*x**2)*(33*x**2) + (4*x**2)*(-22*x**3) + (33*x**2)*(-50) - 22*x**3*(-50)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-22*x**3)*-50 = 1100*x**3
  (-22*x**3)*(4*x**2) = -88*x**5
  (33*x**2)*-50 = -1650*x**2
  (33*x**2)*(4*x**2) = 132*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2</replace>
No more calculations needed.
<answer>-88*x**5 + 132*x**4 + 1100*x**3 - 1650*x**2</answer>


Question:
Simplify this expression: (-45*y**2 + 22*y)*(28*y**3 - 30*y**2 - 2*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1260*y**5 + 1966*y**4 - 570*y**3 - 44*y**2


Question:
Simplify this expression: (-19*x**3 - 36*x**2)*(20*x**3 + 39)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -380*x**6 - 720*x**5 - 741*x**3 - 1404*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: (-19*x**3 - 36*x**2)*(20*x**3 + 39)
Expanding the part (20*x**3 + 39) using the distributive property, and we got: (20*x**3)*(-19*x**3 - 36*x**2) + 39*(-19*x**3 - 36*x**2)
<replace-#Step 1>#Step 2:
Current expression: (20*x**3)*(-19*x**3 - 36*x**2) + 39*(-19*x**3 - 36*x**2)</replace>
Simplifying the partial expression: 39*(-19*x**3 - 36*x**2)
Expanding the part (-19*x**3 - 36*x**2) using the distributive property, and we got: -36*x**2*39 - 19*x**3*39
Replacing 39*(-19*x**3 - 36*x**2) with -36*x**2*39 - 19*x**3*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -36*x**2*39 - 19*x**3*39 + (20*x**3)*(-19*x**3 - 36*x**2)</replace>
Simplifying the partial expression: (20*x**3)*(-19*x**3 - 36*x**2)
Expanding the part (-19*x**3 - 36*x**2) using the distributive property, and we got: (-36*x**2)*(20*x**3) + (-19*x**3)*(20*x**3)
Replacing (20*x**3)*(-19*x**3 - 36*x**2) with (-36*x**2)*(20*x**3) + (-19*x**3)*(20*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-36*x**2)*(20*x**3) - 36*x**2*39 + (-19*x**3)*(20*x**3) - 19*x**3*39</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-36*x**2)*39 = -1404*x**2
  (-36*x**2)*(20*x**3) = -720*x**5
  (-19*x**3)*39 = -741*x**3
  (-19*x**3)*(20*x**3) = -380*x**6
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2</replace>
No more calculations needed.
<answer>-380*x**6 - 720*x**5 - 741*x**3 - 1404*x**2</answer>


Question:
Simplify this expression: (17 - 33*z**2)*(35*z**3 - 44*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: -1155*z**5 + 1452*z**4 + 595*z**3 - 748*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: (17 - 33*z**2)*(35*z**3 - 44*z**2)
Expanding the part (17 - 33*z**2) using the distributive property, and we got: (-33*z**2)*(35*z**3 - 44*z**2) + 17*(35*z**3 - 44*z**2)
<replace-#Step 1>#Step 2:
Current expression: (-33*z**2)*(35*z**3 - 44*z**2) + 17*(35*z**3 - 44*z**2)</replace>
Simplifying the partial expression: 17*(35*z**3 - 44*z**2)
Expanding the part (35*z**3 - 44*z**2) using the distributive property, and we got: -44*z**2*17 + (35*z**3)*17
Replacing 17*(35*z**3 - 44*z**2) with -44*z**2*17 + (35*z**3)*17 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -44*z**2*17 + (-33*z**2)*(35*z**3 - 44*z**2) + (35*z**3)*17</replace>
Simplifying the partial expression: (-33*z**2)*(35*z**3 - 44*z**2)
Expanding the part (35*z**3 - 44*z**2) using the distributive property, and we got: (-44*z**2)*(-33*z**2) + (-33*z**2)*(35*z**3)
Replacing (-33*z**2)*(35*z**3 - 44*z**2) with (-44*z**2)*(-33*z**2) + (-33*z**2)*(35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-44*z**2)*(-33*z**2) - 44*z**2*17 + (-33*z**2)*(35*z**3) + (35*z**3)*17</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-44*z**2)*17 = -748*z**2
  (-44*z**2)*(-33*z**2) = 1452*z**4
  (35*z**3)*17 = 595*z**3
  (35*z**3)*(-33*z**2) = -1155*z**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2</replace>
No more calculations needed.
<answer>-1155*z**5 + 1452*z**4 + 595*z**3 - 748*z**2</answer>


Question:
Calculate the following: (25 - 36*z**2)*(-3*z**3 + 55*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: 108*z**5 - 2055*z**3 + 1375*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: (25 - 36*z**2)*(-3*z**3 + 55*z)
Expanding the part (25 - 36*z**2) using the distributive property, and we got: (-36*z**2)*(-3*z**3 + 55*z) + 25*(-3*z**3 + 55*z)
<replace-#Step 1>#Step 2:
Current expression: (-36*z**2)*(-3*z**3 + 55*z) + 25*(-3*z**3 + 55*z)</replace>
Simplifying the partial expression: 25*(-3*z**3 + 55*z)
Expanding the part (-3*z**3 + 55*z) using the distributive property, and we got: (55*z)*25 - 3*z**3*25
Replacing 25*(-3*z**3 + 55*z) with (55*z)*25 - 3*z**3*25 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (55*z)*25 + (-36*z**2)*(-3*z**3 + 55*z) - 3*z**3*25</replace>
Simplifying the partial expression: (-36*z**2)*(-3*z**3 + 55*z)
Expanding the part (-3*z**3 + 55*z) using the distributive property, and we got: (55*z)*(-36*z**2) + (-36*z**2)*(-3*z**3)
Replacing (-36*z**2)*(-3*z**3 + 55*z) with (55*z)*(-36*z**2) + (-36*z**2)*(-3*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (55*z)*(-36*z**2) + (55*z)*25 + (-36*z**2)*(-3*z**3) - 3*z**3*25</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*z**3)*25 = -75*z**3
  (-3*z**3)*(-36*z**2) = 108*z**5
  (55*z)*25 = 1375*z
  (55*z)*(-36*z**2) = -1980*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 108*z**5 - 1980*z**3 - 75*z**3 + 1375*z</replace>
Combining like terms, got 108*z**5 - 2055*z**3 + 1375*z
<replace-#Step 5>#Step 6:
Current expression: 108*z**5 - 2055*z**3 + 1375*z</replace>
No more calculations needed.
<answer>108*z**5 - 2055*z**3 + 1375*z</answer>


Question:
Simplify this expression: (-80*z**3 - 43)*(-49*z**3 + 33*z**2 - 7)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 3920*z**6 - 2640*z**5 + 2667*z**3 - 1419*z**2 + 301


Question:
Calculate the following: (-45*y**3 + 30*y**2 - 39)*(-13*y**3 - 33*y**2 - 10*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 585*y**6 + 1095*y**5 - 540*y**4 + 207*y**3 + 1287*y**2 + 390*y


Question:
Calculate the following: (79 - 34*x**3)*(16*x**2 + 92*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: -544*x**5 - 3128*x**4 + 1264*x**2 + 7268*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: (79 - 34*x**3)*(16*x**2 + 92*x)
Expanding the part (79 - 34*x**3) using the distributive property, and we got: (-34*x**3)*(16*x**2 + 92*x) + 79*(16*x**2 + 92*x)
<replace-#Step 1>#Step 2:
Current expression: (-34*x**3)*(16*x**2 + 92*x) + 79*(16*x**2 + 92*x)</replace>
Simplifying the partial expression: 79*(16*x**2 + 92*x)
Expanding the part (16*x**2 + 92*x) using the distributive property, and we got: (92*x)*79 + (16*x**2)*79
Replacing 79*(16*x**2 + 92*x) with (92*x)*79 + (16*x**2)*79 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (92*x)*79 + (16*x**2)*79 + (-34*x**3)*(16*x**2 + 92*x)</replace>
Simplifying the partial expression: (-34*x**3)*(16*x**2 + 92*x)
Expanding the part (16*x**2 + 92*x) using the distributive property, and we got: (92*x)*(-34*x**3) + (16*x**2)*(-34*x**3)
Replacing (-34*x**3)*(16*x**2 + 92*x) with (92*x)*(-34*x**3) + (16*x**2)*(-34*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (92*x)*(-34*x**3) + (92*x)*79 + (16*x**2)*(-34*x**3) + (16*x**2)*79</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (16*x**2)*79 = 1264*x**2
  (16*x**2)*(-34*x**3) = -544*x**5
  (92*x)*79 = 7268*x
  (92*x)*(-34*x**3) = -3128*x**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x</replace>
No more calculations needed.
<answer>-544*x**5 - 3128*x**4 + 1264*x**2 + 7268*x</answer>


Question:
Calculate the following: (-65*z**3 + 38*z)*(12*z**3 - 41*z**2 - 8*z + 5)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -780*z**6 + 2665*z**5 + 976*z**4 - 1883*z**3 - 304*z**2 + 190*z


Question:
Simplify this expression: (-34*x**2 - 42)*(-10*x**3 - 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: 340*x**5 + 420*x**3 + 1700*x**2 + 2100

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-34*x**2 - 42)*(-10*x**3 - 50)
Expanding the part (-10*x**3 - 50) using the distributive property, and we got: (-10*x**3)*(-34*x**2 - 42) - 50*(-34*x**2 - 42)
<replace-#Step 1>#Step 2:
Current expression: (-10*x**3)*(-34*x**2 - 42) - 50*(-34*x**2 - 42)</replace>
Simplifying the partial expression: -50*(-34*x**2 - 42)
Expanding the part (-34*x**2 - 42) using the distributive property, and we got: -34*x**2*(-50) - 42*(-50)
Replacing -50*(-34*x**2 - 42) with -34*x**2*(-50) - 42*(-50) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -34*x**2*(-50) + (-10*x**3)*(-34*x**2 - 42) + 2100</replace>
Simplifying the partial expression: (-10*x**3)*(-34*x**2 - 42)
Expanding the part (-34*x**2 - 42) using the distributive property, and we got: -(-1)*420*x**3 + (-34*x**2)*(-10*x**3)
Replacing (-10*x**3)*(-34*x**2 - 42) with -(-1)*420*x**3 + (-34*x**2)*(-10*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -42*(-10)*x**3 + (-34*x**2)*(-10*x**3) - 34*x**2*(-50) + 2100</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-34*x**2)*-50 = 1700*x**2
  (-34*x**2)*(-10*x**3) = 340*x**5
  -42*-10*x**3 = 420*x**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 340*x**5 + 420*x**3 + 1700*x**2 + 2100</replace>
No more calculations needed.
<answer>340*x**5 + 420*x**3 + 1700*x**2 + 2100</answer>


Question:
Simplify this expression: (34*y + 55)*(36*y + 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: 1224*y**2 + 2694*y + 1155

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (34*y + 55)*(36*y + 21)
Expanding the part (36*y + 21) using the distributive property, and we got: (36*y)*(34*y + 55) + 21*(34*y + 55)
<replace-#Step 1>#Step 2:
Current expression: (36*y)*(34*y + 55) + 21*(34*y + 55)</replace>
Simplifying the partial expression: 21*(34*y + 55)
Expanding the part (34*y + 55) using the distributive property, and we got: (34*y)*21 + 55*21
Replacing 21*(34*y + 55) with (34*y)*21 + 55*21 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (34*y)*21 + (36*y)*(34*y + 55) + 1155</replace>
Simplifying the partial expression: (36*y)*(34*y + 55)
Expanding the part (34*y + 55) using the distributive property, and we got: 55*(36*y) + (34*y)*(36*y)
Replacing (36*y)*(34*y + 55) with 55*(36*y) + (34*y)*(36*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 55*36*y + (34*y)*(36*y) + (34*y)*21 + 1155</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (34*y)*21 = 714*y
  (34*y)*(36*y) = 1224*y**2
  55*36*y = 1980*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1224*y**2 + 714*y + 1980*y + 1155</replace>
Combining like terms, got 1224*y**2 + 2694*y + 1155
<replace-#Step 5>#Step 6:
Current expression: 1224*y**2 + 2694*y + 1155</replace>
No more calculations needed.
<answer>1224*y**2 + 2694*y + 1155</answer>


Question:
Calculate the following: (10 - 41*x**2)*(93 - 39*x**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: 1599*x**5 - 390*x**3 - 3813*x**2 + 930

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 - 41*x**2)*(93 - 39*x**3)
Expanding the part (10 - 41*x**2) using the distributive property, and we got: (-41*x**2)*(93 - 39*x**3) + 10*(93 - 39*x**3)
<replace-#Step 1>#Step 2:
Current expression: (-41*x**2)*(93 - 39*x**3) + 10*(93 - 39*x**3)</replace>
Simplifying the partial expression: 10*(93 - 39*x**3)
Expanding the part (93 - 39*x**3) using the distributive property, and we got: -39*x**3*10 + 93*10
Replacing 10*(93 - 39*x**3) with -39*x**3*10 + 93*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-41*x**2)*(93 - 39*x**3) - 39*x**3*10 + 930</replace>
Simplifying the partial expression: (-41*x**2)*(93 - 39*x**3)
Expanding the part (93 - 39*x**3) using the distributive property, and we got: 93*(-41*x**2) + (-41*x**2)*(-39*x**3)
Replacing (-41*x**2)*(93 - 39*x**3) with 93*(-41*x**2) + (-41*x**2)*(-39*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 93*(-41)*x**2 + (-41*x**2)*(-39*x**3) - 39*x**3*10 + 930</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-39*x**3)*10 = -390*x**3
  (-39*x**3)*(-41*x**2) = 1599*x**5
  93*-41*x**2 = -3813*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1599*x**5 - 390*x**3 - 3813*x**2 + 930</replace>
No more calculations needed.
<answer>1599*x**5 - 390*x**3 - 3813*x**2 + 930</answer>


Question:
Calculate the following: (-2*z**3 - 27)*(35*z**3 - 12)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -70*z**6 - 921*z**3 + 324

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 - 27)*(35*z**3 - 12)
Expanding the part (-2*z**3 - 27) using the distributive property, and we got: (-2*z**3)*(35*z**3 - 12) - 27*(35*z**3 - 12)
<replace-#Step 1>#Step 2:
Current expression: (-2*z**3)*(35*z**3 - 12) - 27*(35*z**3 - 12)</replace>
Simplifying the partial expression: -27*(35*z**3 - 12)
Expanding the part (35*z**3 - 12) using the distributive property, and we got: (35*z**3)*(-27) - 12*(-27)
Replacing -27*(35*z**3 - 12) with (35*z**3)*(-27) - 12*(-27) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-2*z**3)*(35*z**3 - 12) + (35*z**3)*(-27) + 324</replace>
Simplifying the partial expression: (-2*z**3)*(35*z**3 - 12)
Expanding the part (35*z**3 - 12) using the distributive property, and we got: -(-1)*24*z**3 + (-2*z**3)*(35*z**3)
Replacing (-2*z**3)*(35*z**3 - 12) with -(-1)*24*z**3 + (-2*z**3)*(35*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -12*(-2)*z**3 + (-2*z**3)*(35*z**3) + (35*z**3)*(-27) + 324</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (35*z**3)*-27 = -945*z**3
  (35*z**3)*(-2*z**3) = -70*z**6
  -12*-2*z**3 = 24*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -70*z**6 - 945*z**3 + 24*z**3 + 324</replace>
Combining like terms, got -70*z**6 - 921*z**3 + 324
<replace-#Step 5>#Step 6:
Current expression: -70*z**6 - 921*z**3 + 324</replace>
No more calculations needed.
<answer>-70*z**6 - 921*z**3 + 324</answer>


Question:
Calculate the following: (-22*z**2 - 10*z - 35)*(49*z**2 + 37*z - 3)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -1078*z**4 - 1304*z**3 - 2019*z**2 - 1265*z + 105


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

Answer: 196*y**3 - 658*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: -14*y**2*(47 - 14*y)
Expanding the part (47 - 14*y) using the distributive property, and we got: (-14*y)*(-14*y**2) + 47*(-14*y**2)
<replace-#Step 1>#Step 2:
Current expression: (-14*y)*(-14*y**2) + 47*(-14*y**2)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  47*(-14*y**2) = -658*y**2
  (-14*y)*(-14*y**2) = 196*y**3
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 196*y**3 - 658*y**2</replace>
No more calculations needed.
<answer>196*y**3 - 658*y**2</answer>


Question:
Simplify this expression: (-5*x**3 + 40*x)*(52*x**2 + 8*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: -260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*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: (-5*x**3 + 40*x)*(52*x**2 + 8*x - 31)
Expanding the part (-5*x**3 + 40*x) using the distributive property, and we got: (40*x)*(52*x**2 + 8*x - 31) + (-5*x**3)*(52*x**2 + 8*x - 31)
<replace-#Step 1>#Step 2:
Current expression: (40*x)*(52*x**2 + 8*x - 31) + (-5*x**3)*(52*x**2 + 8*x - 31)</replace>
Simplifying the partial expression: (-5*x**3)*(52*x**2 + 8*x - 31)
Expanding the part (52*x**2 + 8*x - 31) using the distributive property, and we got: -(-1)*155*x**3 + (8*x)*(-5*x**3) + (52*x**2)*(-5*x**3)
Replacing (-5*x**3)*(52*x**2 + 8*x - 31) with -(-1)*155*x**3 + (8*x)*(-5*x**3) + (52*x**2)*(-5*x**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -31*(-5)*x**3 + (8*x)*(-5*x**3) + (40*x)*(52*x**2 + 8*x - 31) + (52*x**2)*(-5*x**3)</replace>
Simplifying the partial expression: (40*x)*(52*x**2 + 8*x - 31)
Expanding the part (52*x**2 + 8*x - 31) using the distributive property, and we got: -1240*x + (8*x)*(40*x) + (40*x)*(52*x**2)
Replacing (40*x)*(52*x**2 + 8*x - 31) with -1240*x + (8*x)*(40*x) + (40*x)*(52*x**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -31*(-5)*x**3 - 31*40*x + (8*x)*(40*x) + (8*x)*(-5*x**3) + (40*x)*(52*x**2) + (52*x**2)*(-5*x**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (8*x)*(-5*x**3) = -40*x**4
  (8*x)*(40*x) = 320*x**2
  (52*x**2)*(-5*x**3) = -260*x**5
  (52*x**2)*(40*x) = 2080*x**3
  -31*-5*x**3 = 155*x**3
  -31*40*x = -1240*x
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -260*x**5 - 40*x**4 + 155*x**3 + 2080*x**3 + 320*x**2 - 1240*x</replace>
Combining like terms, got -260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x
<replace-#Step 5>#Step 6:
Current expression: -260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x</replace>
No more calculations needed.
<answer>-260*x**5 - 40*x**4 + 2235*x**3 + 320*x**2 - 1240*x</answer>


Question:
Calculate the following: (22*x**2 + 24)*(44*x**3 + 2*x**2 - 18*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: 968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (22*x**2 + 24)*(44*x**3 + 2*x**2 - 18*x)
Expanding the part (22*x**2 + 24) using the distributive property, and we got: (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + 24*(44*x**3 + 2*x**2 - 18*x)
<replace-#Step 1>#Step 2:
Current expression: (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + 24*(44*x**3 + 2*x**2 - 18*x)</replace>
Simplifying the partial expression: 24*(44*x**3 + 2*x**2 - 18*x)
Expanding the part (44*x**3 + 2*x**2 - 18*x) using the distributive property, and we got: -18*x*24 + (2*x**2)*24 + (44*x**3)*24
Replacing 24*(44*x**3 + 2*x**2 - 18*x) with -18*x*24 + (2*x**2)*24 + (44*x**3)*24 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -18*x*24 + (2*x**2)*24 + (22*x**2)*(44*x**3 + 2*x**2 - 18*x) + (44*x**3)*24</replace>
Simplifying the partial expression: (22*x**2)*(44*x**3 + 2*x**2 - 18*x)
Expanding the part (44*x**3 + 2*x**2 - 18*x) using the distributive property, and we got: (-18*x)*(22*x**2) + (2*x**2)*(22*x**2) + (22*x**2)*(44*x**3)
Replacing (22*x**2)*(44*x**3 + 2*x**2 - 18*x) with (-18*x)*(22*x**2) + (2*x**2)*(22*x**2) + (22*x**2)*(44*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-18*x)*(22*x**2) - 18*x*24 + (2*x**2)*(22*x**2) + (2*x**2)*24 + (22*x**2)*(44*x**3) + (44*x**3)*24</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-18*x)*24 = -432*x
  (-18*x)*(22*x**2) = -396*x**3
  (2*x**2)*24 = 48*x**2
  (2*x**2)*(22*x**2) = 44*x**4
  (44*x**3)*24 = 1056*x**3
  (44*x**3)*(22*x**2) = 968*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 968*x**5 + 44*x**4 - 396*x**3 + 1056*x**3 + 48*x**2 - 432*x</replace>
Combining like terms, got 968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x
<replace-#Step 5>#Step 6:
Current expression: 968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x</replace>
No more calculations needed.
<answer>968*x**5 + 44*x**4 + 660*x**3 + 48*x**2 - 432*x</answer>


Question:
Simplify this expression: (55 - 3*y)*(23*y + 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: -69*y**2 + 1235*y + 550

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (55 - 3*y)*(23*y + 10)
Expanding the part (23*y + 10) using the distributive property, and we got: (23*y)*(55 - 3*y) + 10*(55 - 3*y)
<replace-#Step 1>#Step 2:
Current expression: (23*y)*(55 - 3*y) + 10*(55 - 3*y)</replace>
Simplifying the partial expression: 10*(55 - 3*y)
Expanding the part (55 - 3*y) using the distributive property, and we got: -3*y*10 + 55*10
Replacing 10*(55 - 3*y) with -3*y*10 + 55*10 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -3*y*10 + (23*y)*(55 - 3*y) + 550</replace>
Simplifying the partial expression: (23*y)*(55 - 3*y)
Expanding the part (55 - 3*y) using the distributive property, and we got: (-3*y)*(23*y) + 55*(23*y)
Replacing (23*y)*(55 - 3*y) with (-3*y)*(23*y) + 55*(23*y) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-3*y)*(23*y) - 3*y*10 + 55*23*y + 550</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-3*y)*10 = -30*y
  (-3*y)*(23*y) = -69*y**2
  55*23*y = 1265*y
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -69*y**2 - 30*y + 1265*y + 550</replace>
Combining like terms, got -69*y**2 + 1235*y + 550
<replace-#Step 5>#Step 6:
Current expression: -69*y**2 + 1235*y + 550</replace>
No more calculations needed.
<answer>-69*y**2 + 1235*y + 550</answer>


Question:
Calculate the following: (-29*z**3 - 13*z**2)*(-23*z**3 + 108*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: 667*z**6 + 299*z**5 - 3132*z**4 - 1404*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: (-29*z**3 - 13*z**2)*(-23*z**3 + 108*z)
Expanding the part (-29*z**3 - 13*z**2) using the distributive property, and we got: (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3 + 108*z)
<replace-#Step 1>#Step 2:
Current expression: (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3 + 108*z)</replace>
Simplifying the partial expression: (-29*z**3)*(-23*z**3 + 108*z)
Expanding the part (-23*z**3 + 108*z) using the distributive property, and we got: (108*z)*(-29*z**3) + (-29*z**3)*(-23*z**3)
Replacing (-29*z**3)*(-23*z**3 + 108*z) with (108*z)*(-29*z**3) + (-29*z**3)*(-23*z**3) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (108*z)*(-29*z**3) + (-13*z**2)*(-23*z**3 + 108*z) + (-29*z**3)*(-23*z**3)</replace>
Simplifying the partial expression: (-13*z**2)*(-23*z**3 + 108*z)
Expanding the part (-23*z**3 + 108*z) using the distributive property, and we got: (108*z)*(-13*z**2) + (-13*z**2)*(-23*z**3)
Replacing (-13*z**2)*(-23*z**3 + 108*z) with (108*z)*(-13*z**2) + (-13*z**2)*(-23*z**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (108*z)*(-13*z**2) + (108*z)*(-29*z**3) + (-13*z**2)*(-23*z**3) + (-29*z**3)*(-23*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-23*z**3)*(-29*z**3) = 667*z**6
  (-23*z**3)*(-13*z**2) = 299*z**5
  (108*z)*(-29*z**3) = -3132*z**4
  (108*z)*(-13*z**2) = -1404*z**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3</replace>
No more calculations needed.
<answer>667*z**6 + 299*z**5 - 3132*z**4 - 1404*z**3</answer>


Question:
Simplify this expression: (-29*x**2 - 40)*(-25*x**3 + 37*x - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: (-29*x**2 - 40)*(-25*x**3 + 37*x - 20)
Expanding the part (-29*x**2 - 40) using the distributive property, and we got: (-29*x**2)*(-25*x**3 + 37*x - 20) - 40*(-25*x**3 + 37*x - 20)
<replace-#Step 1>#Step 2:
Current expression: (-29*x**2)*(-25*x**3 + 37*x - 20) - 40*(-25*x**3 + 37*x - 20)</replace>
Simplifying the partial expression: -40*(-25*x**3 + 37*x - 20)
Expanding the part (-25*x**3 + 37*x - 20) using the distributive property, and we got: (37*x)*(-40) - 25*x**3*(-40) - 20*(-40)
Replacing -40*(-25*x**3 + 37*x - 20) with (37*x)*(-40) - 25*x**3*(-40) - 20*(-40) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (37*x)*(-40) + (-29*x**2)*(-25*x**3 + 37*x - 20) - 25*x**3*(-40) + 800</replace>
Simplifying the partial expression: (-29*x**2)*(-25*x**3 + 37*x - 20)
Expanding the part (-25*x**3 + 37*x - 20) using the distributive property, and we got: -(-1)*580*x**2 + (37*x)*(-29*x**2) + (-29*x**2)*(-25*x**3)
Replacing (-29*x**2)*(-25*x**3 + 37*x - 20) with -(-1)*580*x**2 + (37*x)*(-29*x**2) + (-29*x**2)*(-25*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: -20*(-29)*x**2 + (37*x)*(-29*x**2) + (37*x)*(-40) + (-29*x**2)*(-25*x**3) - 25*x**3*(-40) + 800</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-25*x**3)*-40 = 1000*x**3
  (-25*x**3)*(-29*x**2) = 725*x**5
  (37*x)*-40 = -1480*x
  (37*x)*(-29*x**2) = -1073*x**3
  -20*-29*x**2 = 580*x**2
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 725*x**5 - 1073*x**3 + 1000*x**3 + 580*x**2 - 1480*x + 800</replace>
Combining like terms, got 725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800
<replace-#Step 5>#Step 6:
Current expression: 725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800</replace>
No more calculations needed.
<answer>725*x**5 - 73*x**3 + 580*x**2 - 1480*x + 800</answer>


Question:
Simplify this expression: 37*y**2*(43*y**3 + 48)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1591*y**5 + 1776*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: 37*y**2*(43*y**3 + 48)
Expanding the part (43*y**3 + 48) using the distributive property, and we got: 48*(37*y**2) + (37*y**2)*(43*y**3)
<replace-#Step 1>#Step 2:
Current expression: 48*(37*y**2) + (37*y**2)*(43*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  48*(37*y**2) = 1776*y**2
  (43*y**3)*(37*y**2) = 1591*y**5
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1591*y**5 + 1776*y**2</replace>
No more calculations needed.
<answer>1591*y**5 + 1776*y**2</answer>


Question:
Simplify this expression: (27*x**2 + 32*x - 33)*(9*x**3 + 28*x**2 + 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: 243*x**5 + 1044*x**4 + 599*x**3 + 345*x**2 + 1504*x - 1551


Question:
Simplify this expression: (4*y - 48)*(44*y**3 - 12*y**2 - 18*y + 47)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 176*y**4 - 2160*y**3 + 504*y**2 + 1052*y - 2256


Question:
Simplify this expression: (-34*z**3 + 15*z**2)*(24*z**3 - 24*z - 15)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -816*z**6 + 360*z**5 + 816*z**4 + 150*z**3 - 225*z**2


Question:
Calculate the following: 1804 - 1886*y**3
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1804 - 1886*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: 1804 - 1886*y**3
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: 1804 - 1886*y**3</replace>
No more calculations needed.
<answer>1804 - 1886*y**3</answer>


Question:
Calculate the following: (34*x**2 + 28*x)*(37*x**3 - 44)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*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: (34*x**2 + 28*x)*(37*x**3 - 44)
Expanding the part (37*x**3 - 44) using the distributive property, and we got: (37*x**3)*(34*x**2 + 28*x) - 44*(34*x**2 + 28*x)
<replace-#Step 1>#Step 2:
Current expression: (37*x**3)*(34*x**2 + 28*x) - 44*(34*x**2 + 28*x)</replace>
Simplifying the partial expression: -44*(34*x**2 + 28*x)
Expanding the part (34*x**2 + 28*x) using the distributive property, and we got: (28*x)*(-44) + (34*x**2)*(-44)
Replacing -44*(34*x**2 + 28*x) with (28*x)*(-44) + (34*x**2)*(-44) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (28*x)*(-44) + (34*x**2)*(-44) + (37*x**3)*(34*x**2 + 28*x)</replace>
Simplifying the partial expression: (37*x**3)*(34*x**2 + 28*x)
Expanding the part (34*x**2 + 28*x) using the distributive property, and we got: (28*x)*(37*x**3) + (34*x**2)*(37*x**3)
Replacing (37*x**3)*(34*x**2 + 28*x) with (28*x)*(37*x**3) + (34*x**2)*(37*x**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (28*x)*(37*x**3) + (28*x)*(-44) + (34*x**2)*(37*x**3) + (34*x**2)*(-44)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (28*x)*-44 = -1232*x
  (28*x)*(37*x**3) = 1036*x**4
  (34*x**2)*-44 = -1496*x**2
  (34*x**2)*(37*x**3) = 1258*x**5
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x</replace>
No more calculations needed.
<answer>1258*x**5 + 1036*x**4 - 1496*x**2 - 1232*x</answer>


Question:
Simplify this expression: -22*x*(11*x - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -242*x**2 + 792*x

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -22*x*(11*x - 36)
Expanding the part (11*x - 36) using the distributive property, and we got: (-22*x)*(11*x) - (-1)*792*x
<replace-#Step 1>#Step 2:
Current expression: (-22*x)*(11*x) - (-1)*792*x</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  -36*(-22*x) = 792*x
  (11*x)*(-22*x) = -242*x**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -242*x**2 + 792*x</replace>
No more calculations needed.
<answer>-242*x**2 + 792*x</answer>


Question:
Calculate the following: (-49*z - 38)*(-32*z**3 - 41*z**2 + 27*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 1568*z**4 + 3225*z**3 + 235*z**2 - 1026*z


Question:
Calculate the following: (66 - 27*y**3)*(29*y**2 - 59*y - 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: -783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706

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: (66 - 27*y**3)*(29*y**2 - 59*y - 41)
Expanding the part (66 - 27*y**3) using the distributive property, and we got: (-27*y**3)*(29*y**2 - 59*y - 41) + 66*(29*y**2 - 59*y - 41)
<replace-#Step 1>#Step 2:
Current expression: (-27*y**3)*(29*y**2 - 59*y - 41) + 66*(29*y**2 - 59*y - 41)</replace>
Simplifying the partial expression: 66*(29*y**2 - 59*y - 41)
Expanding the part (29*y**2 - 59*y - 41) using the distributive property, and we got: -59*y*66 + (29*y**2)*66 - 41*66
Replacing 66*(29*y**2 - 59*y - 41) with -59*y*66 + (29*y**2)*66 - 41*66 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -59*y*66 + (29*y**2)*66 + (-27*y**3)*(29*y**2 - 59*y - 41) - 2706</replace>
Simplifying the partial expression: (-27*y**3)*(29*y**2 - 59*y - 41)
Expanding the part (29*y**2 - 59*y - 41) using the distributive property, and we got: (-59*y)*(-27*y**3) - (-1)*1107*y**3 + (29*y**2)*(-27*y**3)
Replacing (-27*y**3)*(29*y**2 - 59*y - 41) with (-59*y)*(-27*y**3) - (-1)*1107*y**3 + (29*y**2)*(-27*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-59*y)*(-27*y**3) - 59*y*66 - 41*(-27)*y**3 + (29*y**2)*(-27*y**3) + (29*y**2)*66 - 2706</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-59*y)*66 = -3894*y
  (-59*y)*(-27*y**3) = 1593*y**4
  (29*y**2)*66 = 1914*y**2
  (29*y**2)*(-27*y**3) = -783*y**5
  -41*-27*y**3 = 1107*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706</replace>
No more calculations needed.
<answer>-783*y**5 + 1593*y**4 + 1107*y**3 + 1914*y**2 - 3894*y - 2706</answer>


Question:
Calculate the following: (39*z**2 + 53*z)*(-14*z**3 + 92*z**2 - 20)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -546*z**5 + 2846*z**4 + 4876*z**3 - 780*z**2 - 1060*z


Question:
Calculate the following: 56*y*(32*y**3 + 18*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: 1792*y**4 + 1008*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: 56*y*(32*y**3 + 18*y**2)
Expanding the part (32*y**3 + 18*y**2) using the distributive property, and we got: (56*y)*(18*y**2) + (56*y)*(32*y**3)
<replace-#Step 1>#Step 2:
Current expression: (56*y)*(18*y**2) + (56*y)*(32*y**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (18*y**2)*(56*y) = 1008*y**3
  (32*y**3)*(56*y) = 1792*y**4
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: 1792*y**4 + 1008*y**3</replace>
No more calculations needed.
<answer>1792*y**4 + 1008*y**3</answer>


Question:
Simplify this expression: (8*z**3 - 48*z**2 - 28*z)*(31*z**3 - 15*z**2 + 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: 248*z**6 - 1608*z**5 - 148*z**4 + 756*z**3 - 2016*z**2 - 1176*z


Question:
Calculate the following: -47*z*(14*z**3 + 41*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -658*z**4 - 1927*z**2

Let's solve the polynomial multiplication step by step. We can expand all partial products first, then add all of them together. Here's the solution steps:
#Step 1:
Current expression: -47*z*(14*z**3 + 41*z)
Expanding the part (14*z**3 + 41*z) using the distributive property, and we got: (-47*z)*(41*z) + (-47*z)*(14*z**3)
<replace-#Step 1>#Step 2:
Current expression: (-47*z)*(41*z) + (-47*z)*(14*z**3)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (14*z**3)*(-47*z) = -658*z**4
  (41*z)*(-47*z) = -1927*z**2
Replacing them in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -658*z**4 - 1927*z**2</replace>
No more calculations needed.
<answer>-658*z**4 - 1927*z**2</answer>


Question:
Calculate the following: (57*y - 14)*(-47*y**3 + 18*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: -2679*y**4 + 1684*y**3 - 252*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: (57*y - 14)*(-47*y**3 + 18*y**2)
Expanding the part (57*y - 14) using the distributive property, and we got: (57*y)*(-47*y**3 + 18*y**2) - 14*(-47*y**3 + 18*y**2)
<replace-#Step 1>#Step 2:
Current expression: (57*y)*(-47*y**3 + 18*y**2) - 14*(-47*y**3 + 18*y**2)</replace>
Simplifying the partial expression: -14*(-47*y**3 + 18*y**2)
Expanding the part (-47*y**3 + 18*y**2) using the distributive property, and we got: (18*y**2)*(-14) - 47*y**3*(-14)
Replacing -14*(-47*y**3 + 18*y**2) with (18*y**2)*(-14) - 47*y**3*(-14) in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (57*y)*(-47*y**3 + 18*y**2) + (18*y**2)*(-14) - 47*y**3*(-14)</replace>
Simplifying the partial expression: (57*y)*(-47*y**3 + 18*y**2)
Expanding the part (-47*y**3 + 18*y**2) using the distributive property, and we got: (57*y)*(18*y**2) + (57*y)*(-47*y**3)
Replacing (57*y)*(-47*y**3 + 18*y**2) with (57*y)*(18*y**2) + (57*y)*(-47*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (57*y)*(18*y**2) + (57*y)*(-47*y**3) + (18*y**2)*(-14) - 47*y**3*(-14)</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-47*y**3)*-14 = 658*y**3
  (-47*y**3)*(57*y) = -2679*y**4
  (18*y**2)*-14 = -252*y**2
  (18*y**2)*(57*y) = 1026*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -2679*y**4 + 658*y**3 + 1026*y**3 - 252*y**2</replace>
Combining like terms, got -2679*y**4 + 1684*y**3 - 252*y**2
<replace-#Step 5>#Step 6:
Current expression: -2679*y**4 + 1684*y**3 - 252*y**2</replace>
No more calculations needed.
<answer>-2679*y**4 + 1684*y**3 - 252*y**2</answer>


Question:
Simplify this expression: (31 - 29*z**2)*(z**3 + 27*z**2 - 30*z)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*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: (31 - 29*z**2)*(z**3 + 27*z**2 - 30*z)
Expanding the part (31 - 29*z**2) using the distributive property, and we got: (-29*z**2)*(z**3 + 27*z**2 - 30*z) + 31*(z**3 + 27*z**2 - 30*z)
<replace-#Step 1>#Step 2:
Current expression: (-29*z**2)*(z**3 + 27*z**2 - 30*z) + 31*(z**3 + 27*z**2 - 30*z)</replace>
Simplifying the partial expression: 31*(z**3 + 27*z**2 - 30*z)
Expanding the part (z**3 + 27*z**2 - 30*z) using the distributive property, and we got: -30*z*31 + z**3*31 + (27*z**2)*31
Replacing 31*(z**3 + 27*z**2 - 30*z) with -30*z*31 + z**3*31 + (27*z**2)*31 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: -30*z*31 + z**3*31 + (-29*z**2)*(z**3 + 27*z**2 - 30*z) + (27*z**2)*31</replace>
Simplifying the partial expression: (-29*z**2)*(z**3 + 27*z**2 - 30*z)
Expanding the part (z**3 + 27*z**2 - 30*z) using the distributive property, and we got: (-30*z)*(-29*z**2) + (-29*z**2)*z**3 + (-29*z**2)*(27*z**2)
Replacing (-29*z**2)*(z**3 + 27*z**2 - 30*z) with (-30*z)*(-29*z**2) + (-29*z**2)*z**3 + (-29*z**2)*(27*z**2) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-30*z)*(-29*z**2) - 30*z*31 + (-29*z**2)*z**3 + z**3*31 + (-29*z**2)*(27*z**2) + (27*z**2)*31</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  z**3*31 = 31*z**3
  z**3*(-29*z**2) = -29*z**5
  (-30*z)*31 = -930*z
  (-30*z)*(-29*z**2) = 870*z**3
  (27*z**2)*31 = 837*z**2
  (27*z**2)*(-29*z**2) = -783*z**4
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -29*z**5 - 783*z**4 + 31*z**3 + 870*z**3 + 837*z**2 - 930*z</replace>
Combining like terms, got -29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z
<replace-#Step 5>#Step 6:
Current expression: -29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z</replace>
No more calculations needed.
<answer>-29*z**5 - 783*z**4 + 901*z**3 + 837*z**2 - 930*z</answer>


Question:
Simplify this expression: (48 - 17*y**3)*(31*y**3 + 59)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: -527*y**6 + 485*y**3 + 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: (48 - 17*y**3)*(31*y**3 + 59)
Expanding the part (48 - 17*y**3) using the distributive property, and we got: (-17*y**3)*(31*y**3 + 59) + 48*(31*y**3 + 59)
<replace-#Step 1>#Step 2:
Current expression: (-17*y**3)*(31*y**3 + 59) + 48*(31*y**3 + 59)</replace>
Simplifying the partial expression: 48*(31*y**3 + 59)
Expanding the part (31*y**3 + 59) using the distributive property, and we got: (31*y**3)*48 + 59*48
Replacing 48*(31*y**3 + 59) with (31*y**3)*48 + 59*48 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-17*y**3)*(31*y**3 + 59) + (31*y**3)*48 + 2832</replace>
Simplifying the partial expression: (-17*y**3)*(31*y**3 + 59)
Expanding the part (31*y**3 + 59) using the distributive property, and we got: 59*(-17*y**3) + (-17*y**3)*(31*y**3)
Replacing (-17*y**3)*(31*y**3 + 59) with 59*(-17*y**3) + (-17*y**3)*(31*y**3) in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: 59*(-17)*y**3 + (-17*y**3)*(31*y**3) + (31*y**3)*48 + 2832</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (31*y**3)*48 = 1488*y**3
  (31*y**3)*(-17*y**3) = -527*y**6
  59*-17*y**3 = -1003*y**3
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: -527*y**6 - 1003*y**3 + 1488*y**3 + 2832</replace>
Combining like terms, got -527*y**6 + 485*y**3 + 2832
<replace-#Step 5>#Step 6:
Current expression: -527*y**6 + 485*y**3 + 2832</replace>
No more calculations needed.
<answer>-527*y**6 + 485*y**3 + 2832</answer>


Question:
Calculate the following: (39 - 19*z)*(-50*z**2 + 33*z - 23)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.

Answer: 950*z**3 - 2577*z**2 + 1724*z - 897

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: (39 - 19*z)*(-50*z**2 + 33*z - 23)
Expanding the part (39 - 19*z) using the distributive property, and we got: (-19*z)*(-50*z**2 + 33*z - 23) + 39*(-50*z**2 + 33*z - 23)
<replace-#Step 1>#Step 2:
Current expression: (-19*z)*(-50*z**2 + 33*z - 23) + 39*(-50*z**2 + 33*z - 23)</replace>
Simplifying the partial expression: 39*(-50*z**2 + 33*z - 23)
Expanding the part (-50*z**2 + 33*z - 23) using the distributive property, and we got: (33*z)*39 - 50*z**2*39 - 23*39
Replacing 39*(-50*z**2 + 33*z - 23) with (33*z)*39 - 50*z**2*39 - 23*39 in the overall expression.
<replace-#Step 2>#Step 3:
Current expression: (-19*z)*(-50*z**2 + 33*z - 23) + (33*z)*39 - 50*z**2*39 - 897</replace>
Simplifying the partial expression: (-19*z)*(-50*z**2 + 33*z - 23)
Expanding the part (-50*z**2 + 33*z - 23) using the distributive property, and we got: (-19*z)*(33*z) + (-19*z)*(-50*z**2) - (-1)*437*z
Replacing (-19*z)*(-50*z**2 + 33*z - 23) with (-19*z)*(33*z) + (-19*z)*(-50*z**2) - (-1)*437*z in the overall expression.
<replace-#Step 3>#Step 4:
Current expression: (-19*z)*(33*z) + (-19*z)*(-50*z**2) - 23*(-19)*z + (33*z)*39 - 50*z**2*39 - 897</replace>
No partial expression needs using the distributive property to simplify.
Calculating the product of the terms in the current expression:
  (-50*z**2)*39 = -1950*z**2
  (-50*z**2)*(-19*z) = 950*z**3
  (33*z)*39 = 1287*z
  (33*z)*(-19*z) = -627*z**2
  -23*-19*z = 437*z
Replacing them in the overall expression.
<replace-#Step 4>#Step 5:
Current expression: 950*z**3 - 1950*z**2 - 627*z**2 + 437*z + 1287*z - 897</replace>
Combining like terms, got 950*z**3 - 2577*z**2 + 1724*z - 897
<replace-#Step 5>#Step 6:
Current expression: 950*z**3 - 2577*z**2 + 1724*z - 897</replace>
No more calculations needed.
<answer>950*z**3 - 2577*z**2 + 1724*z - 897</answer>