Solve -4((x)^(3)+8x-1)-(8(x)^(3)-(x)^(2)-7)(-(x)^(2)+5x+9) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$-4( { x }^{ 3 } +8x-1)-(8 { x }^{ 3 } - { x }^{ 2 } -7)(- { x }^{ 2 } +5x+9)$$

Evaluate

$8x^{5}-41x^{4}-71x^{3}+2x^{2}+3x+67$

Solution Steps

Use the distributive property to multiply $-4$ by $x^{3}+8x-1$.

$$-4x^{3}-32x+4-\left(8x^{3}-x^{2}-7\right)\left(-x^{2}+5x+9\right)$$

Use the distributive property to multiply $8x^{3}-x^{2}-7$ by $-x^{2}+5x+9$ and combine like terms.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}-x^{2}\left(-x^{2}\right)-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Multiply $-1$ and $-1$ to get $1$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}+x^{2}x^{2}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

To multiply powers of the same base, add their exponents. Add $2$ and $2$ to get $4$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}+x^{4}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Combine $40x^{4}$ and $x^{4}$ to get $41x^{4}$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Multiply $-7$ and $-1$ to get $7$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-9x^{2}+7x^{2}-35x-63\right)$$

Combine $-9x^{2}$ and $7x^{2}$ to get $-2x^{2}$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-2x^{2}-35x-63\right)$$

To find the opposite of $8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-2x^{2}-35x-63$, find the opposite of each term.

$$-4x^{3}-32x+4-8x^{3}\left(-x^{2}\right)-41x^{4}-67x^{3}+2x^{2}+35x+63$$

Multiply $-8$ and $-1$ to get $8$.

$$-4x^{3}-32x+4+8x^{3}x^{2}-41x^{4}-67x^{3}+2x^{2}+35x+63$$

To multiply powers of the same base, add their exponents. Add $3$ and $2$ to get $5$.

$$-4x^{3}-32x+4+8x^{5}-41x^{4}-67x^{3}+2x^{2}+35x+63$$

Combine $-4x^{3}$ and $-67x^{3}$ to get $-71x^{3}$.

$$-71x^{3}-32x+4+8x^{5}-41x^{4}+2x^{2}+35x+63$$

Combine $-32x$ and $35x$ to get $3x$.

$$-71x^{3}+3x+4+8x^{5}-41x^{4}+2x^{2}+63$$

Add $4$ and $63$ to get $67$.

$$-71x^{3}+3x+67+8x^{5}-41x^{4}+2x^{2}$$

Expand

$8x^{5}-41x^{4}-71x^{3}+2x^{2}+3x+67$

Solution Steps

Use the distributive property to multiply $-4$ by $x^{3}+8x-1$.

$$-4x^{3}-32x+4-\left(8x^{3}-x^{2}-7\right)\left(-x^{2}+5x+9\right)$$

Use the distributive property to multiply $8x^{3}-x^{2}-7$ by $-x^{2}+5x+9$ and combine like terms.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}-x^{2}\left(-x^{2}\right)-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Multiply $-1$ and $-1$ to get $1$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}+x^{2}x^{2}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

To multiply powers of the same base, add their exponents. Add $2$ and $2$ to get $4$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+40x^{4}+67x^{3}+x^{4}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Combine $40x^{4}$ and $x^{4}$ to get $41x^{4}$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-9x^{2}-7\left(-x^{2}\right)-35x-63\right)$$

Multiply $-7$ and $-1$ to get $7$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-9x^{2}+7x^{2}-35x-63\right)$$

Combine $-9x^{2}$ and $7x^{2}$ to get $-2x^{2}$.

$$-4x^{3}-32x+4-\left(8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-2x^{2}-35x-63\right)$$

To find the opposite of $8x^{3}\left(-x^{2}\right)+41x^{4}+67x^{3}-2x^{2}-35x-63$, find the opposite of each term.

$$-4x^{3}-32x+4-8x^{3}\left(-x^{2}\right)-41x^{4}-67x^{3}+2x^{2}+35x+63$$

Multiply $-8$ and $-1$ to get $8$.

$$-4x^{3}-32x+4+8x^{3}x^{2}-41x^{4}-67x^{3}+2x^{2}+35x+63$$

To multiply powers of the same base, add their exponents. Add $3$ and $2$ to get $5$.

$$-4x^{3}-32x+4+8x^{5}-41x^{4}-67x^{3}+2x^{2}+35x+63$$

Combine $-4x^{3}$ and $-67x^{3}$ to get $-71x^{3}$.

$$-71x^{3}-32x+4+8x^{5}-41x^{4}+2x^{2}+35x+63$$

Combine $-32x$ and $35x$ to get $3x$.

$$-71x^{3}+3x+4+8x^{5}-41x^{4}+2x^{2}+63$$

Add $4$ and $63$ to get $67$.

$$-71x^{3}+3x+67+8x^{5}-41x^{4}+2x^{2}$$