Solve 12x-(3x^3+5x^2-(7x^2-(4-3x-x^3)+6{x}^3)-3x)

$$12x-(3 { x }^{ 3 } +5 { x }^{ 2 } -(7 { x }^{ 2 } -(4-3x- { x }^{ 3 } )+6 { x }^{ 3 } )-3x)$$

Evaluate

$$2\left(2x^{3}+x^{2}+9x-2\right)$$

Solution Steps

To find the opposite of 4-3x-x^{3}, find the opposite of each term.

$$12x-\left(3x^{3}+5x^{2}-\left(7x^{2}-4+3x+x^{3}+6x^{3}\right)-3x\right)$$

Combine x^{3} and 6x^{3} to get 7x^{3}.

$$12x-\left(3x^{3}+5x^{2}-\left(7x^{2}-4+3x+7x^{3}\right)-3x\right)$$

To find the opposite of 7x^{2}-4+3x+7x^{3}, find the opposite of each term.

$$12x-\left(3x^{3}+5x^{2}-7x^{2}+4-3x-7x^{3}-3x\right)$$

Combine 5x^{2} and -7x^{2} to get -2x^{2}.

$$12x-\left(3x^{3}-2x^{2}+4-3x-7x^{3}-3x\right)$$

Combine 3x^{3} and -7x^{3} to get -4x^{3}.

$$12x-\left(-4x^{3}-2x^{2}+4-3x-3x\right)$$

Combine -3x and -3x to get -6x.

$$12x-\left(-4x^{3}-2x^{2}+4-6x\right)$$

To find the opposite of -4x^{3}-2x^{2}+4-6x, find the opposite of each term.

$$12x+4x^{3}+2x^{2}-4+6x$$

Combine 12x and 6x to get 18x.

$$18x+4x^{3}+2x^{2}-4$$

Expand

$$4x^{3}+2x^{2}+18x-4$$

Solution Steps

To find the opposite of 4-3x-x^{3}, find the opposite of each term.

$$12x-\left(3x^{3}+5x^{2}-\left(7x^{2}-4+3x+x^{3}+6x^{3}\right)-3x\right)$$

Combine x^{3} and 6x^{3} to get 7x^{3}.

$$12x-\left(3x^{3}+5x^{2}-\left(7x^{2}-4+3x+7x^{3}\right)-3x\right)$$

To find the opposite of 7x^{2}-4+3x+7x^{3}, find the opposite of each term.

$$12x-\left(3x^{3}+5x^{2}-7x^{2}+4-3x-7x^{3}-3x\right)$$

Combine 5x^{2} and -7x^{2} to get -2x^{2}.

$$12x-\left(3x^{3}-2x^{2}+4-3x-7x^{3}-3x\right)$$

Combine 3x^{3} and -7x^{3} to get -4x^{3}.

$$12x-\left(-4x^{3}-2x^{2}+4-3x-3x\right)$$

Combine -3x and -3x to get -6x.

$$12x-\left(-4x^{3}-2x^{2}+4-6x\right)$$

To find the opposite of -4x^{3}-2x^{2}+4-6x, find the opposite of each term.

$$12x+4x^{3}+2x^{2}-4+6x$$

Combine 12x and 6x to get 18x.

$$18x+4x^{3}+2x^{2}-4$$