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

$$x - [ 3 x ^ { 3 } + 5 x ^ { 2 } - \{ 7 x ^ { 2 } - ( 4 - 3 x - x ^ { 3 } ) + 6 x ^ { 3 } \} - 3 x ]$$

Evaluate

$$4x^{3}+2x^{2}+7x-4$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Combine x and 6x to get 7x.

$$7x+4x^{3}+2x^{2}-4$$

Expand

$$4x^{3}+2x^{2}+7x-4$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Combine x and 6x to get 7x.

$$7x+4x^{3}+2x^{2}-4$$