Solve 2(4x^2+x+4)-[4x^2+x+4-2x^3-x^2+3x-6]

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

Evaluate

$$2x^{3}+5x^{2}-2x+10$$

Solution Steps

Use the distributive property to multiply 2 by 4x^{2}+x+4.

$$8x^{2}+2x+8-\left(4x^{2}+x+4-2x^{3}-x^{2}+3x-6\right)$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$8x^{2}+2x+8-\left(3x^{2}+x+4-2x^{3}+3x-6\right)$$

Combine x and 3x to get 4x.

$$8x^{2}+2x+8-\left(3x^{2}+4x+4-2x^{3}-6\right)$$

Subtract 6 from 4 to get -2.

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

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

$$8x^{2}+2x+8-3x^{2}-4x+2+2x^{3}$$

Combine 8x^{2} and -3x^{2} to get 5x^{2}.

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

Combine 2x and -4x to get -2x.

$$5x^{2}-2x+8+2+2x^{3}$$

Add 8 and 2 to get 10.

$$5x^{2}-2x+10+2x^{3}$$

Expand

$$2x^{3}+5x^{2}-2x+10$$

Solution Steps

Use the distributive property to multiply 2 by 4x^{2}+x+4.

$$8x^{2}+2x+8-\left(4x^{2}+x+4-2x^{3}-x^{2}+3x-6\right)$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$8x^{2}+2x+8-\left(3x^{2}+x+4-2x^{3}+3x-6\right)$$

Combine x and 3x to get 4x.

$$8x^{2}+2x+8-\left(3x^{2}+4x+4-2x^{3}-6\right)$$

Subtract 6 from 4 to get -2.

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

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

$$8x^{2}+2x+8-3x^{2}-4x+2+2x^{3}$$

Combine 8x^{2} and -3x^{2} to get 5x^{2}.

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

Combine 2x and -4x to get -2x.

$$5x^{2}-2x+8+2+2x^{3}$$

Add 8 and 2 to get 10.

$$5x^{2}-2x+10+2x^{3}$$