Solve (-2x^2+4x-3)-[(4x^2-3x+8)-2(-x^2+x+1)]

$$( - 2 x ^ { 2 } + 4 x - 3 ) - [ ( 4 x ^ { 2 } - 3 x + 8 ) - 2 ( - x ^ { 2 } + x + 1 ) ]$$

Evaluate

$$-8x^{2}+9x-9$$

Solution Steps

Use the distributive property to multiply -2 by -x^{2}+x+1.

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

Multiply -2 and -1 to get 2.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

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

Combine -3x and -2x to get -5x.

$$-2x^{2}+4x-3-\left(6x^{2}-5x+8-2\right)$$

Subtract 2 from 8 to get 6.

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

To find the opposite of 6x^{2}-5x+6, find the opposite of each term.

$$-2x^{2}+4x-3-6x^{2}+5x-6$$

Combine -2x^{2} and -6x^{2} to get -8x^{2}.

$$-8x^{2}+4x-3+5x-6$$

Combine 4x and 5x to get 9x.

$$-8x^{2}+9x-3-6$$

Subtract 6 from -3 to get -9.

$$-8x^{2}+9x-9$$

Expand

$$-8x^{2}+9x-9$$

Solution Steps

Use the distributive property to multiply -2 by -x^{2}+x+1.

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

Multiply -2 and -1 to get 2.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

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

Combine -3x and -2x to get -5x.

$$-2x^{2}+4x-3-\left(6x^{2}-5x+8-2\right)$$

Subtract 2 from 8 to get 6.

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

To find the opposite of 6x^{2}-5x+6, find the opposite of each term.

$$-2x^{2}+4x-3-6x^{2}+5x-6$$

Combine -2x^{2} and -6x^{2} to get -8x^{2}.

$$-8x^{2}+4x-3+5x-6$$

Combine 4x and 5x to get 9x.

$$-8x^{2}+9x-3-6$$

Subtract 6 from -3 to get -9.

$$-8x^{2}+9x-9$$