Solve (2x^2-x+2)(-x-3)

$$( 2 x ^ { 2 } - x + 2 ) ( - x - 3 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 2x^{2}-x+2 by -x-3.

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

Multiply -1 and -1 to get 1.

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

Multiply x and x to get x^{2}.

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

Combine -6x^{2} and x^{2} to get -5x^{2}.

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

Multiply 2 and -1 to get -2.

$$-2x^{2}x-5x^{2}+3x+2\left(-1\right)x-6$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2x^{3}-5x^{2}+3x+2\left(-1\right)x-6$$

Multiply 2 and -1 to get -2.

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

Combine 3x and -2x to get x.

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

Expand

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

Solution Steps

Use the distributive property to multiply 2x^{2}-x+2 by -x-3.

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

Multiply -1 and -1 to get 1.

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

Multiply x and x to get x^{2}.

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

Combine -6x^{2} and x^{2} to get -5x^{2}.

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

Multiply 2 and -1 to get -2.

$$-2x^{2}x-5x^{2}+3x+2\left(-1\right)x-6$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-2x^{3}-5x^{2}+3x+2\left(-1\right)x-6$$

Multiply 2 and -1 to get -2.

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

Combine 3x and -2x to get x.

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