Solve (x+3)(-x+5)-(-x^2+2x+3)

$$( x + 3 ) ( - x + 5 ) - ( - x ^ { 2 } + 2 x + 3 )$$

Evaluate

$$12$$

Solution Steps

Use the distributive property to multiply x+3 by -x+5.

$$x\left(-x\right)+5x+3\left(-x\right)+15-\left(-x^{2}+2x+3\right)$$

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

$$x\left(-x\right)+5x+3\left(-x\right)+15-\left(-x^{2}\right)-2x-3$$

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

$$x\left(-x\right)+3x+3\left(-x\right)+15-\left(-x^{2}\right)-3$$

Subtract 3 from 15 to get 12.

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

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

$$x^{2}\left(-1\right)+3x+3\left(-1\right)x+12-\left(-x^{2}\right)$$

Multiply 3 and -1 to get -3.

$$x^{2}\left(-1\right)+3x-3x+12-\left(-x^{2}\right)$$

Combine 3x and -3x to get 0.

$$x^{2}\left(-1\right)+12-\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$x^{2}\left(-1\right)+12+x^{2}$$

Combine x^{2}\left(-1\right) and x^{2} to get 0.

$$12$$

Factor

$$2^{2}\times 3$$