Solve (x-3)(x-5)-2(x+1)(x-1)=

$$( x - 3 ) ( x - 5 ) - 2 ( x + 1 ) ( x - 1 ) =$$

Evaluate

$$17-8x-x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x-5.

$$x^{2}-5x-3x+15-2\left(x+1\right)\left(x-1\right)$$

Combine -5x and -3x to get -8x.

$$x^{2}-8x+15-2\left(x+1\right)\left(x-1\right)$$

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

$$x^{2}-8x+15+\left(-2x-2\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -2x-2 by each term of x-1.

$$x^{2}-8x+15-2x^{2}+2x-2x+2$$

Combine 2x and -2x to get 0.

$$x^{2}-8x+15-2x^{2}+2$$

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

$$-x^{2}-8x+15+2$$

Add 15 and 2 to get 17.

$$-x^{2}-8x+17$$

Expand

$$17-8x-x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x-5.

$$x^{2}-5x-3x+15-2\left(x+1\right)\left(x-1\right)$$

Combine -5x and -3x to get -8x.

$$x^{2}-8x+15-2\left(x+1\right)\left(x-1\right)$$

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

$$x^{2}-8x+15+\left(-2x-2\right)\left(x-1\right)$$

Apply the distributive property by multiplying each term of -2x-2 by each term of x-1.

$$x^{2}-8x+15-2x^{2}+2x-2x+2$$

Combine 2x and -2x to get 0.

$$x^{2}-8x+15-2x^{2}+2$$

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

$$-x^{2}-8x+15+2$$

Add 15 and 2 to get 17.

$$-x^{2}-8x+17$$