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

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

Evaluate

$$x^{2}-2x+13$$

Solution Steps

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

$$\left(2x+2\right)\left(x-1\right)-\left(x-3\right)\left(x+5\right)$$

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

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

Combine -2x and 2x to get 0.

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

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

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

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

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

To find the opposite of x^{2}+2x-15, find the opposite of each term.

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

The opposite of -15 is 15.

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

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

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

Add -2 and 15 to get 13.

$$x^{2}+13-2x$$

Expand

$$x^{2}-2x+13$$

Solution Steps

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

$$\left(2x+2\right)\left(x-1\right)-\left(x-3\right)\left(x+5\right)$$

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

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

Combine -2x and 2x to get 0.

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

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

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

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

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

To find the opposite of x^{2}+2x-15, find the opposite of each term.

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

The opposite of -15 is 15.

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

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

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

Add -2 and 15 to get 13.

$$x^{2}+13-2x$$