Solve (x-y)*(x+2)-(x+y)*(x-2)

$$(x-y) \times (x+2)-(x+y) \times (x-2)$$

Evaluate

$$4x-2xy$$

Solution Steps

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

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

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

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

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

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

The opposite of -2x is 2x.

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

The opposite of -2y is 2y.

$$x^{2}+2x-yx-2y-x^{2}+2x-yx+2y$$

Combine x^{2} and -x^{2} to get 0.

$$2x-yx-2y+2x-yx+2y$$

Combine 2x and 2x to get 4x.

$$4x-yx-2y-yx+2y$$

Combine -yx and -yx to get -2yx.

$$4x-2yx-2y+2y$$

Combine -2y and 2y to get 0.

$$4x-2yx$$

Expand

$$4x-2xy$$

Solution Steps

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

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

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

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

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

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

The opposite of -2x is 2x.

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

The opposite of -2y is 2y.

$$x^{2}+2x-yx-2y-x^{2}+2x-yx+2y$$

Combine x^{2} and -x^{2} to get 0.

$$2x-yx-2y+2x-yx+2y$$

Combine 2x and 2x to get 4x.

$$4x-yx-2y-yx+2y$$

Combine -yx and -yx to get -2yx.

$$4x-2yx-2y+2y$$

Combine -2y and 2y to get 0.

$$4x-2yx$$