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

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

Evaluate

$$2x^{2}$$

Solution Steps

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

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

Combine -xy and 2yx to get xy.

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

Use the distributive property to multiply y by x-y.

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

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

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

The opposite of -y^{2} is y^{2}.

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

Combine xy and -yx to get 0.

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

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

$$2x^{2}$$

Expand

$$2x^{2}$$

Solution Steps

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

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

Combine -xy and 2yx to get xy.

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

Use the distributive property to multiply y by x-y.

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

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

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

The opposite of -y^{2} is y^{2}.

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

Combine xy and -yx to get 0.

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

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

$$2x^{2}$$