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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply x by 2x-2y.

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

Use the distributive property to multiply x by 2y-x.

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

Combine -2xy and 2xy to get 0.

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

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

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

Use the distributive property to multiply -2 by x^{2}-y^{2}.

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply x by 2x-2y.

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

Use the distributive property to multiply x by 2y-x.

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

Combine -2xy and 2xy to get 0.

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

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

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

Use the distributive property to multiply -2 by x^{2}-y^{2}.

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

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

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