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

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

Evaluate

$$-y\left(4x+y\right)$$

Solution Steps

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

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

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

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

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

$$-2xy-2xy-y^{2}$$

Combine -2xy and -2xy to get -4xy.

$$-4xy-y^{2}$$

Expand

$$-4xy-y^{2}$$

Solution Steps

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+y\right)^{2}.

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

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

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

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

$$-2xy-2xy-y^{2}$$

Combine -2xy and -2xy to get -4xy.

$$-4xy-y^{2}$$