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

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

Evaluate

$$-y\left(x+3y\right)$$

Solution Steps

Use the distributive property to multiply x+2y by x-y and combine like terms.

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

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

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

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

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

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

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

Combine xy and -2xy to get -xy.

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

Combine -2y^{2} and -y^{2} to get -3y^{2}.

$$-xy-3y^{2}$$

Expand

$$-xy-3y^{2}$$

Solution Steps

Use the distributive property to multiply x+2y by x-y and combine like terms.

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

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

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

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

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

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

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

Combine xy and -2xy to get -xy.

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

Combine -2y^{2} and -y^{2} to get -3y^{2}.

$$-xy-3y^{2}$$