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

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

Evaluate

$$2y\left(x+y\right)$$

Solution Steps

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

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

Multiply -1 and -1 to get 1.

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

Combine xy and -yx to get 0.

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

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

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

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

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

Multiply x and x to get x^{2}.

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

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

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

Expand

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

Solution Steps

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

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

Multiply -1 and -1 to get 1.

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

Combine xy and -yx to get 0.

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

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

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

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

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

Multiply x and x to get x^{2}.

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

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

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