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

$$( - x - y ) \cdot ( x + y ) - ( - x - y ) ^ { 2 } =$$

Evaluate

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

Solution Steps

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

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

Combine -yx and -2xy to get -3yx.

$$\left(-x\right)x+\left(-x\right)y-3yx-y^{2}-x^{2}-y^{2}$$

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

$$\left(-x\right)x+\left(-x\right)y-3yx-2y^{2}-x^{2}$$

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

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

Combine -xy and -3yx to get -4xy.

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

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

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

Expand

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

Solution Steps

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

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

Combine -yx and -2xy to get -3yx.

$$\left(-x\right)x+\left(-x\right)y-3yx-y^{2}-x^{2}-y^{2}$$

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

$$\left(-x\right)x+\left(-x\right)y-3yx-2y^{2}-x^{2}$$

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

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

Combine -xy and -3yx to get -4xy.

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

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

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