Solve (x+y+1)*(x-y-1)

$$( x + y + 1 ) \times ( x - y - 1 )$$

Evaluate

$$-\left(y+1\right)^{2}+x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+y+1 by each term of x-y-1.

$$x^{2}-xy-x+yx-y^{2}-y+x-y-1$$

Combine -xy and yx to get 0.

$$x^{2}-x-y^{2}-y+x-y-1$$

Combine -x and x to get 0.

$$x^{2}-y^{2}-y-y-1$$

Combine -y and -y to get -2y.

$$x^{2}-y^{2}-2y-1$$

Expand

$$x^{2}-y^{2}-2y-1$$

Solution Steps

Apply the distributive property by multiplying each term of x+y+1 by each term of x-y-1.

$$x^{2}-xy-x+yx-y^{2}-y+x-y-1$$

Combine -xy and yx to get 0.

$$x^{2}-x-y^{2}-y+x-y-1$$

Combine -x and x to get 0.

$$x^{2}-y^{2}-y-y-1$$

Combine -y and -y to get -2y.

$$x^{2}-y^{2}-2y-1$$