Solve (x+y-z)(x+y+z)

$$( x + y - z ) ( x + y + z )$$

Evaluate

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

Solution Steps

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

$$x^{2}+xy+xz+yx+y^{2}+yz-zx-zy-z^{2}$$

Combine xy and yx to get 2xy.

$$x^{2}+2xy+xz+y^{2}+yz-zx-zy-z^{2}$$

Combine xz and -zx to get 0.

$$x^{2}+2xy+y^{2}+yz-zy-z^{2}$$

Combine yz and -zy to get 0.

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

Expand

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

Solution Steps

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

$$x^{2}+xy+xz+yx+y^{2}+yz-zx-zy-z^{2}$$

Combine xy and yx to get 2xy.

$$x^{2}+2xy+xz+y^{2}+yz-zx-zy-z^{2}$$

Combine xz and -zx to get 0.

$$x^{2}+2xy+y^{2}+yz-zy-z^{2}$$

Combine yz and -zy to get 0.

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