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

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

Evaluate

$$-z^{2}$$

Solution Steps

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

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

Use the distributive property to multiply z by x+z.

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

To find the opposite of zx+z^{2}, find the opposite of each term.

$$zx-z^{2}-zx-z^{2}+z^{2}$$

Combine zx and -zx to get 0.

$$-z^{2}-z^{2}+z^{2}$$

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

$$-2z^{2}+z^{2}$$

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

$$-z^{2}$$

Expand

$$-z^{2}$$

Solution Steps

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

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

Use the distributive property to multiply z by x+z.

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

To find the opposite of zx+z^{2}, find the opposite of each term.

$$zx-z^{2}-zx-z^{2}+z^{2}$$

Combine zx and -zx to get 0.

$$-z^{2}-z^{2}+z^{2}$$

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

$$-2z^{2}+z^{2}$$

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

$$-z^{2}$$