# How do you factor completely x^2 - y^2 +xz - yz?

May 5, 2016

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

#### Explanation:

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

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

$= \left(x - y\right) \left(x + y\right) + \left(x - y\right) z$

$= \left(x - y\right) \left(\left(x + y\right) + z\right)$

$= \left(x - y\right) \left(x + y + z\right)$

Note the step where we replace $\left({x}^{2} - {y}^{2}\right)$ with $\left(x - y\right) \left(x + y\right)$

The identity:

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

is known as the difference of squares identity.