# How do you factor x^6 - y^6?

${x}^{6} - {y}^{6} = \left(x - y\right) \left(x + y\right) \left({x}^{4} + {y}^{4} + {x}^{2} {y}^{2}\right)$

#### Explanation:

${x}^{6} - {y}^{6}$

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

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

$= \left({x}^{2} - {y}^{2}\right) \left({x}^{4} + {y}^{4} + {x}^{2} {y}^{2}\right)$

$= \left(x - y\right) \left(x + y\right) \left({x}^{4} + {y}^{4} + {x}^{2} {y}^{2}\right)$