# How do you factor x^3y^3 + z^3?

Jul 22, 2015

Use sum of cubes identity to find:

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

#### Explanation:

Use the sum of cubes identity:

${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$

with $a = x y$ and $b = z$ as follows:

${x}^{3} {y}^{3} + {z}^{3}$

$= {\left(x y\right)}^{3} + {z}^{3}$

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

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