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

Nov 30, 2015

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

#### Explanation:

This is a sum of cubes.

This is a semi-important identity to know:

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

Although it doesn't apply directly to this question, it's also important to know that $\left({x}^{3} - {y}^{3}\right) = \left(x - y\right) \left({x}^{2} + x y + {y}^{2}\right)$.

This gives us the rule: (x^3+-y^3)=(x+-y)(x^2∓xy+y^2)