# How do you factor a^3 + b^3?

Feb 19, 2017

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

#### Explanation:

In order to factor ${a}^{3} + {b}^{3}$
we must recognize that ${a}^{3}$ is a perfect cube with a factor of $a$
and ${b}^{3}$ is a perfect cube with a factor of $b$

The factor pattern for a binomial of perfect cubes is
$\left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$
The factor of ${a}^{3}$ and the factor of ${b}^{3}$ go in the first parenthesis.
The second parenthesis has
the factor of ${a}^{3}$ squared $\left({a}^{2}\right)$
the factor of ${a}^{3}$ times the factor of ${b}^{3}$ $\left(a b\right)$
and the factor of ${b}^{3}$ squared. $\left({b}^{2}\right)$

For the signs we use the SOAP rule.

The First sign is the SAME as the sign in the binomial.