# How do you factor 256a^3 + 4?

Mar 17, 2018

$4 \left(4 a + 1\right) \left(16 {a}^{2} - 4 a + 1\right)$

#### Explanation:

Given: $256 {a}^{3} + 4$

Factor out the greatest common factor.

$= 4 \left(64 {a}^{3} + 1\right)$

Now, we need a simple observation that $64 {a}^{3} = {\left(4 a\right)}^{3}$.

$= 4 \left({\left(4 a\right)}^{3} + {1}^{3}\right)$

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

$= 4 \left(4 a + 1\right) \left(16 {a}^{2} - 4 a + 1\right)$