# How do you factor 192u^3 - 81?

Mar 23, 2018

$3 \left(16 {u}^{2} + 12 u + 9\right)$

#### Explanation:

$3 \left(64 {u}^{3} - 27\right)$
3[(4u)^3-(3)^3)]
We know that ${a}^{3} - {b}^{3} = \left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right)$
In this case, $a = 4 u$ and $b = 3$
Therefore:
${\left(4 u\right)}^{3} - {\left(3\right)}^{3} = \left(4 u - 3\right) \left(16 {u}^{2} + 12 u + 9\right)$
$3 \left(16 {u}^{2} + 12 u + 9\right)$ (we still have the 3 leftover from before)