# How do you factor 125x^3+1/125?

Apr 14, 2018

$125 {x}^{3} + \frac{1}{125} = \left(5 x + \frac{1}{5}\right) \left(25 {x}^{2} - x + \frac{1}{25}\right)$.
Recall that, ${a}^{3} + {b}^{3} = \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right)$.
With $a = 5 x , \mathmr{and} , b = \frac{1}{5}$, we get,
$125 {x}^{3} + \frac{1}{125} = \left(5 x + \frac{1}{5}\right) \left(25 {x}^{2} - x + \frac{1}{25}\right)$.