Question

Factorize:
$216x^3+\frac{1}{125}$

Answer 1

$$\begin{gathered} 216x^3+\frac{1}{125}={\left(6x\right)}^3+{\left(\frac{1}{5}\right)}^3 \\ =\left(6x+\frac{1}{5}\right)\left[{\left(6x\right)}^2-6x\times \frac{1}{5}+{\left(\frac{1}{5}\right)}^2\right] \\ =\left(6x+\frac{1}{5}\right)\left(36x^2-\frac{6x}{5}+\frac{1}{25}\right) \end{gathered}$$