Question

Factorize:
$125a^3+\frac{1}{8}$

Answer 1

$$\begin{gathered} 125a^3+\frac{1}{8}={\left(5a\right)}^3+{\left(\frac{1}{2}\right)}^3 \\ =\left(5a+\frac{1}{2}\right)\left[{\left(5a\right)}^2-5a\times \frac{1}{2}+{\left(\frac{1}{2}\right)}^2\right] \\ =\left(5a+\frac{1}{2}\right)\left(25a^2-\frac{5a}{2}+\frac{1}{4}\right) \end{gathered}$$