Question:
Factorize:
$125 a^{3}+\frac{1}{8}$
Solution:
$125 a^{3}+\frac{1}{8}=(5 a)^{3}+\left(\frac{1}{2}\right)^{3}$
$=\left(5 a+\frac{1}{2}\right)\left[(5 a)^{2}-5 a \times \frac{1}{2}+\left(\frac{1}{2}\right)^{2}\right]$
$=\left(5 a+\frac{1}{2}\right)\left(25 a^{2}-\frac{5 a}{2}+\frac{1}{4}\right)$
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