Question

Factorize:

$\frac{x^3}{216}-8y^3$

Answer 1

$\frac{x^3}{216}-8y^3={\left(\frac{x}{6}\right)}^3-(2y{)}^3=(\frac{x}{6}-2y)[{\left(\frac{x}{6}\right)}^2+\frac{x}{6}\times 2y+(2y{)}^2]=(\frac{x}{6}-2y)[\frac{x^2}{36}+\frac{xy}{3}+4y^2]$