Question

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

Answer 1

We know
$a^3-b^3=\left(a-b\right)\left(a^2+b^2+ab\right)$
We have,
$\frac{x^3}{216}-8y^3={\left(\frac{x}{6}\right)}^3-{\left(2y\right)}^3$
So, $a=\frac{x}{6},b=2y$
$\frac{x^3}{216}-8y^3=\left(\frac{x}{6}-2y\right)\left({\left(\frac{x}{6}\right)}^2+\frac{x}{6}\times 2y+{\left(2y\right)}^2\right)=\left(\frac{x}{6}-2y\right)\left(\frac{x^2}{36}+\frac{xy}{3}+4y^2\right)$