Question

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

Answer 1

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

According to the equation,

$a^3+b^3=(a+b)(a^2-ab+b^2)$

So we get,

$216x^3+\frac{1}{125}$$=(6x{)}^3+{\left(\frac{1}{5}\right)}^3$

Based on the equation,

$=(6x+\frac{1}{5})\left(\right(6x{)}^2-\left(6x\right)\left(\frac{1}{5}\right)+{\left(\frac{1}{5}\right)}^2)$

$216x^3+\frac{1}{125}$$=(6x+\frac{1}{5})({36}^2-\frac{6x}{5}+\frac{1}{25})$