Question

Factorise : $27x^3-\frac{1}{216}-\frac{9}{2}{x}^2+\frac{1}{4}x$

Answer 1

$27x^3-\frac{1}{216}-\frac{9}{2}{x}^2+\frac{1}{4}x$

$={\left(3x\right)}^3-{\left(\frac{1}{6}\right)}^3-3\left({\left(3x\right)}^2\left(\frac{1}{6}\right)\right)+3.3x{\left(\frac{1}{6}\right)}^2$

$={(3x-\frac{1}{6})}^3$.