Question

Factorise this question

Answer 1

$x {}^{3} - \frac{1}{125} - \frac{1}{15} x {}^{2} + \frac{1}{25} x$
It is the algebraic Identity form of:-
$(a - b) {}^{3} = {a}^{3} - {b}^{3} - 3 {a}^{2} b+ 3a {b}^{2}$
So, it can be factorised as,
$( \frac{x}{3} ) {}^{3} - ( \frac{1}{5} ) {}^{3} - 3 \times ( \frac{x}{3} ) {}^{2} \times \frac{1}{5} \\ + 3 \times \frac{x}{3} \times ( \frac{1}{5} ) {}^{2} \\ = ( \frac{x}{3} - \frac{1}{5} ) {}^{3} \\ = ( \frac{x}{3} - \frac{1}{5} )( \frac{x}{3} - \frac{1}{5} )( \frac{x}{3} - \frac{1}{5} )$