Question

Factorise: $27a^3-\frac{27}{5}{a}^2+\frac{9}{25}a-\frac{1}{125}$

Answer 1

$27a^3-\frac{27}{5}{a}^2+\frac{9}{25}a-\frac{1}{125}$
$=(3a{)}^3+3\times \frac{-1}{5}\times (3a{)}^2+3\times \frac{1}{25}\times 3a-{\frac{1}{5}}^3$
$=(3a{)}^3+3\times \frac{-1}{5}\times (3a\left)\right(\frac{-1}{5}+3a)-{\frac{1}{5}}^3$
Using,$(a-b{)}^3=a^3-b^3-3ab(a-b)$
$={(3a-\frac{1}{5})}^3$
$=(3a-\frac{1}{5})(3a-\frac{1}{5})(3a-\frac{1}{5})$