Question

Factorize :

$27-125a^3-135a+225a^2$

Answer 1

given, $27-125a^3-135a+225a^2$

$=3^3+(-5a{)}^3-45a(3-5a)$

$=(3{)}^3+(-5a{)}^3+3\times 3\times (-5a)[3+(-5a\left)\right]$

$=[3+(-5a){]}^3$

$=(3-5a{)}^3$

$=(3-5a)(3-5a)(3-5a)$