Question
Factorise : $27-125 a^3-135 a+225 a^2$
✓
Answer
$27-125 a^3-135 a+225 a^2$
$=(3)^3-(5 a)^3-3(3)(5 a)(3-5 a)$
$=(3-5 a)^3$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=(3-5 a)(3-5 a)(3-5 a)$
$=(3)^3-(5 a)^3-3(3)(5 a)(3-5 a)$
$=(3-5 a)^3$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=(3-5 a)(3-5 a)(3-5 a)$
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