Factorise: 8 a b^2-18 a^3 - Vidyadip

Question

Factorise:
$8 a b^2-18 a^3$

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Answer

$8 a b^2-18 a^3$
$=2 a\left(4 b^2-9 a^2\right)$
$=2 a\left[(2 b)^2-(3 a)^2\right]$
$=2 a(2 b+3 a)(2 b-3 a)\left[\therefore a^2-b^2=(a-b)(a+b)\right]$

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