Factorise: 27 a^2-48 b^2 - Vidyadip

Question

Factorise:
$27 a^2-48 b^2$

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Answer

$27 a^2-48 b^2=3\left(9 a^2-16 b^2\right)$
$=3\left[(3 a)^2-(4 b)^2\right]$
$=3(3 a+4 b)(3 a-4 b)$
$\left[\therefore a^2-b^2=(a-b)(a+b)\right]$

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