Factorise the following using the identity a^2- b^2= (a + b)(a - … - Vidyadip

Question

Factorise the following using the identity $a^2- b^2= (a + b)(a - b).$
$3a^2b^3- 27a^4b$

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Answer

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

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