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

Question

Factorise the following using the identity $a^2-b^2=(a+b)(a-b)$.
$\frac{\text{x}^3\text{y}}{9}-\frac{\text{xy}^3}{16}$

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Answer

$\frac{\text{x}^3\text{y}}{9}-\frac{\text{xy}^3}{16}$$=\text{xy}\Big(\frac{\text{x}^2}{9}-\frac{\text{y}^2}{16}\Big)$
$=\text{xy}\bigg[\Big(\frac{\text{x}}{3}\Big)^2-\Big(\frac{\text{y}}{4}\Big)^2\bigg]$
$=\text{xy}\Big(\frac{\text{x}}{3}+\frac{\text{y}}{4}\Big)\Big(\frac{\text{x}}{3}-\frac{\text{y}}{4}\Big)$

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