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Expansion of (x^2 - y^2)

Factorise the...

Question

Factorise the following:
$12 x y (9 x^{2} - 16 y^{2}) \div 4 x y (3 x + 4 y)$

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Solution

$12 x y (9 x^{2} - 16 y^{2}) = 12 x y (3 x)^{2} - (4 y)^{2}$
$= 12 x y (3 x + 4 y) (3 x - 4 y)$ ......... (1)
$\frac{12 x y (9 x^{2} - 16 y^{2})}{4 x y (3 x + 4 y)}$ [from (1)]
$= \frac{12 x y (3 x + 4 y) (3 x - 4 y)}{4 x y (3 x + 4 y)}$
$= 3 (3 x - 4 y)$

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