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Expansion of (x^2 - y^2)

Factorise usi...

Question

Factorise using suitable identiy:.
$64 x^{2} y^{2} - {9 x}^{2} + 18 x y - {9 y}^{2}$

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Solution

$64 x^{2} y^{2} - 9 x^{2} + 18 x y - {9 y}^{2}$
$= 64 x^{2} y^{2} - ({9 x}^{2} - 18 x y + 9 y^{2})$
$= 64 x^{2} y^{2} - ({(3 x - 3 y)}^{2})$
$= {(8 x y)}^{2} - {(3 x - 3 y)}^{2}$
$= (3 x - 3 y + 8 x y) (8 x y - (3 x - 3 y))$

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