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Expansion of (x^2 - y^2)

Factorise usi...

Question

Factorise using suitable identity:
$9 {(x - y)}^{2} - 16 {(p - 2 q)}^{2}$

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Solution

$9 {(x - y)}^{2} - 16 {(p - 2 q)}^{2}$
$= {(3 x - 3 y)}^{2} - {(4 p - 8 q)}^{2}$
$= (3 x - 3 y + 4 q - 8 q) (3 x - 3 y - (4 p - 8 q))$

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