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Expansion of (x^2 - y^2)

Factorise usi...

Question

Factorise using suitable identity:
$16 p^{2} - 8 p q - {25 r}^{2} + q^{2}$

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Solution

${16 p}^{2} - 8 p q - {25 r}^{2} + q^{2}$
$= {16 p}^{2} - 8 p q + q^{2} - 25 r^{2}$
$= {(4 p - q)}^{2} - {25 r}^{2}$
$= (4 p - q + 5 r) (4 p - q - 5 r)$

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