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Factorisation Using Algebraic Identities

Factorise: 49...

Question

Factorise:
$49 a^{2} + 84 a b + 36 b^{2}$

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Solution

$49 a^{2} + 84 a b + 36 b^{2} = (7 a)^{2} + 2 \times 7 a \times 6 b + (6 b)^{2} {∵ a^{2} + 2 a b + b^{2} = (a + b)^{2}} = (7 a + 6 b)^{2}$

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