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Factorisation Using Algebraic Identities

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Question

Factorise $36 a^{2} - 49 b^{2}$

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Solution

Observe that $36 a^{2} = (6 a)^{2}$ and $49 b^{2} = (7 b)^{2}$ . Thus we get
$36 a^{2} - 49 b^{2} = (6 a)^{2} - (7 b)^{2} = (6 a + 7 b) (6 a - 7 b)$ .

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