Factorize each of the following expressions:

$144 a^{2} - 169 b^{2}$

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Solution

Given: $144 a^{2} - 169 b^{2}$

$∴ 144 a^{2} - 169 b^{2}$
$= (12 a)^{2} - (13 b)^{2}$
$= (12 a + 13 b) (12 a - 13 b)$
$[∵ a^{2} - b^{2} = (a + b) (a - b)]$

Hence, $144 a^{2} - 169 b^{2} = (12 a + 13 b) (12 a - 13 b)$ .

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