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Factorize:a2+...

Question

Factorize:
$a^{2} + 2 a b + b^{2} - 9 c^{2}$

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Solution

$a^{2} + 2 a b + b^{2} - 9 c^{2}$
$= (a + b)^{2} - (3 c)^{2}$
$= (a + b - 3 c) (a + b + 3 c)$ , [Since, $a^{2} - b^{2} = (a + b) (a - b)$ ]

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