Factorize the equation $a^{2} - {(2 a + 3 b)}^{2}$

3 (a - b) (a - 3 b)

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- 3 (a + b) (a + 3 b)

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3 (a - b) (3 a + b)

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- 3 (3 a + b) (a - 3 b)

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Solution

The correct option is A $- 3 (a + b) (a + 3 b)$
$a^{2} - {(2 a + 3 b)}^{2}$
Using,
$a^{2} - b^{2} = (a + b) (a - b)$
$= (a + 2 a + 3 b) (a - (2 a + 3 b))$
$= (3 a + 3 b) (- a - 3 b)$
$= - 3 (a + b) (a + 3 b)$

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