Factorise $a^{2} - (2 a + 3 b)^{2}$ is _____.

- 2 a (a + b^{2}) (a^{2} + 3 b)

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- 6 a (8 a + b) (3 a + b^{2})

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(2 a + 5 b) (7 a + 3 b)

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

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Solution

The correct option is D $- a (a + b) (a + 3 b)$
$a^{2} - (2 a + 3 b)^{2}$
We know $a^{2} - b^{2} = (a + b) (a - b)$
$a^{2} - (2 a + 3 b)^{2}$
$= (a + (2 a + 3 b)) (a - (2 a + 3 b))$
$= (3 a + 3 b) (- a + 3 b)$
$= - a (a + b) (a + 3 b)$

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