Factorize:
$9 a^{2} + 3 a - 8 b - 64 b^{2}$

(3 a - 8 b) (3 a + 8 b + 1)

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(3 a - 8 b) (a + 8 b + 1)

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(3 a - 8 b) (3 a + b + 1)

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(3 a - 8 b) (3 a + 8 b + 9)

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Solution

The correct option is A $(3 a - 8 b) (3 a + 8 b + 1)$
$9 a^{2} + 3 a - 8 b - 64 b^{2}$

$= 9 a^{2} - 64 b^{2} + 3 a - 8 b$

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

$= (3 a + 8 b) (3 a - 8 b) + (3 a - 8 b)$

$= (3 a - 8 b) (3 a + 8 b + 1)$

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9 a^{2} + 3 a - 8 b - 64 b^{2}

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