Factorize the equation $4 a^{2} - 12 a + 9 - 49 b^{2}$

(2 a - 7 b - 3) (a - 7 b - 3)

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(2 a + b - 3) (2 a - 11 b - 3)

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

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

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Solution

The correct option is A $(2 a + 7 b - 3) (2 a - 7 b - 3)$
$4 a^{2} - 12 a + 9 - 49 b^{2}$
$= (2 a)^{2} - 2 (2 a) (3) + (3)^{2} - (7 b)^{2}$
$= (2 a - 3)^{2} - (7 b)^{2}$
$= (2 a - 3 + 7 b) (2 a - 3 - 7 b)$

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4 a^{2} - 49 b^{2} + 2 a - 7 b

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