Factorize: $a^{2} + 4 b^{2} - 3 a + 6 b - 4 a b$

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

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

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

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

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Solution

The correct option is B $(a - 2 b) (a - 2 b - 3)$
$a^{2} + 4 b^{2} - 3 a + 6 b - 4 a b$
$= a^{2} - 4 a b + (2 b)^{2} - 3 a + 6 b$
$= a^{2} - 2 (a) (2 b) + (2 b)^{2} - 3 (a - 2 b)$
$= (a - 2 b)^{2} - 3 (a - 2 b)$
$= (a - 2 b) (a - 2 b - 3)$

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