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

(2 a + b + 4) (a + b + 1)

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(2 a - b - 4) (2 a + b + 1)

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(2 a + b + 4) (a - b - 1)

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(2 a + b - 4) (2 a + b + 1)

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Solution

The correct option is D $(2 a + b - 4) (2 a + b + 1)$
$(2 a + b)^{2} - 6 a - 3 b - 4$
$= (2 a + b)^{2} - 3 (2 a + b) - 4$
$= (2 a + b)^{2} - 4 (2 a + b) + (2 a + b) - 4$
$= (2 a + b) ((2 a + b) - 4) + 1 ((2 a + b) - 4)$
$= (2 a + b - 4) (2 a + b + 1)$

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