Factorise the given polynomial:
$4 a^{2} - 12 a b + 9 b^{2} + 4 a - 6 b$

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

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

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

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

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Solution

The correct option is A $(2 a - 3 b) (2 a - 3 b + 2)$
Given eq $4 a^{2} - 12 a b + 9 b^{2} + 4 a - 6 b$
$[4 a^{2} - 12 a b + 9 b^{2}] + 4 a - 6 b$
Now factorizing
$[4 a^{2} - 6 a b - 6 a b + 9 b^{2}] + 2 (2 a - 3 b)$
$[2 a (2 a - 3 b) - 3 b (2 a - 3 b)] + 2 (2 a - 3 b)$
$[(2 a - 3 b) (2 a - 3 b)] + 2 (2 a - 3 b)$
$[2 a - 3 b (2 a - 3 b) + 2]$
$(2 a - 3 b + 2) (2 a - 3 b)$

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