Factorise Completely : $4 a^{2} - 12 a b + 9 b^{2} + 4 a - 6 b$

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Solution

$[4 a^{2} - 12 a b + 9 b^{2}] + [4 a - 6 b] = [(2 a)^{2} - 2 \times 2 a \times 3 b + (3 b)^{2}] + 2 (2 a - 3 b) = (2 a - 3 b)^{2} + 2 (2 a - 3 b) = (2 a - 3 b) (2 a - 3 b + 2)$

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