Factorise $4 a^{2} - 4 a b + b^{2} - 9 c^{2} + 12 c d - 4 d^{2}$

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

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

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

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

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Solution

The correct option is B $(2 a - b + 3 c - 2 d) (2 a - b - 3 c + 2 d)$
$4 a^{2} - 4 a b + b^{2} - 9 c^{2} + 12 c d - 4 d^{2} = (4 a^{2} - 4 a b + b^{2}) - (9 c^{2} - 12 c d + 4 d^{2}) = (2 a - b)^{2} - (3 c - 2 d)^{2} = (2 a - b + 3 c - 2 d) (2 a - b - 3 c + 2 d)$

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