Factorize the following expression
$4 a^{2} + b^{2} + 9 c^{2} - 4 a b - 6 b c + 12 c a$

(2 a - b + 3 c)^{2}

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(2 a - b - 3 c)^{2}

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(2 a + b + 3 c)^{2}

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None of these

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Solution

The correct option is A $(2 a - b + 3 c)^{2}$
$4 a^{2} + b^{2} + 9 c^{2} - 4 a b - 6 b c + 12 c a$

$= (2 a)^{2} + (- b)^{2} + (3 c)^{2} - 2 (2 a) (b) - 2 (b) - 2 (b) (3 c) + 2 (3 c) (2 a)$

Using identity $= (A + B + C)^{2} = A^{2} + B^{2} + C^{2} + 2 A B + 2 B C + 2 C A$ ...........(i)

$= (2 a)^{2} + (b)^{2} + (3 c)^{2} + 2 (2 a) (- b) + 2 (3 c) (- b) + 2 (2 a) (3 c)$

$= (2 a - b + 3 c)^{2}$ ( using Identity )

Suggest Corrections

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(b) $(2 a - b + 2)^{2}$

(d) None of these

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