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

4 a^{2} + 9 b^{2} + c^{2} + 12 a b - 6 b c - 4 c a

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4 a^{2} - 9 b^{2} + c^{2} + 12 a b - 6 b c - 4 c a

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4 a^{2} + 9 b^{2} - c^{2} + 12 a b - 6 b c - 4 c a

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None of these

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Solution

The correct option is B $4 a^{2} + 9 b^{2} + c^{2} + 12 a b - 6 b c - 4 c a$
According to the identity: $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

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

$= 4 a^{2} + 9 b^{2} + c^{2} + 12 a b - 6 b c - 4 c a$

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