Find the square of $2 a - b - 3 c$

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

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a^{3} + b^{3} + c^{2} - 4 a b + 6 b c - c a

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

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4 a^{3} + b^{3} + 9 c^{2} - 4 a b - 6 b c - 12 c a

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Solution

The correct option is A $4 a^{2} + b^{2} + 9 c^{2} - 4 a b + 6 b c - 12 c a$
$2 a - b - 3 c$
Squaring, we get
$(2 a - b - 3 c)^{2}$
Using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$
$= (2 a)^{2} + (- b)^{2} + (- 3 c)^{2} + 2 (2 a) (- b) + 2 (- b) (- 3 c) + 2 (2 a) (- 3 c)$
$= 4 a^{2} + b^{2} + 9 c^{2} - 4 a b + 6 b c - 12 c a$

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