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Q.

$a^{2} + b^{2} + c^{2} - 2 a b + 2 b c - 2 c a =$

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a

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

b

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

c

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

answer is A.

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Detailed Solution

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

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

$(o r) {(a - b - c)}^{2}$

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