The determinant a2 a2-(b-c)2 bcb2 b2-(c-a)2 cac2 c2-(a-b)2 abis divisible by

( a + b ) ( b + c ) ( c + a ) , ( a - b ) ( b - c ) ( c - a ) , a + b + c

Using C 2 → C 2 − C 1 − 2 C 3 , then C 1 → C 1 + C 2 take a 2 + b 2 + c 2 common from first column]

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The determinant $|\begin{matrix} a^{2} & a^{2} - {(b - c)}^{2} & b c \\ b^{2} & b^{2} - {(c - a)}^{2} & c a \\ c^{2} & c^{2} - {(a - b)}^{2} & a b \end{matrix}|$ is divisible by

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$(a + b) (b + c) (c + a)$

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

$(a - b) (b - c) (c - a)$

$a + b + c$

answer is A, C, D.

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Using $C_{2} \to C_{2} - C_{1} - 2 C_{3}, then C_{1} \to C_{1} + C_{2} take a^{2} + b^{2} + c^{2}$ common from first column]

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