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Factors of a Term

If the factor...

Question

If the factors of $a^{2} + b^{2} + 2 (a b + b c + c a)$ are $(a + b + m)$ and $(a + b + n c)$ , then the value of $(m + n)$ is

0

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Solution

The correct option is D $2$
$a^{2} + b^{2} + 2 a b + 2 b c + 2 c a + c^{2} - c^{2}$
$= (a + b + c)^{2} - c^{2}$
$= (a + b) (a + b + 2 c)$
On comparision we get,
$m = 0, n = 2$
$m + n = 0 + 2 = 2$

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