Factorize:

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

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Solution

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

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