Factorize:$a^2 + b^2 + 2(ab + bc + ca)$

Given :

$a^2 + b^2 + 2(ab + bc + ca)$

To do :

We have to factorize the given expression.

Solution :

$a^2 + b^2 + 2(ab + bc + ca) = a^2 + b^2 + 2 ab + 2 bc + 2 ca$

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

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

$= (a + b) (a + b + 2c)$

Hence, $a^2 + b^2 + 2(ab + bc + ca) = (a + b) (a + b + 2c)$.

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Updated on: 10-Oct-2022

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