Factorize each of the following expressions:$a^3 + b^3 + a + b$

Given:

$a^3 + b^3 + a + b$

To do:

We have to factorize the given expression.

Solution:

We know that,

$a^3 + b^3 = (a + b) (a^2 - ab + b^2)$

$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Therefore,

$a^3 + b^3 + a + b = (a + b) (a^2 - ab + b^2) + 1 (a + b)$

$= (a + b) (a^2 - ab + b^2 + 1)$

Hence, $a^3 + b^3 + a + b = (a + b) (a^2 - ab + b^2 + 1)$.

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Updated on: 10-Oct-2022

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