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Factorize eac...

Question

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

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Solution

Given: $a^{3} + b^{3} + a + b$

$∴ a^{3} + b^{3} + a + b$
$= (a^{3} + b^{3}) + (a + b)$
$= (a + b) (a^{2} - a b + b^{2}) + (a + b)$
$[∴ a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})]$

$= (a + b) (a^{2} - a b + b^{2} + 1)$

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

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