Factorize:$ a(a+b)^{3}-3 a^2b(a+b) $

Given :

\( a(a+b)^{3}-3a^2b(a+b) \)

To do :

We have to factorize the given expression.

Solution :

$a(a + b)^3 – 3a^2b(a + b)= a(a + b) [(a + b)^2 – 3ab]$

$= a(a + b) [a^2 + b^2 + 2ab – 3ab]$

$= a(a + b) (a^2 – ab + b^2)$

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

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Updated on: 10-Oct-2022

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