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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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