Find the value


Find the value

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


Taking (a + b) common in the two terms

$=(a+b)\left\{a(a+b)^{2}-3 a^{2} b\right\}$

Now, using $(a+b)^{2}=a^{2}+b^{2}+2 a b$

$=(a+b)\left\{a\left(a^{2}+b^{2}+2 a b\right)-3 a^{2} b\right\}$

$=(a+b)\left\{a^{3}+a b^{2}+2 a^{2} b-3 a^{2} b\right\}$

$=(a+b)\left\{a^{3}+a b^{2}-a^{2} b\right\}$

$=(a+b) p\left\{a^{2}+b^{2}-a b\right\}$

$=p(a+b)\left(a^{2}+b^{2}-a b\right)$

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


$=a(a+b)\left(a^{2}+b^{2}-a b\right)$


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