Question:
Find the value
$a^{3}+b^{3}+a+b$
Solution:
$=\left(a^{3}+b^{3}\right)+1(a+b)$
$=(a+b)\left(a^{2}-a b+b^{2}\right)+1(a+b)$
$\left[\therefore a^{3}+b^{3}=(a+b)\left(a^{2}-a b+b^{2}\right)\right]$
$=(a+b)\left(a^{2}-a b+b^{2}+1\right)$
$\therefore a^{3}+b^{3}+a+b=(a+b)\left(a^{2}-a b+b^{2}+1\right)$
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