Find the value
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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