Question
Factorize the following expressions: $a^3 + b^3 + a + b$
✓
Answer
$a^3+b^3+a+b=\left(a^3+b^3\right)+1(a+b)$
$=(a+b)\left(a^2-a b+b^2\right)+1(a+b)$
${\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]}$
$=(a+b)\left(a^2-a b+b^2+1\right)$
$\therefore a^3+b^3+a+b$
$=(a+b)\left(a^2-a b+b^2+1\right)$
$=(a+b)\left(a^2-a b+b^2\right)+1(a+b)$
${\left[\therefore a^3+b^3=(a+b)\left(a^2-a b+b^2\right)\right]}$
$=(a+b)\left(a^2-a b+b^2+1\right)$
$\therefore a^3+b^3+a+b$
$=(a+b)\left(a^2-a b+b^2+1\right)$
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