Question:
Factorize:
$a^{3}+3 a^{2} b+3 a b^{2}+b^{3}-8$
Solution:
$a^{3}+3 a^{2} b+3 a b^{2}+b^{3}-8=\left(a^{3}+b^{3}+3 a^{2} b+3 a b^{2}\right)-8$
$=\left[a^{3}+b^{3}+3 a b(a+b)\right]-8$
$=(a+b)^{3}-2^{3}$
$=(a+b-2)\left[(a+b)^{2}+2(a+b)+2^{2}\right]$
$=(a+b-2)\left[(a+b)^{2}+2(a+b)+4\right]$
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