Question
Factorise:
$a^3+3 a^2 b+3 a b^2+b^3-8$
$a^3+3 a^2 b+3 a b^2+b^3-8$
✓
Answer
$a^3+3 a^2 b+3 a b^2+b^3-8$
$=(a+b)^3-2^3$
$=[(a+b)-2]\left[(a+b)^2+(a+b) 2+2^2\right]$
$=(a+b-2)\left[(a+b)^2+2(a+b)+4\right]$
$=(a+b)^3-2^3$
$=[(a+b)-2]\left[(a+b)^2+(a+b) 2+2^2\right]$
$=(a+b-2)\left[(a+b)^2+2(a+b)+4\right]$
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