Question
Factorise:
$(a+b)^3-a-b$
$(a+b)^3-a-b$
✓
Answer
$(a+b)^3-a-b$
$=(a+b)^3-(a+b)$
$=(a+b)\left[(a+b)^2-1^2\right]\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=(a+b)(a+b+1)(a+b-1)$
$=(a+b)^3-(a+b)$
$=(a+b)\left[(a+b)^2-1^2\right]\left[\therefore a^2-b^2=(a-b)(a+b)\right]$
$=(a+b)(a+b+1)(a+b-1)$
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