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)[(a + b)2 - 12] $\big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
= (a + b)(a + b + 1)(a + b - 1)
= (a + b)3 - (a + b)
= (a + b)[(a + b)2 - 12] $\big[\therefore\ \text{a}^2-\text{b}^2=(\text{a}-\text{b})(\text{a}+\text{b})\big]$
= (a + b)(a + b + 1)(a + b - 1)
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