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Question
Simplify:
(a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab)
Solution
We have,
(a – b) (a2 + b2 + ab) – (a + b) (a2 + b2 – ab) = a(a2 + b2 + ab) – b(a2 + b2 + ab) – a(a2 + b2 – ab) – b(a2 + b2 – ab)
= a3 + ab2 + a2b – ba2 – b3 – ab2 – a3 – ab2 + a2b – ba2 – b3 + ab2
= (a3 – a3) + (– b3 – b3) + (ab2 – ab2) + (a2b – a2b + a2b – a2b)
= 0 – 2b3 + 0 + 0 + 0
= – 2b3
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