Question

If a=3+b prove that a³+b³-9ab=27

Answer 1

Given a = 3 + b
a3 – b3 – 9ab
= (a – b) (a2 + ab + b2) – 9ab
= (a – b) [(a – b)2 + 2ab + ab] – 9ab
= (a – b) [(a – b)2 + 3ab] – 9ab
= (3) [(3)2 + 3ab] – 9ab (a – b = 3)
= 3 (9 + 3ab) – 9ab
= 27 + 9ab – 9ab
= 27
Thus, the value of a3 – b3 – 9ab is27.
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