If a+2b+3c = 0 show that a^3+8b^3+27c^3=18abc [ ICSE Class 9 S.Chand (Fundamentals of Mathematics) Chapter 3 Exercise-3.1 Question Number 14 Solution Expansion and Factorisation]
a+2b+3c = 0
⟹ a+2b = -3c
Cubing both side we get,
(a+2b)3 = (-3c)3
⟹ a3 + (2b)3 +3.a.(2b) +(a+2b) = -27c3
⟹ a3+8b3+6ab(-3c) = -27c3 [as, a+2b = -3c]
⟹ a3+8b3-18abc = -27c3
⟹ a3+8b3+27c3 =18abc
Therefore a3+8b3+27c3 =18abc [Proved]