If (a + b + c) = 9, find (a – 4)^{3} + (b – 2)^{3} + ( c – 3)^{3} – 3(a – 4 ) (b – 2 ) (c – 3)?

a + b + c = 9 a + b + c = 4 + 2 + 3 (a – 4 ) + (b – 2) + (c – 3) = 0 If x + y + z = 0 then x3 + y3 +z3 = 3xyz (a – 4)3 + (b – 2) 3 + ( c – 3) 3 = 3(a – 4 ) (b – 2 ) (c – 3) Hence (a – 4)3 + (b – 2) 3 + ( c – 3) 3 – 3(a – 4 ) (b – 2 ) (c – 3) = 0

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