Question

Without actually calculating the cubes find the value of "{1/2x-1/3y}^3+{1/3y-1/4 z}^3+{1/4z-1/2 x}^3"

Answer 1

3(1/2 x - 1/3 y)(1/3y - 1/4 z)(1/4 z - 1/2 y)

Use the fact that a^3 + b^3 + c^3 = 3abc when a + b + c = 0