AoPS

MATHEMATICS · Subjective · AoPS · Mathematics · Special Factorizations · Special Factorizations

Problem

12. Verify that x3+y3+z3−3xyz=12(x+y+z)[(x−y)2+(y−z)2+(z−x)2]x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right]

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