Prove2Me

lean_workbook_plus_79495

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that x3+y3+z3−3xyz=12(x+y+z)(∑cyc(x−y)2)x^3+y^3+z^3-3xyz=\frac {1}{2}(x+y+z)\left (\sum_{cyc}(x-y)^2\right) .

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_79495 (x y z : ℝ) :
  x^3 + y^3 + z^3 - 3 * x * y * z =
    1 / 2 * (x + y + z) * ((x - y)^2 + (y - z)^2 + (z - x)^2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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