lean_workbook_plus_1576

Proved

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

Prove that $a^3+b^3+c^3-3abc = \frac{1}{2}(a+b+c)((a-b)^2 + (b-c)^2 + (c-a)^2)$ given $a+b+c=0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1576 (a b c : ℝ) (h : a + b + c = 0) : a^3 + b^3 + c^3 - 3 * a * b * c = 1 / 2 * (a + b + c) * ((a - b)^2 + (b - c)^2 + (c - a)^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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