lean_workbook_plus_16617

Proved

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

Substituting $d=-a-b-c$ , we wish to show $a^3+b^3+c^3-(a+b+c)^3 =3(abc-(a+b+c)ab -(a+b+c)bc-(a+b+c)ca)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_16617 (a b c d : ℝ) (h₁ : d = -a - b - c) :
  a^3 + b^3 + c^3 - (a + b + c)^3 =
    3 * (a * b * c - (a + b + c) * a * b - (a + b + c) * b * c - (a + b + c) * c * a)   :=  by sorry

Source

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

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