A fourth degree polynomial identity

Proved

WorkbookSource.problem_48767

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove the identity $a^4 + b^4 + c^4 - a^3 b - b^3 c - c^3 a = (a^2 + b^2 + ab) (a - b)^2 + (b^2 + bc + c^2)(a - c)(b - c)$

Source: InternLM Lean-Workbook, record lean_workbook_48767 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_48767 : ∀ a b c : ℝ, a^4 + b^4 + c^4 - a^3 * b - b^3 * c - c^3 * a = (a^2 + b^2 + a * b) * (a - b)^2 + (b^2 + b * c + c^2) * (a - c) * (b - c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_48767; Apache-2.0

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