Factoring a cyclic quartic expression

Proved

WorkbookSource.problem_29260

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

lean-workbooksource-checked

The expression $f(M)$ can be factored as $f(M) = a^3(b - c) + b^3(c - a) + c^3(a - b) = c(b^3 - a^3) - ba(b^2 - a^2) - c^3(b - a) = (b - a)\left[c(b^2 + ba + a^2) - ba(b + a) - c^3\right]$

Source: InternLM Lean-Workbook, record lean_workbook_29260 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_29260 : ∀ a b c : ℝ, a * b * c = b * c * a → a^3 * (b - c) + b^3 * (c - a) + c^3 * (a - b) = (b - a) * (c * (b^2 + b * a + a^2) - b * a * (b + a) - c^3)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29260; Apache-2.0

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