Prove2Me

A symmetric cubic as a weighted sum of squared differences

Proved
WorkbookSource.problem_41523

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

lean-workbooksource-checked

Prove that 2 (a+b+c)3+9 abc−7 (a+b+c)(ab+ac+bc)=(a−b)2(a+b)+(b−c)2(b+c)+(c−a)2(c+a)2\, \left( a+b+c \right) ^{3}+9\,abc-7\, \left( a+b+c \right) \left( ab+ac+bc \right) = \left( a-b \right) ^{2} \left( a+b \right) + \left( b-c \right) ^{2} \left( b+c \right) + \left( c-a \right) ^{2} \left( c+a \right)

Source: InternLM Lean-Workbook, record lean_workbook_41523 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_41523 : ∀ a b c : ℝ, 2 * (a + b + c)^3 + 9 * a * b * c - 7 * (a + b + c) * (a * b + b * c + c * a) = (a - b)^2 * (a + b) + (b - c)^2 * (b + c) + (c - a)^2 * (c + a)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_41523; Apache-2.0

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