Expanding a symmetric cubic product

Proved

WorkbookSource.problem_42097

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

lean-workbooksource-checked

For real $a,b,c$ ,

a^3+b^3+c^3+ab(a+b)+bc(b+c)+ca(c+a)=(a^2+b^2+c^2)(a+b+c).

Source: InternLM Lean-Workbook, record lean_workbook_42097 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_42097 (a b c : ℝ) : a^3 + b^3 + c^3 + a * b * (a + b) + b * c * (b + c) + c * a * (c + a) = (a^2 + b^2 + c^2) * (a + b + c)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_42097; Apache-2.0

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