Factoring the denominator of a cubic quotient

Proved

WorkbookSource.problem_40509

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

lean-workbooksource-checked

Prove that $\displaystyle \frac{a^3}{b^3+c^3}=\frac{a}{b+c}\cdot \frac{a^2}{b^2+c^2-bc}$

Source: InternLM Lean-Workbook, record lean_workbook_40509 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_40509 : ∀ a b c : ℝ, (a^3 / (b^3 + c^3) : ℝ) = (a / (b + c) : ℝ) * (a^2 / (b^2 + c^2 - b * c) : ℝ)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_40509; Apache-2.0

View graph