A quadratic product minus a square

Proved

WorkbookSource.problem_34802

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

lean-workbooksource-checked

$(a^2+ab+b^2)(a^2+ac+c^2)-\left(a^2+\frac{a(b+c)}{2}+bc\right)^2=...$ $=\frac{3}{4}a^2(b-c)^2$

Source: InternLM Lean-Workbook, record lean_workbook_34802 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_34802 (a b c : ℝ) : (a^2 + a * b + b^2) * (a^2 + a * c + c^2) - (a^2 + a * (b + c) / 2 + b * c)^2 = 3 / 4 * a^2 * (b - c)^2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34802; Apache-2.0

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