Toolkit 27Expansion (or factorization) of two binomialsa2+ab+ac+bc=(a+b)(a+c)a^2+ab+ac+bc=(a+b)(a+c)a2+ab+ac+bc=(a+b)(a+c)ProofUsing the distributive law,(a+b)(a+c)=a2+ac+ab+bc=a2+ab+ac+bc.□\begin{aligned} (a+b)(a+c) &= a^2+ac+ab+bc \\ &= a^2+ab+ac+bc. \quad\square \end{aligned}(a+b)(a+c)=a2+ac+ab+bc=a2+ab+ac+bc.□Related ProblemsCoreHMMT 2025 — Algebra & Number Theory Round (Problem 7)