Toolkit 7Square of a difference(a−b)2=a2−2ab+b2(a-b)^2=a^2-2ab+b^2(a−b)2=a2−2ab+b2ProofUsing the distributive law,(a−b)2=(a−b)(a−b)=a2−ab−ba+b2=a2−2ab+b2.□\begin{aligned} (a-b)^2 &= (a-b)(a-b) \\ &= a^2 - ab - ba + b^2 \\ &= a^2 - 2ab + b^2. \quad\square \end{aligned}(a−b)2=(a−b)(a−b)=a2−ab−ba+b2=a2−2ab+b2.□Related ProblemsCoreAMC 10A 2020 (Problem 5)MATHCOUNTS State Sprint 2025 (Problem 26)MajorBMO1 2016/2017 (Problem 3)MinorMathCounts 2025 State — Sprint Round (Problem 30)AMC 10A 2025 (Problem 9)