Toolkit 19Factoring quadratic by groupingx2+(a+b)x+ab=(x+a)(x+b)x^2+(a+b)x+ab=(x+a)(x+b)x2+(a+b)x+ab=(x+a)(x+b)ProofUsing the distributive law,(x+a)(x+b)=x2+bx+ax+ab=x2+(a+b)x+ab.□\begin{aligned} (x+a)(x+b) &= x^2+bx+ax+ab \\ &= x^2+(a+b)x+ab. \quad\square \end{aligned}(x+a)(x+b)=x2+bx+ax+ab=x2+(a+b)x+ab.□Related ProblemsCoreAMC 10A 2020 (Problem 5)MajorAMC 10B 2025 (Problem 15)AMC 10B 2025 (Problem 10)MinorAMC 12A 2024 (Problem 19)