Algebra 1: Common Core (15th Edition)

Areas of (blue square) + 2(green rectangles) +(yellow square) equals the area of the square with side $a$: $(a-b)^{2}+2b(a-b)+b^{2}=a^{2}$ ... subtract $2b(a-b)+b^{2}$ from both sides $(a-b)^{2}=a^{2}-2b(a-b)-b^{2}$ ... distribute on the RHS $(a-b)^{2}=a^{2}-2ab+2b^{2}-b^{2}$ ... simplify (add like terms) $(a-b)^{2}=a^{2}-2ab+b^{2}$