Answer
Please see "step-by-step"
Work Step by Step
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)
$(a-b)^{2}=a^{2}-2ab+b^{2}$
