Answer
$(a+b)^{2}$ = $a^{2}$ + $b^{2}$ + 2ab
Work Step by Step
We know area of square A = side * side
The given drawing consist of 4 rectangles
The area of Square = (a+b)(a+b)= $(a+b)^{2}$
Lets find the area of all the 4 rectangles separately
Rectangle I = ab
Rectange II = $b^{2}$
Rectangle III = ab
Rectangle IV = $a^{2}$
The total area of square = Area of I + Area of II + Area of III + Area of IV
= ab+ $b^{2}$+ab+ $a^{2}$
=2ab+ $b^{2}$ + $a^{2}$
Therefore $(a+b)^{2}$ = $a^{2}$ + $b^{2}$ + 2ab
