Answer
The sum of the areas separately on the left side equals the area of the square formed by rearranging them.
We arrive at the conclusion that $x^2$ + $y^2$ + 2xy = $(x+y)^2$ .
Work Step by Step
If we add the areas on the left side we add the terms $x^2$ , $y^2$ , 2xy.
If we take the area of the square with side (x+y) , we get $(x+y)^2$.
We find that this is equal to the sum of areas on the left side since the square is formed from rearranging these areas geometrically.
Hence we arrive at the conclusion that $x^2$ + $y^2$ + 2xy = $(x+y)^2$ .
