(a+b) squared

Hey this is only for better understanding... may be some of those who find it useful can pick it up from here... not my original work, but this is the way I understood it!!

We have had the identity:
(a+b)^2 = a^2 + b^2+ 2ab
Now to understand what this identity means, I used the graphical repsentation,
Now we can assume safely that 'a^2' represents a sqare of side 'a'

So as well should (a+b)^2, but then what does the identity mean?
Well it means that to make a square of side (a+b)^2 just given geometrically to be proven.
ok that should be simple rt!!!
a figure with area ab will have to be a rectangle
so,
To form a sqare of side (a+b)^2 we have to just add up the geometrical figures 2 squares one each of side a and b.
But then we have to have the space that can be filled by rectangles with side a&b... we have to have 2 such.. so there fore we have
(a+b)^2 = a^2 + b^2+ 2ab
ie
sq of side = sq of side + sq of side + 2 rectangles of area
a + b a b a * b