GEOMETRIC PROOF OF (a+b)^2

PROOF OF THE FORMULA (a+b) ² 

We all know that  (a+b) ² = a²+2ab+b²
EVER WONDERED WHY? Lets prove this formula geometrically!

Area of a square with side L is L²  , and we want to find  (a+b) ² .

Do you find any similarity between these two above?

YES YOU DID! Basically,  (a+b) ² is the area of a square with side length = (a+b)

We know that the area of this square is (a+b) ²

Now, lets divide this square into following parts: 

Now, our square contains two squares and two rectangles.

So, the area of the square with side (a+b) = area of two squares + area of rectangles

Now, you can observe that the area of the two squares is a² and b², and the area of the two rectangles is ab and ab.

So, lets add area of all parts of the square of length (a+b) :

= a² + ab + ab + b²

= a² + 2ab + b²

As the Area of square of length (a+b) =  a² + 2ab + b²

Hence, (a+b)² = a²+2ab+b²