A Word from the BPE

Today I'm going to show you a nifty graphical proof of the fact that (a+b)^2 = a^2 + b^2 + 2ab.

I begin with the following geometric axiom: the area of a rectange is equal to its base times its height.

A square is a special version of a rectangle in which the base equals the height. Suppose that we have a square, and that each side of the square is equal to a + b. Therefore, by our axiom, the area of the square is equal to (a+b)^2. But what is (a+b)^2 equal to?

Allow me to add a picture to asist me (see below). I divide the square up into two squares and two rectanges. The squares have areas equal to a^2 and b^2. The rectanges each have areas of ab. The area of the entire square must be equal to the sum of the areas of the squares within it. Therefore, the (a+b)^2 = a^2 + b^2 + 2ab. QED.