Wednesday, March 11, 2009

Geometrical (visual) proof of the famous formula {(a+b)^2} = {(a^2) + (b^2) + (2*a*b)}

Yesterday, at the lunch table, a friend told me that at one of his IIM interviews, he was asked to prove the well-known identity {(a+b)^2} = {(a^2) + (b^2) + (2*a*b)} geometrically. He asked me to try this problem. It took me over 5 minutes to come up with a solution, but gladly, I did come up with one. Here it is:

I can imagine that the same method can be applied to prove the identity [(a+b)^3] = [(a^3) + (b^3) + {3*a*b*(a+b)}], and many other identities as well. It'll require the use of Google SketchUp or AutoCAD to create 3D models for these. Let's see if I have the time some day to create a model.

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