Proof of (a+b)² revisited

All of us know what (a+b)² formula is, But sometimes even these most basic things have some neat ideas hidden inside them. This post explains the proof of (a+b)² from a geometric perspective(age old) and tries to appreciate its hidden beauty. To start with, lets take a square and divide its length/breadth into a units and call the remaining length b units as shown in the below figure. Now it is evident from the figure
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