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Why cross method of multiplication or vedic method of multiplication works?

It is evident the truth remains eternal even though you have many ways to reach it.

With that quote .. So one perspective of the famous vedic method of multiplication can be broken down as follows:

let there be two 2 digit numbers  , say       12     and  21   , so writing with their place values, we get (10+2)  and (20+1)  , so if we watch the operation we do in (a+b)(c+d)  is  ac+ad+bc+bd , the same holds good for any numbers. The application of  (a+b)^2 for square of a number is also a simplified version of the above notion.


SO the cross multiplication method isn't that spooky , right?
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