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Square 2+ Digit Numbers Mentally

Step 4Prove It!

For most of you, using the trick and assuming it works is enough to satisfy you. Still, some of the mathematical purists out there need a proof, so they can take security in knowing this technique is general. A wise user by the name of PKM posted the same proof in the comments below, but I added a step, so that people who don't read comments could have the proof as well.

So, we start with the following algebraic expression, which always holds true (foil out the right side and this can be seen):
x2-a2 = (x+a)(x-a)

Now, simply isolate the x2 term:
x2 = (x+a)(x-a) + a2

The above expression is the mathematical form of the vedic sutra.
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Author:purduecer(NBitWonder)
When life gives me lemons, I make batteries. Check out my website at http://nbitwonder.com