Vedic Mathematics

Easy Subtraction Rule: How to do a quick mental calculation

If you want to subtract 4679 from 10000, you can easily apply the Nikhilam Navatashcaramam Dashatah sutra ("All from 9 and the last from 10"). Each figure in 4679 is subtracted from 9 and the last figure is subtracted from 10, yielding 5321.

"Whatever the extent of its deficiency, lessen it still further to that very extent; and also set up the square of that deficiency"

For instance, in computing the square of 9 we go through the following steps:
The nearest power of 10 to 9 is 10. Therefore, let us take 10 as our base.
Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer.
On the right hand side put the square of the deficiency that is 1.sq. Hence the answer is 81.
Similarly, 8 square = 64, 7 square = 49.
For numbers above 10, instead of looking at the deficit we look at the surplus. For example:
and so on.

This is based on the identities (a − b)(a − b) = a.sq − 2ab + b.sq and (a + b).sq = a.sq + 2ab + b.sq.