Vedic Sutras With Algebraic proof

1. Urdhav-Triyagbhyam

This is a general formula i.e applicable to all cases of multiplication and also in diviaion of a large number by another large number.

(a) Multiplication of two 2-digit numbers.
Consider two numbers ab and cd.
(Where a and b are digits not numbers in multiplication.)

We can write ab and cd as:
ab=(10× a + b)
cd=(10×c + d)

Now the multiplication of  ab and cd:
(10×a + b)×(10×c + d)
By multiplying we got this form

10^2(a×c)+ 10(ad+cd)+bd     ....(1)

Short-cut that can be deduced from (1).

While multiplying two 2-digit numbers ab and cd.(where ab and cd are numbers not a*b and c*d)
     ab × cd = X
1)Where the ones digit of answer is b×d.
2)the tens digit number of answer is (a×d + b×c).
3) the Hundredth digit of answer is  ( a×c).

Short cut for Multiplication of two three- digit number can be done by using the expanding three digit numbers and performing the multiplication as we have done above.