Vedic Mathematics - Easy and Faster Calculation of Cubes

To find out cubes of the two digit number, we generally take help of the following formula:

(a+b)’cubes= a’cube+3a’square b+ 3ab’square +b’cube.

This can be written as:

  a’cube +a’square b+ab’square +b’cube

  2a’square b 2 a b’square
  --------------------------------

  We have simply broken 3a’square b and 3ab’square in to two parts a’square and a b’square and 2 a b’square, to simplify the matter.
  In the above formula, we see that the terms a’cube, a’square b, a b’square and b’cube are placed at the top and the 2a’squareb and 2ab’square are placed at the bottom.
The complete formula comes into being when you add the terms at the top to those at the bottom.
If we scrutinize the top term closely, then we find that:
A’cube x b/a=a’square b
A’square b x b/a= a b’square and a b; square and a b’square x b/a= b’cube
The common ratio between the top terms is b/a. this is the ultimate finding. We have to dig out b/a and our desired result will be there. Let me explain with the help of the example:

1 2’cube, we have a=1,b=2 and b/a=2
a b

Steps:
• Our first term is a’cube= 1’ cube=1.
• The second term is a’square b= a’ cube x b/a= 1x2=2.
• The third term is a b’square= a’square b x b/a= 2x2=4.
• The fourth term is b’ cube= a b’square x b/a= 4 x 2=8.
• Put all this in the first row, maintaining a space.
• For the second row, double the two middle terms i.e. a’ square b=2 so that 2 a’ square b=4 and a b’square=4 so 2 a b’square=8.Second row comes as 4 and 8.
• Now add them

  1 2 4 8  
  4 8
  -----------------
  1 7 2 8- Answer
  1 - Remainder at each stage

Let us find 16’ cube; here a=1, b=6 and b/a=6. a’cube=1
16’cube=1 6 36 216
12 72
4 0 9 6 -answer
  ----------------------------
3 12 21 --- Remainder at each stage.

Steps:
• From the digit in the right 216, the unit digit 6 is retained as a part of the answer and the remainder 21 is added to the left
• After adding remainder 21 to (36+72) we get 129. 9 is retained as a answer and 12 is added to the left
• On adding the remainder 12 to the left we get 30. 0 is retained and 3 is added to the left.
• Adding the digits on the extreme left gives 4. The answer is 4096. Our procedure is over now.