Vedic Math Trick-Expanding for higher powers

Here we will learn Vedic Math Trick-Expanding for higher powers. Here we will adopt the method which is different from what we have learnt in our schools.

In lower classes we have learnt , the below formulas :

But how to deal with higher powers i.e. 

We cannot learn and remember formulas for higher powers, so we generally proceed as below

But this is a time consuming method. We will do the same expansion with another method using Pascal's Triangle. In this method, we will create a table starting as below :

 

Now, below each of the center of two digits write their sum.

Here, fisrt 3(from left) is the sum of its upper 1 and 2 and second 3 is the sum of its upper 2 and 1.

Proceed for further rows with the same procedure to construct a triangle as below

Now, if you want to expand :

• for power of 2 then go for second row
• for power 3, go for third row
• for power of 4, go for fourth row
• ...................................................

Now starting for expansion, start multiply the multiplication of first number (a) and seond number(b) with the digits of a particular row(as per selection of power) with an addition sign between each of the terms. Keep on decreasing the power of first number(starting from highest power 2) and increasing the power of second number(starting from 0).

Let us start for expansion of square of

For this we will start with the 2nd row where the digits are in the order

1   2   1

So, we will proceed as below,

Therefore, 

Another Example

To expand (a + b) 5 we have to use fifth row

Therefore, 

Learn More :

• Subtracting a number from 100/1000/10000
• Multiplying  a number by same number of 9's
• Multiplying  a number by lesser number of 9's
• Multiplying  a number by greater number of 9's
  
• Multiplication of two digit numbers