Hello students ,Previously we have discussed about column multiplication and in this blog we are going to discuss about the Binomial Expansion which is a part of secondary school board andhra pradesh. Binomial Expansion is related to the algebraic expansion of powers of a Binomial Distributions. We have a case when n is a positive integer then the expansion of ( 1 + a )n is equal to ∑nr=0 crn ar. Coefficients of 'a' that appear in the expansion of ( 1 + a )n are known as binomial coefficients. (Know more about Binomial Expansion in broad manner, here,)
By using the formula of expansion you can easily expand the series without doing the multiplication. There are mainly two properties of binomial expansion that include :
- ( n + 1 ) terms contained by an expansion .
- Binomial coefficients crn should be integers .
We can understand it by an example as ( a + b )2 is described in terms of expansion as
a2 + 2ab + b2 where ab is the coefficient .
Binomial Expansion examples :
( a + b ) 4 : It expands as a4 + 4 a3 b + 6 a2 b2 + 4 a b3 + b4 . Here in each term exponents of a and b are non negative integers with sum of the powers of a and b is equal to n. In above example n is equal to the 4 .
Binomial Expansion can be understood using Pascale's triangle that applies to expand the terms in form of ( a + b ) n .
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
We can take an example to understand the Pascale's triangle as ( a + b )3 is expanded by taking the row of triangles starting with 1 and 3 is 1 3 3 1 therefore expansion of ( a + b )3 is described as
( a + b )3 = a3 + 3 a2b + 3 ab2 + b3 .
In the next session we are going to discuss Solving Binomial Expansion
and if anyone want to know about Math Blog on Estimating Quotients then they can refer to Internet and text books for understanding it more precisely.