Binomial expansion

In a binomial raised to a certain power, it can be difficult to calculate the coefficients and exponents of the seperate terms. However there are patterns that are noticeable when expanding a binomial.

1. In each expansion, there are n+1 terms.

2. X and y symmetric roles. The powers of x decrease while the powers of y increases by 1 successively.

3. The sum of powers of each term is n. 

4. Coefficients increase and decrease

Binomial coefficients 

nCr = n!/(n-r)!r! 

r is the specific term in the expansion. The fourth term would be r =3 which means the number of term is r+1. 

For instance...

The third term for (x+y)^4 is 6

4C2 = 4!/(4-2)!2! =6

The pascal Triangle is also a means of determining the coefficients since it already states the coefficients for an (x+y)^n. 

Here's an example of an expansion...