Binomial Expansion is the expansion (multiplying out) of a

binomial according to its power

Binomial Theorem

(x + y)2

(x + y)3

(x + y)4

(x + y)5

Some Observations:

1) Sum of the exponents of each term is equal to the power of the binomial

2) # of terms is always 1 more than the power of the binomial

3) Pattern of the exponents:- 1st term of binomial goes down by 1- 2nd term of binomial goes up by 1 in expansion

Q: If given (x + y) is there an easy way to: a) write out the expansion? b) find a given term?

Use the Binomial Theorem

n

ex. Expand (x + y)7

ex. Expand (x + 2y)5

ex. Expand (4a2 - 2b)3

Finding a Particular Term

General form tk+1 = nCk(x)n-k(y)k

Determine the 9th term of (x - 3)10

ex. Find the 6th term of (3x - 2y)8