The document discusses binomial expansion, which is the process of multiplying out terms with two variables according to their power using the binomial theorem. It provides examples of expanding binomial expressions like (x + y)2, (x + y)3, and (x + y)4. It also notes that the sum of the exponents in each term equals the overall power, and the number of terms is always one more than the power. Finally, it provides the binomial theorem for expanding any binomial expression and finding a particular term.

1. 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

2. 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

3. ex. Expand (x + y)7

4. ex. Expand (x + 2y)5

5. ex. Expand (4a2 - 2b)3

6. Finding a Particular Term
General form tk+1 = nCk(x)n-k(y)k
Determine the 9th term of (x - 3)10

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