TOPIC: BINOMIAL EXPANSION
BINOMIAL EXPANSION
(a + b)0 = ______
(a + b)1 = ___________
(a + b)2 = _________________
(a + b)3 = ________________________
What pattern do you notice in the exponents?
Write just the coefficients and describe the pattern:
Complete the table through n = 6. Use these patterns to expand the following binomial:
1. (a + b)5
There’s an easier way to find the coefficients, but first we need to know …………………..
2. 6! =
(Calculator: MATH, PRB)
3. [pic]=
(Calculator: MATH, PRB)
4. Find [pic] [pic] [pic] [pic] [pic] [pic] [pic]
Compare the answers to the sixth row of Pascal’s Triangle.
5. Expand (2a – 3)5
6. (x2 – 5y)4
7. Find the 3rd term of (x + 4)9
8. In the expansion of ( x2 - 3 )9, find the term containing x12
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N 19-1
N 19-1
Factorials, n!
If n is a positive integer, then
n! = _________________
Note: 0! = 1 (By definition)
Combinations, [pic]
Combinations of n taken j at a time:
[pic] = (((((
Binomial Expansion
(a + b)n = [pic]anb0 + [pic]an-1b1 + [pic]an-2b2 + …+ [pic]a0bn
The kth term: [pic]a b
N 19-1
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