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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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

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