1

Objectives:

- Use Pascal's Triangles & the Binomial Theorem to

expand a binomial raised to a power.

2

c. 4 of 5 letters d. 1 of 5 letters e. 5 of 5 letters f. 0 of 5 letters

Do you remember the name for this process? Combinations!

3

The Binomial Theorem:

Let's start by expanding these binomials by distributing:

4

But where do the coefficients come from?????

5

Pascal's Triangle 1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

Row 0

Row 1

Row 2

Row 3

Row 4

Row 5

Row 6

Can you see a pattern?

Fill out the 5th & 6th rows.

What do you notice about the numbers in row 5?

6

7

8

9

This problem is not in your book.

10

11

12

Important!!!

13

This problem is not in your book.

14

15

Does this work for higher powers of 11? No; the numbers in Pascal's Triangle up to & including row 4 have only 1 digit. Once you get to row 5 & beyond, because there are numbers with more than 1 digit, the pattern doesn't work so nicely.

16

For #4, instead of expanding it, can you find just the 4th term?

4th term

(You don't have to write out the other terms ­ you just have to know the patterns to get to the 4th term & write it.)

17

Examples:

Expand:

Expand:

18

Assignment:Section 7.6: problems 5-18, 20, 22-25, 27,

32, 34-36, 38, 39