1. Essential Questions
How do we use the Binomial Theorem to expand a binomial raised to a power?
How do we find binomial probabilities and test hypotheses?

2. You used Pascal’s triangle to find binomial expansions in Lesson 6-2
You used Pascal’s triangle to find binomial expansions in Lesson 6-2. The coefficients of the expansion of (x + y)n are the numbers in Pascal’s triangle, which are actually combinations.

3. The pattern in the table can help you expand any binomial by using the Binomial Theorem.

4. Example 1: Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(a + b)5
The sum of the exponents for each term is 5.
(a + b)5 = 5C0a5b0
+ 5C1a4b1
+ 5C2a3b2
+ 5C3a2b3
+ 5C4a1b4
+ 5C5a0b5

5. Example 2: Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(2x + y)3
(2x + y)3 = 3C0(2x)3y0
+ 3C1(2x)2y1
+ 3C2(2x)1y2
+ 3C3(2x)0y3

6. In the expansion of (x + y)n, the powers of x decrease from n to 0 and the powers of y increase from 0 to n. Also, the sum of the exponents is n for each term. (Lesson 6-2)
Remember!

7. Example 3: Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(x – y)5
(x – y)5 = 5C0x5(–y)0
+ 5C1x4(–y)1
+ 5C2x3(–y)2
+ 5C3x2(–y)3
+ 5C4x1(–y)4
+ 5C5x0(–y)5

8. Example 4: Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(a + 2b)3
(a + 2b)3 = 3C0a3(2b)0
+ 3C1a2(2b)1
+ 3C2a1(2b)2
+ 3C3a0(2b)3

9. Lesson 3.3 Practice A