Essential Questions

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. 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 + 5C5a0b5 + 5C4a1b4

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

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 +5C4x1(–y)4 + 5C3x2(–y)3 + 5C5x0(–y)5

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

9. Lesson 3.3 Practice A