1. Pascal’s Triangle

2. Lesson 16.1
In this section, we will learn how to expand binomials of the form (𝑎+𝑏) 𝑛 easily. Expanding a binomial such as (𝑎+𝑏) 𝑛 means to write the factored form as a sum.

3. Expand each of the following
a.) 𝑎+𝑏 0 b.) 𝑎+𝑏 1 c.) 𝑎+𝑏 2 d.) 𝑎+𝑏 3 e.) 𝑎+𝑏 4

4. Pascal’s Triangle
The triangle known as Pascal’s Triangle was produced in It is named after Blaise Pascal, a 17th century philosopher who made important contributions to math and physics.

6. Patterns in Pascal’s Triangle
a.) How many terms are there in the expansion of 𝑎+𝑏 𝑛 b.) What is the coefficient of 𝑎 𝑛 and 𝑏 𝑛 ? c.) What is the coefficient of 𝑎 𝑛−1 𝑏 and 𝑎 𝑏 𝑛−1 ? d.) In each term, what is the sum of the powers of 𝑎 and 𝑏?

7. Using Pascal’s Triangle, expand each of the following
a.) 2𝑥+3𝑦 3 b.) 2 𝑥 2 −1 5 c.) 3𝑎−4 4 d.) 𝑥 2 +𝑦 7

8. Homework
Expand each of the following 1.) 𝑥−4𝑦 4 2.) 𝑛 4 −3 3 3.) 𝑥 3 + 𝑦 ) 𝑢−𝑣 8