Pascal’s Triangle

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.

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

Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 The triangle known as Pascal’s Triangle was produced in 1665 . It is named after Blaise Pascal, a 17th century philosopher who made important contributions to math and physics.

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?

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

Homework Expand each of the following 1.) 𝑥−4𝑦 4 2.) 𝑛 4 −3 3 3.) 𝑥 3 + 𝑦 3 6 4.) 𝑢−𝑣 8