Superlesson
Project 8-1

Superlesson
Project 8-2

Algebra

Chapter 8
Multiplying and Factoring Polynomials

Blaise Pascal made many interesting discoveries after studying a pattern of numbers previously discovered by Omar Khayyam, a mathematician and astronomer who lived from 1048-1122. Let's see how Pascal's triangle can help us multiply and factor polynomials!

Part A, Multiplying and Factoring

1. Open the Pascal's Triangle Web site and read the page.

a. Draw a model of the binomials x + 3 and x² + 1. You may find it helpful to remember your previous workwith algebra tiles.

b. What do you think models of 2x + 3 and 4x² + 4x would look like?

c. What are the factors of each binomial in b above?

 

Part B, Multiplying Binomials

2. Continue exploring the information at the Pascal's Triangle site.

a. Make a model of (x + y)². You may use the chart at the Web site to give you a hint. Algebra tiles can be a big help too!

b. Push your Algebra tiles together and try to make a common geometric shape. What geometric figure is it? Why do you think that is reasonable?

Part E, Making Connections

3. Use the information from the Pascal's Triangle Web site to solve the following problems.

a. How does the binomial expansion of (x + y)² relate to the triangle?

b. How does the binomial expansion of (x + y)⁵ relate to the triangle?

c. What would the binomial expansion of (x + y)⁶ look like? Explain the pattern.