Chapter 1 Projects
BASIC PROPERTIES AND DEFINITIONS

RESEARCH PROJECT: Pascal's Triangle and Binomial Expansions

The triangular array of numbers shown below in knows as Pascal's triangle, after the French philosopher Blaise Pascal (1623-1662).

Look at Pascal's triangle and discover how the numbers in each row of the triangle are obtained from the numbers in the row above it. Once you have discovered how to extend the triangle, write the next two rows.

The title on the diagram below is Binomial Expansions because each line gives the expansion of the binomial raised to a whole number power

The fourth row in the diagram was completed by expanding using the methods developed in this chapter. Next, complete the diagram by expanding the binomials and using the multiplication procedures you have learned in this chapter. Finally, study the completed diagram until you see patterns there that will allow you to continue the diagram one more row without using multiplication. (One pattern that you will see is Pascal's triangle.) When you are finished, write an essay in which you describe what you have done and the results you have obtained.