This chapter deals with binomial expansion; that is, with writing expressions of the form (a + b)n as the sum of several monomials.
Prior to the discussion of binomial expansion, this chapter will present Pascal's Triangle. Pascal's Triangle is a triangle in which each row has one more entry than the preceding row, each row begins and ends with "1," and the interior elements are found by adding the adjacent elements in the preceding row. Section one will display part of Pascal's Triangle, and will provide a formula for finding any element of any row in the triangle.
Pascal's Triangle is essential to the discussion of binomial expansion because, as it turns out, the numbers in Pascal's Triangle are the coefficients of the monomials in the expansion of (a + b)n. The monomials also have other properties, which can be summed up in the Binomial Theorem. This theorem is presented in section two. Using this theorem, we will be able to write out any expansion of any binomial.
Binomial expansion has other uses besides those in algebra II. It is used in statistics to calculate the binomial distribution. This allows statisticians to determine the probability of a given number of favorable outcomes in a repeated number of trials. Binomial expansion is also interesting from a mathematical point of view--it gives mathematicians insight into the properties of polynomials.