Pre-Calculus All-in-One For Dummies

Chapter 21

Expanding Binomials for the Real World

IN THIS CHAPTER

Getting acquainted with the binomial theorem

Creating and expanding Pascal’s triangle

Applying the binomial theorem to expand binomials

The binomial theorem has been around for centuries. Mathematicians were interested in special happenings when operations were performed on just two terms. Euclid mentioned the special case involving the exponent 2 as early as the 4th century B.C. Indian mathematicians were using the formula for creating the binomial coefficient. And Omar Khayyam, mathematician and poet, was familiar with the theorem. Isaac Newton gets credit, though, for generalizing the theorem.

And where do you use the binomial theorem outside of a math class? It’s found in computer networking, economic predictions, ranking of scores for scholarships, and weather forecasting.

Expanding with the Binomial Theorem

A binomial is a polynomial with exactly two terms. Expressing the powers of binomials as a sum of terms is called binomial expansion. Using the binomial theorem to write the power of a binomial allows you to find the coefficients of this expansion.

Expanding many of the same binomials can require a rather ...