Previously, we learned patterns for squaring and cubing binomials.

(x+y)3= x3 + 3x2y + 3xy2 + y3

(x+y)2= x2 + 2xy + y2

If the patterns were not memorized, you could simply write it out and multiply.

(x+y)2= (x + y)(x + y)

(x+y)3= (x + y)(x + y)(x + y)

The square of a binomial is not a problem, just foil. The cube of a binomial is a little work. But any exponent higher than 3 is a problem. That would just be too much work to multiply 4 binomials.

(x+y)4= (x + y)(x + y)(x + y)(x + y) Too much work! Agreed?

The notation:

is read n choose r, “combinations of n things taken r at a time.”

For example if we had 6 people, how many different groups of 2 could we choose?

We can calculate this on a scientific calculator. We will show how to perform this operation on a TI-30XIIS and a graphing calculator. If you calculator different, please go to an assistant or your instructor.

Fortunately we have an alternative method which is the Binomial Theorem. Before we learn the binomial theorem, we need to have a little fun playing with our scientific calculators. We will only show what you need to “get by” on this section. We will not get involved with factorials, permutations, and combinations. We would give more detail on these topics in a course covering probability and statistics.