CHAPTER

9

Adding and Subtracting

with Variables

In This Chapter:

• Understanding terms


• How to identify like terms


• Adding and subtracting
  like terms


• Recognizing when an
  expression is in simplest
  form


• How to name polynomials

The shift from arithmetic to algebra begins with the intro-
duction of variables. Almost immediately, you have to start
doing arithmetic with variables. The rules of arithmetic don’t
change, but working with one or more unknown quantities
requires some new strategies. If you have four 3s, you can do
the multiplication and know you have 12, but if you have four
x’s, all you can do is say that you have 4x. What 4x is worth
depends on what number x stands for.

The statement that you have four x’s, written as 4x, is a
simple form of multiplication. As you saw in the last chapter,
more complicated multiplication requires multiplying the
coefficients, the numbers that tell you how many you have,
and multiplying the variables, which usually requires using
exponents.

In this chapter, we’ll look at more arithmetic with variables,
with a focus on adding and subtracting. I’ll explain when you
can, and when you can’t, add or subtract expressions involving
variables, and how to do it when you can. And I’ll introduce
you to polynomials, a family of expressions built by adding
variable terms.