Basic Math and Pre-Algebra For Dummies (95 page)

No matter how complicated an algebraic expression gets, you can always separate it out into one or more terms.

 When separating an algebraic expression into terms, group the plus or minus sign with the term that it immediately precedes.

When a term has a variable, it's called an
algebraic term.
When it doesn't have a variable, it's called a
constant.
For example, look at the following expression:

The first three terms are algebraic terms, and the last term is a constant. As you can see, in algebra,
constant
is just a fancy word for
number.

Terms are really useful to know about because you can follow rules to move them, combine them, and perform the Big Four operations on them. All these skills are important for solving equations, which I explain in the next chapter. But for now, this section explains a bit about terms and some of their traits.

When you understand how to separate an algebraic expression into terms, you can go one step further by rearranging the terms in any order you like. Each term moves as a unit, kind of like a group of people carpooling to work together — everyone in the car stays together for the whole ride.

For example, suppose you begin with the expression –5
x
+ 2. You can rearrange the two terms of this expression without changing its value. Notice that each term's sign stays with that term, although dropping the plus sign at the beginning of an expression is customary:

• = 2 – 5
  x
  

Rearranging terms in this way doesn't affect the value of the expression because addition is
commutative
— that is, you can rearrange things that you're adding without changing the answer. (See Chapter
4
for more on the commutative property of addition.)

For example, suppose
x
= 3. Then the original expression and its rearrangement evaluate as follows (using the rules that I outline earlier in “
Evaluating algebraic expressions
”):

Rearranging expressions in this way becomes handy later in this chapter, when you simplify algebraic expressions. As another example, suppose you have this expression:

• 4
  x
  –
  y
  + 6
  

You can rearrange it in a variety of ways:

Because the term 4
x
has no sign, it's positive, so you can write in a plus sign as needed when rearranging terms.

 As long as each term's sign stays with that term, rearranging the terms in an expression has no effect on its value.

For example, suppose that
x
= 2 and
y
= 3. Here's how to evaluate the original expression and the two rearrangements:

Every term in an algebraic expression has a coefficient. The
coefficient
is the signed numerical part of a term in an algebraic expression — that is, the number and the sign (+ or –) that goes with that term. For example, suppose you're working with the following algebraic expression:

The following table shows the four terms of this expression, with each term's coefficient:

Notice that the sign associated with the term is part of the coefficient. So the coefficient of –4
x
³
is –4.