110 Part 2: Into the Unknown
When Are Terms “Like Terms”?
You’re often going to see the word term in this chapter, so let’s start by making sure you under-
stand what it means. A term is a constant, a variable, or an expression involving multiplication of
constants and variables. You use the more general word expression to cover just about anything you
write using numbers and variables. Terms are a particular subset of expressions that involve only
multiplication.DEFINITION
A term is an algebraic expression made up of numbers, variables, or both that are
connected only by multiplication.Any number on its own is a term. Constants, like 1 or -7, are terms. Any variable, such as x or y,
is a term. When you multiply numbers and variables, you get terms like -4y, or xy, or x^2 , or
18 xy^2. You can have numbers, variables, numbers and variables multiplied together, and variables
multiplied together, which may give you exponents. That’s all okay in a term. You just can’t
add or subtract, divide by a variable, or have a variable under a square root sign. Dividing by a
constant is the same as multiplying by a fraction, so that’s allowed.Simplify to Find Terms
It’s possible that an expression may not look at first like it fits the definition of a term, but you
might find that you can simplify the expression and the simplified form does fit the definition
of term.
For example, the expression 5 2 62
x 1 xx seems to break all the rules. There’s addition, there’s a
variable under a square root sign and there’s division by a variable. But you can do that division.
6 x^26
x^5 x
so you can make the expression 5 2 6 56(^22)
x (^15) xx xx 1.
Then you might notice that x^2 x, so 5 2 6 56
(^22)
x x
x
xx = 5x + 6x.
5 x + 6x is 11x, and that’s a term. Take a minute to think about whether you can simplify an
expression before you decide if it fits the definition.
CHECK POINT
Decide if each expression is a term.
- 4x
- -12
- -2t^7
4.^6 y
5. a
6