# Can You Define "Term" and "Expression" in Math?

## Main Question or Discussion Point

I have heard different things and want to get a "professional" opinion on this.

It seems like the words "term" and "expression" are technical terms with specific definitions in math and I want to know what they technically refer to (not just the personal slang or informal definitions someone might assign to them, but rather their formal mathematical definitions).

Thanks!!

(p.s. I know this is simple algebra stuff, but that's my level right now.)

Mark44
Mentor
Terms are expressions that are added or subtracted, such as 3xy + 2z or b2 - 4ac. In the first expression, 3xy is one term and 2z is another term. In the second expression, the terms are b2 and -4ac.

In the 3xy term, 3, x, and y are factors, which are expressions that are multiplied to make up the term.

Expressions are more loosely defined. They could be made up from any of the arithmetic operations - addition, subtraction, multiplication, or division, but can also be made up by raising an expression to some power (such as (a + b)3/2), roots (such as ##\sqrt{a - 1}##), or involve trig or exponential or log functions, just to name a few.

Hi, Mark44:

Thanks for the answer. So to clarify, terms are only expressions that are ADDED or SUBTRACTED - nothing else?

What about division of expressions, such as 3x/y or perhaps a simple exponent like 4^2? These don't have addition or subtraction of the expressions. So, you're saying these wouldn't be terms, correct?

TVM!

Mark44
Mentor
Hi, Mark44:

Thanks for the answer. So to clarify, terms are only expressions that are ADDED or SUBTRACTED - nothing else?
Correct.
bballwaterboy said:
What about division of expressions, such as 3x/y or perhaps a simple exponent like 4^2? These don't have addition or subtraction of the expressions. So, you're saying these wouldn't be terms, correct?
If you had 3x/y + 4x2, the 3x/y and 4x2 parts might be considered terms, although "term" is probably more often used in the context of polynomials, where each term is a constant or a constant times integer powers of one or more variables, such as 3, 2x, 5xy3, and so on. As far as I know, "term" isn't rigidly defined.