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

[bballwaterboy]

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.)

 

[jedishrfu]

take the formula F = (C * 5/9) + 32

the (C * 5/9) + 32 is an expression and the C * 5/9 is a term in the expression composed of 3 factors.

Here's something that may help:

http://en.wikipedia.org/wiki/Algebraic_expression

 

[Mark44]

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 $\sqrt[3]{a - 1}$), or involve trig or exponential or log functions, just to name a few.

 

[bballwaterboy]

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]

Hi, Mark44:

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

Correct.

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.