Term

Pronunciation: /tɜrm/ Explain

A term is a part of an expression that is separated from other terms by addition or subtraction. A term consists of a coefficient and zero or more variables.

Terms are enumerated (counted) from left to right.

Constant Term

A constant term of an expression is a term without any variables. In the expression 3x² + 5x - 2, the constant term is -2.

Like Terms

Two terms are like terms if they have the same variable(s) and each variable has the same exponent. 3x² is like 5x² because the variable x is both, and the exponent of x is 2 in both.

Understanding Check

1. Are the terms 2b and 0.5b like terms?
   Yes.
   Correct. Since both terms contain the variable b and the exponent (an implied 1) is the same in both, they are like terms.
   No.
   Incorrect. Since both terms contain the variable b and the exponent (an implied 1) is the same in both, they are like terms.
2. Are the terms 3y² and 3y³ like terms?
   Yes.
   Incorrect. While both terms contain the variable y, in the first term the y is squared and in the second term the y is cubed. The exponents are different so the terms are not like terms.
   No.
   Correct. While both terms contain the variable y, in the first term the y is squared and in the second term the y is cubed. The exponents are different so the terms are not like terms.
3. Are the terms 3y and 3 like terms?
   Yes.
   Incorrect. Both terms do not have the variable y in them, so they can not be like terms.
   No.
   Correct. Both terms do not have the variable y in them, so they can not be like terms.
4. Are the terms 2 and 7 like terms?
   Yes.
   Correct. Neither term has a variable, so they are like terms.
   No.
   Incorrect. Neither term has a variable, so they are like terms.
5. Are the terms xy and 12xy like terms?
   Yes.
   Correct. Both terms have variables x and y. Both variables have an implied exponent of 1.
   No.
   Incorrect. Both terms have variables x and y. Both variables have an implied exponent of 1.
6. Are the terms 2xy² and 4xy like terms?
   Yes.
   Incorrect. In term 1, the exponent of the variable y is 2. In term 2, the implied exponent is 1. Since the exponents are different, the terms are not like terms.
   No.
   Correct. In term 1, the exponent of the variable y is 2. In term 2, the implied exponent is 1. Since the exponents are different, the terms are not like terms.

References

1. McAdams, David E.. All Math Words Dictionary, term. 2nd Classroom edition 20150108-4799968. pg 177. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

• McAdams, David E.. Expression. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem, LLC. 12/16/2018. http://www.allmathword.org/en/e/expression.html.

Cite this article as:

McAdams, David E. Term. 5/13/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/t/term.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

5/13/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/16/2018: Corrected checkbox code for fifth understanding check. (McAdams, David E.)
12/13/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
1/30/2009: Added constant term. (McAdams, David E.)
11/27/2008: Added parts of a term. (McAdams, David E.)
5/20/2008: Added enumeration of terms, like terms, and 'More Information'. (McAdams, David E.)
7/11/2007: Initial version. (McAdams, David E.)