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
3x^{2} + 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.
3x^{2} is like
5x^{2} because the variable
x
is both, and the exponent of x is
2
in both.
Understanding Check
- 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.
- Are the terms 3y^{2} and
3y^{3} 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.
- 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.
- 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.
- 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.
- Are the terms 2xy^{2} 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
- 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
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.)