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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: be familiar with algebraic expressions, understand the difference between a term and a factor, be familiar with the concept of common factors, know the function of a coefficient.


  • Algebraic Expressions
  • Terms and Factors
  • Common Factors
  • Coefficients

Algebraic expressions

Algebraic expression

An algebraic expression is a number, a letter, or a collection of numbers and letters along with meaningful signs of operation.


Algebraic expressions are often referred to simply as expressions , as in the following examples:

x 3 x 2 y 7 + 9 x is an expression.

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The number 8 is an expression. 8 can be written with explicit signs of operation by writing it as 8 + 0 or 8 1 .

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3 x 2 + 6 = 4 x 1 is not an expression, it is an equation . We will study equations in the next section.

Terms and factors


In an algebraic expression, the quantities joined by " + " signs are called terms.

In some expressions it will appear that terms are joined by " " signs. We must keep in mind that subtraction is addition of the negative, that is, a b = a + ( b ) .

An important concept that all students of algebra must be aware of is the difference between terms and factors .


Any numbers or symbols that are multiplied together are factors of their product.

Terms are parts of sums and are therefore joined by addition (or subtraction) signs.
Factors are parts of products and are therefore joined by multiplication signs.

Sample set a

Identify the terms in the following expressions.

3 x 4 + 6 x 2 + 5 x + 8 .

This expression has four terms: 3 x 4 , 6 x 2 , 5 x , and 8.

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15 y 8 .

In this expression there is only one term. The term is 15 y 8 .

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14 x 5 y + ( a + 3 ) 2 .

In this expression there are two terms: the terms are 14 x 5 y and ( a + 3 ) 2 . Notice that the term ( a + 3 ) 2 is itself composed of two like factors, each of which is composed of the two terms, a and 3.

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m 3 3 .

Using our definition of subtraction, this expression can be written in the form m 3 + ( 3 ) . Now we can see that the terms are m 3 and 3 .

Rather than rewriting the expression when a subtraction occurs, we can identify terms more quickly by associating the + or - sign with the individual quantity.

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p 4 7 p 3 2 p 11 .

Associating the sign with the individual quantities we see that the terms of this expression are p 4 , 7 p 3 , 2 p , and 11 .

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Practice set a

Let’s say it again. The difference between terms and factors is that terms are joined by signs and factors are joined by signs.

addition, multiplication

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List the terms in the following expressions.

4 x 2 8 x + 7

4 x 2 , 8 x , 7

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2 x y + 6 x 2 + ( x y ) 4

2 x y , 6 x 2 , ( x y ) 4

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5 x 2 + 3 x 3 x y 7 + ( x y ) ( x 3 6 )

5 x 2 , 3 x , 3 x y 7 , ( x y ) ( x 3 6 )

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Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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