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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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