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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.

Overview

  • 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.

Expressions

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

Terms

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 .

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

Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
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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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