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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

show that the set of all natural number form semi group under the composition of addition
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The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
on number 2 question How did you got 2x +2
combine like terms. x + x + 2 is same as 2x + 2
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
how do I set up the problem?
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find the subring of gaussian integers?
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find the value of 2x=32
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divide by 2 on each side of the equal sign to solve for x
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
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use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
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Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Need help solving this problem (2/7)^-2
Simone Reply
what is the coefficient of -4×
Mehri Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
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how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
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
Eleven fifteenths of two more than a number is eight.
Leny 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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