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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Muhammad Reply
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Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir 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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