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5 x 3 ( y 7 ) means there are five x 3 ( y 7 ) ' s . It could also mean there are 5 x 3 ( x 7 ) ' s . It could also mean there are 5 ( x 7 ) x 3 ' s .

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Practice set d

What does the coefficient of a quantity tell us?

The difference between coefficients and exponents

It is important to keep in mind the difference between coefficients and exponents .

Coefficients record the number of like terms in an algebraic expression.
x + x + x + x 4 terms = 4 x coefficient is 4
Exponents record the number of like factors in a term.
x x x x 4 factors = x 4 exponent is 4

In a term, the coefficient of a particular group of factors is the remaining group of factors.

how many of that quantity there are

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Sample set e

3 x .

The coefficient of x is 3.

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6 a 3 .

The coefficient of a 3 is 6.

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9 ( 4 a ) .

The coefficient of ( 4 a ) is 9.

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3 8 x y 4 .

The coefficient of x y 4 is 3 8 .

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3 x 2 y .

The coefficient of x 2 y is 3; the coefficient of y is 3 x 2 ; and the coefficient of 3 is x 2 y .

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4 ( x + y ) 2 .

The coefficient of ( x + y ) 2 is 4; the coefficient of 4 is ( x + y ) 2 ; and the coefficient of ( x + y ) is 4 ( x + y ) since 4 ( x + y ) 2 can be written as 4 ( x + y ) ( x + y ) .

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Practice set e

Determine the coefficients.
In the term 6 x 3 , the coefficient of
(a) x 3 is .
(b) 6 is .

(a) 6 (b) x 3

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In the term 3 x ( y 1 ) , the coefficient of
(a) x ( y 1 ) is .
(b) ( y 1 ) is .
(c) 3 ( y 1 ) is .
(d) x is .
(e) 3 is .
(f) The numerical coefficient is .

(a) 3 (b) 3 x (c) x (d) 3 ( y 1 ) (e) x ( y 1 ) (f) 3

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In the term 10 a b 4 , the coefficient of
(a) a b 4 is .
(b) b 4 is .
(c) a is .
(d) 10 is .
(e) 10 a b 3 is .

(a) 10 (b) 10 a (c) 10 b 4 (d) a b 4 (e) b

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Exercises

What is an algebraic expression?

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

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Why is the number 14 considered to be an expression?

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Why is the number x considered to be an expression?

x is an expression because it is a letter (see the definition).

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For the expressions in the following problems, write the number of terms that appear and then list the terms.

6 x 10

two : 6 x , 10

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5 x 2 + 6 x 2

three : 5 x 2 , 6 x , 2

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5 c z

one : 5 c z

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4 y 3

one : 4 y 3

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a + 1

two : a , 1

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2 x + x + 7

three : 2 x , x , 7

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( a + 1 ) + ( a 1 )

two : ( a + b ) , ( a 1 )

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For the following problems, list, if any should appear, the common factors in the expressions.

x 2 + 5 x 2 2 x 2

x 2

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2 ( a + b ) 3 ( a + b )

( a + b )

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8 a 2 ( b + 1 ) 10 a 2 ( b + 1 )

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14 a b 2 c 2 ( c + 8 ) + 12 a b 2 c 2

2 a b 2 c 2

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9 a ( a 3 ) 2 + 10 b ( a 3 )

( a 3 )

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12 a 3 b 2 c 7 ( b + 1 ) ( c a )

no commom factors

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5.2 ( a + 7 ) 2 + 17.1 ( a + 7 )

( a + 7 )

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3 4 x 2 y 2 z 2 + 3 8 x 2 z 2

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9 16 ( a 2 b 2 ) + 9 32 ( b 2 a 2 )

9 32

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For the following problems, note how many:

z ' s in 12 z ?

12

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x 2 's in 5 x 2 ?

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y 3 's in 6 y 3 ?

6

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x y ' s in 9 x y ?

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a 2 b ' s in 10 a 2 b ?

10

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( a + 1 ) ' s in 4 ( a + 1 ) ?

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( 9 + y ) ' s in 8 ( 9 + y ) ?

8

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y 2 's in 3 x 3 y 2 ?

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12 x ' s in 12 x 2 y 5 ?

x y 5

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( a + 5 ) ' s in 2 ( a + 5 ) ?

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( x y ) ' s in 5 x ( x y ) ?

5 x

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( x + 1 ) ' s in 8 ( x + 1 ) ?

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2 ' s in 2 x 2 ( x 7 ) ?

x 2 ( x 7 )

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3 ( a + 8 ) ' s in 6 x 2 ( a + 8 ) 3 ( a 8 ) ?

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For the following problems, a term will be given followed by a group of its factors. List the coefficient of the given group of factors.

12 a 2 b 3 c 2 r 7 ; a 2 c 2 r 7

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6 x 2 b 2 ( c 1 ) ; c 1

6 x 2 b 2

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10 x ( x + 7 ) 2 ; 10 ( x + 7 )

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9 a 2 b 5 ; 3 a b 3

3 a b 2

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15 x 4 y 4 ( z + 9 a ) 3 ; ( z + 9 a )

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( 4 ) a 6 b 2 ; a b

( 4 ) a 5 b

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( 11 a ) ( a + 8 ) 3 ( a 1 ) ; ( a + 8 ) 2

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Exercises for review

( [link] ) Simplify [ 2 x 8 ( x 1 ) 5 x 4 ( x 1 ) 2 ] 4 .

16 x 16 ( x 1 ) 12

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( [link] ) Supply the missing phrase. Absolute value speaks to the question of and not "which way."

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( [link] ) Find the value of [ 6 ( 4 2 ) + 7 ( 3 + 5 ) ] .

50

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( [link] ) Find the value of 2 5 4 2 3 2 .

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( [link] ) Express 0.0000152 using scientific notation.

1.52 × 10 5

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Questions & Answers

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
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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah 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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