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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

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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