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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.This module provides an exercise supplement for the chapter "Algebraic Expressions and Equations".

Exercise supplement

Algebraic expressions ( [link] )

For the following problems, write the number of terms that appear, then write the terms.

4 x 2 + 7 x + 12

three:  4 x 2 , 7 x , 12

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List, if any should appear, the common factors for the following problems.

12 x 2 y 3 + 36 y 3

12 y 3

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6 ( a + 4 ) + 12 ( a + 4 )

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4 ( a + 2 b ) + 6 ( a + 2 b )

2 ( a + 2 b )

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17 x 2 y ( z + 4 ) + 51 y ( z + 4 )

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6 a 2 b 3 c + 5 x 2 y

no common factors

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For the following problems, answer the question of how many.

( a + b ) ' s in 12 ( a + b ) ?

12

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a 4 ' s in 6 a 4 ?

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c 3 ' s in 2 a 2 b c 3 ?

2 a 2 b

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( 2 x + 3 y ) 2 ' s in 5 ( x + 2 y ) ( 2 x + 3 y ) 3 ?

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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.

16 a 3 b 2 c 4 , c 4

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7 y ( y + 3 ) , 7 y

( y + 3 )

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( 5 ) a 5 b 5 c 5 , b c

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Equations ( [link] )

For the following problems, observe the equations and write the relationship being expressed.

a = 3 b

The value of  a  is equal to three time the value of  b .

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f = 1 2 m 2 + 6 g

The value of  f  is equal to six times  g  more then one half time the value of  m  squared .

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P 2 = k a 3

The value of  P  squared is equal to the value of  a  cubed times  k .

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Use numerical evaluation to evaluate the equations for the following problems.

C = 2 π r . Find C if π is approximated by 3.14 and r = 6.

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I = E R . Find I if E = 20 and R = 2.

10

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I = p r t . Find I if p = 1000 , r = 0.06 , and t = 3.

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E = m c 2 . Find E if m = 120 and c = 186 , 000.

4 .1515 × 10 12

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z = x u s . Find z if x = 42 , u = 30 , and s = 12.

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R = 24 C P ( n + 1 ) . Find R if C = 35 , P = 300 , and n = 19.

7 50 or 0.14

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Classification of expressions and equations ( [link] )

For the following problems, classify each of the polynomials as a monomial, binomial, or trinomial. State the degree of each polynomial and write the numerical coefficient of each term.

4 y 3 + 3 y + 1

trinomial; cubic; 4, 3, 1

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9 a b 2 c 2 + 10 a 3 b 2 c 5

binomial; tenth; 9, 10

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( 2 x y 3 ) 0 , x y 3 0

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Why is the expression 4 x 3 x 7 not a polynomial?

. . . because there is a variable in the denominator

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Why is the expression 5 a 3 / 4 not a polynomial?

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For the following problems, classify each of the equations by degree. If the term linear, quadratic, or cubic applies, use it.

y x z + 4 w = 21

linear

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5 x 2 + 2 x 2 3 x + 1 = 19

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( 6 x 3 ) 0 + 5 x 2 = 7

quadratic

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Combining polynomials using addition and subtraction ( [link] ) - special binomial products ( [link] )

Simplify the algebraic expressions for the following problems.

4 a 2 b + 8 a 2 b a 2 b

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21 x 2 y 3 + 3 x y + x 2 y 3 + 6

22 x 2 y 3 + 3 x y + 6

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2 ( 3 y 2 + 4 y + 4 ) + 5 y 2 + 3 ( 10 y + 2 )

11 y 2 + 38 y + 14

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5 [ 3 x + 7 ( 2 x 2 + 3 x + 2 ) + 5 ] 10 x 2 + 4 ( 3 x 2 + x )

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8 { 3 [ 4 y 3 + y + 2 ] + 6 ( y 3 + 2 y 2 ) } 24 y 3 10 y 2 3

120 y 3 + 86 y 2 + 24 y + 45

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4 a 2 b c 3 + 5 a b c 3 + 9 a b c 3 + 7 a 2 b c 2

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x ( 2 x + 5 ) + 3 x 2 3 x + 3

5 x 2 + 2 x + 3

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4 k ( 3 k 2 + 2 k + 6 ) + k ( 5 k 2 + k ) + 16

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2 { 5 [ 6 ( b + 2 a + c 2 ) ] }

60 c 2 + 120 a + 60 b

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9 x 2 y ( 3 x y + 4 x ) 7 x 3 y 2 30 x 3 y + 5 y ( x 3 y + 2 x )

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3 m [ 5 + 2 m ( m + 6 m 2 ) ] + m ( m 2 + 4 m + 1 )

36 m 4 + 7 m 3 + 4 m 2 + 16 m

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2 r [ 4 ( r + 5 ) 2 r 10 ] + 6 r ( r + 2 )

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a b c ( 3 a b c + c + b ) + 6 a ( 2 b c + b c 2 )

3 a 2 b 2 c 2 + 7 a b c 2 + a b 2 c + 12 a b c

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s 10 ( 2 s 5 + 3 s 4 + 4 s 3 + 5 s 2 + 2 s + 2 ) s 15 + 2 s 14 + 3 s ( s 12 + 4 s 11 ) s 10

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6 a 4 ( a 2 + 5 )

6 a 6 + 30 a 4

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2 x 2 y 4 ( 3 x 2 y + 4 x y + 3 y )

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5 m 6 ( 2 m 7 + 3 m 4 + m 2 + m + 1 )

10 m 13 + 15 m 10 + 5 m 8 + 5 m 7 + 5 m 6

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a 3 b 3 c 4 ( 4 a + 2 b + 3 c + a b + a c + b c 2 )

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( x + 2 ) ( x + 3 )

x 2 + 5 x + 6

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( a + 1 ) ( a + 3 )

a 2 + 4 a + 3

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4 x y 10 x y

6 x y

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5 a b 2 3 ( 2 a b 2 + 4 )

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7 x 4 15 x 4

8 x 4

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5 x 2 + 2 x 3 7 x 2 3 x 4 2 x 2 11

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4 ( x 8 )

4 x 32

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3 a ( 5 a 6 )

15 a 2 + 18 a

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4 x 2 y 2 ( 2 x 3 y 5 ) 16 x 3 y 2 3 x 2 y 3

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5 y ( y 2 3 y 6 ) 2 y ( 3 y 2 + 7 ) + ( 2 ) ( 5 )

11 y 3 + 15 y 2 + 16 y + 10

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[ ( { [ ( 5 ) ] } ) ]

5

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x 2 + 3 x 4 4 x 2 5 x 9 + 2 x 2 6

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4 a 2 b 3 b 2 5 b 2 8 q 2 b 10 a 2 b b 2

6 a 2 b 8 q 2 b 9 b 2

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2 x 2 x ( 3 x 2 4 x 5 )

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3 ( a 1 ) 4 ( a + 6 )

a 27

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6 ( a + 2 ) 7 ( a 4 ) + 6 ( a 1 )

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Add 3 x + 4 to 5 x 8 .

2 x 4

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Add 4 ( x 2 2 x 3 ) to 6 ( x 2 5 ) .

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Subtract 3 times ( 2 x 1 ) from 8 times ( x 4 ) .

2 x 29

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( x 3 ) ( x 8 )

x 2 11 x + 24

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( 2 a 5 ) ( 5 a 1 )

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( 8 b + 2 c ) ( 2 b c )

16 b 2 4 b c 2 c 2

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( 3 a ) 2

a 2 6 a + 9

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( 6 x 4 ) 2

36 x 2 48 x + 16

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( x y ) 2

x 2 + 2 x y + y 2

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( m + 1 ) ( m 1 )

m 2 1

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( 3 c + 10 ) ( 3 c 10 )

9 c 2 100

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( 4 a + 3 b ) ( 4 a 3 b )

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( 5 + 2 b ) ( 5 2 b )

25 4 b 2

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( y + 3 a ) ( 2 y + a )

2 y 2 + 7 a y + 3 a 2

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( x 2 + 2 ) ( x 2 3 )

x 4 x 2 6

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8 ( 2 y 4 ) ( 3 y + 8 )

48 y 2 + 32 y 256

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m 2 n ( m + n ) ( m + 2 n )

m 4 n + 3 m 3 n 2 + 2 m 2 n 3

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

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3 p ( p 2 + 5 p + 4 ) ( p 2 + 2 p + 7 )

3 p 5 + 21 p 4 + 63 p 3 + 129 p 2 + 84 p

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( x 2 ) 2

x 2 4 x + 4

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( x 2 + y ) 2

x 4 + 2 x 2 y + y 2

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( 3 x 2 y 3 4 x 4 y ) 2

9 x 4 y 6 24 x 6 y 4 + 16 x 8 y 2

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Terminology associated with equations ( [link] )

Find the domain of the equations for the following problems.

y = 8 x + 7

all real numbers

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y = 4 x 2

all real numbers except 2

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z = 4 x + 5 y + 10

x  can equal any real number;  y  can equal any number except 10

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Questions & Answers

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
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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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