<< Chapter < Page Chapter >> Page >
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

Got questions? Get instant answers now!

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

12 x 2 y 3 + 36 y 3

12 y 3

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2 ( a + 2 b )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

6 a 2 b 3 c + 5 x 2 y

no common factors

Got questions? Get instant answers now!

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

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

12

Got questions? Get instant answers now!

a 4 ' s in 6 a 4 ?

Got questions? Get instant answers now!

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

2 a 2 b

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

7 y ( y + 3 ) , 7 y

( y + 3 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 .

Got questions? Get instant answers now!

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 .

Got questions? Get instant answers now!

P 2 = k a 3

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

10

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

4 .1515 × 10 12

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

7 50 or 0.14

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

binomial; tenth; 9, 10

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

. . . because there is a variable in the denominator

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

quadratic

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

22 x 2 y 3 + 3 x y + 6

Got questions? Get instant answers now!

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

11 y 2 + 38 y + 14

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

5 x 2 + 2 x + 3

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

60 c 2 + 120 a + 60 b

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

6 a 4 ( a 2 + 5 )

6 a 6 + 30 a 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( x + 2 ) ( x + 3 )

x 2 + 5 x + 6

Got questions? Get instant answers now!

( a + 1 ) ( a + 3 )

a 2 + 4 a + 3

Got questions? Get instant answers now!

4 x y 10 x y

6 x y

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

7 x 4 15 x 4

8 x 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

4 ( x 8 )

4 x 32

Got questions? Get instant answers now!

3 a ( 5 a 6 )

15 a 2 + 18 a

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

[ ( { [ ( 5 ) ] } ) ]

5

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

3 ( a 1 ) 4 ( a + 6 )

a 27

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Add 3 x + 4 to 5 x 8 .

2 x 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

2 x 29

Got questions? Get instant answers now!

( x 3 ) ( x 8 )

x 2 11 x + 24

Got questions? Get instant answers now!

( 2 a 5 ) ( 5 a 1 )

Got questions? Get instant answers now!

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

16 b 2 4 b c 2 c 2

Got questions? Get instant answers now!

( 3 a ) 2

a 2 6 a + 9

Got questions? Get instant answers now!

( 6 x 4 ) 2

36 x 2 48 x + 16

Got questions? Get instant answers now!

( x y ) 2

x 2 + 2 x y + y 2

Got questions? Get instant answers now!

( m + 1 ) ( m 1 )

m 2 1

Got questions? Get instant answers now!

( 3 c + 10 ) ( 3 c 10 )

9 c 2 100

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( 5 + 2 b ) ( 5 2 b )

25 4 b 2

Got questions? Get instant answers now!

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

2 y 2 + 7 a y + 3 a 2

Got questions? Get instant answers now!

( x 2 + 2 ) ( x 2 3 )

x 4 x 2 6

Got questions? Get instant answers now!

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

48 y 2 + 32 y 256

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( x 2 ) 2

x 2 4 x + 4

Got questions? Get instant answers now!

( x 2 + y ) 2

x 4 + 2 x 2 y + y 2

Got questions? Get instant answers now!

( 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

Got questions? Get instant answers now!

Terminology associated with equations ( [link] )

Find the domain of the equations for the following problems.

y = 8 x + 7

all real numbers

Got questions? Get instant answers now!

y = 4 x 2

all real numbers except 2

Got questions? Get instant answers now!

z = 4 x + 5 y + 10

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

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask