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  1. Preface
  2. 1 Prerequisites
    1. Introduction to Prerequisites
    2. 1.1 Real Numbers: Algebra Essentials
    3. 1.2 Exponents and Scientific Notation
    4. 1.3 Radicals and Rational Exponents
    5. 1.4 Polynomials
    6. 1.5 Factoring Polynomials
    7. 1.6 Rational Expressions
    8. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 Equations and Inequalities
    1. Introduction to Equations and Inequalities
    2. 2.1 The Rectangular Coordinate Systems and Graphs
    3. 2.2 Linear Equations in One Variable
    4. 2.3 Models and Applications
    5. 2.4 Complex Numbers
    6. 2.5 Quadratic Equations
    7. 2.6 Other Types of Equations
    8. 2.7 Linear Inequalities and Absolute Value Inequalities
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Functions
    1. Introduction to Functions
    2. 3.1 Functions and Function Notation
    3. 3.2 Domain and Range
    4. 3.3 Rates of Change and Behavior of Graphs
    5. 3.4 Composition of Functions
    6. 3.5 Transformation of Functions
    7. 3.6 Absolute Value Functions
    8. 3.7 Inverse Functions
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Linear Functions
    1. Introduction to Linear Functions
    2. 4.1 Linear Functions
    3. 4.2 Modeling with Linear Functions
    4. 4.3 Fitting Linear Models to Data
    5. Chapter Review
      1. Key Terms
      2. Key Concepts
    6. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Polynomial and Rational Functions
    1. Introduction to Polynomial and Rational Functions
    2. 5.1 Quadratic Functions
    3. 5.2 Power Functions and Polynomial Functions
    4. 5.3 Graphs of Polynomial Functions
    5. 5.4 Dividing Polynomials
    6. 5.5 Zeros of Polynomial Functions
    7. 5.6 Rational Functions
    8. 5.7 Inverses and Radical Functions
    9. 5.8 Modeling Using Variation
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Exponential and Logarithmic Functions
    1. Introduction to Exponential and Logarithmic Functions
    2. 6.1 Exponential Functions
    3. 6.2 Graphs of Exponential Functions
    4. 6.3 Logarithmic Functions
    5. 6.4 Graphs of Logarithmic Functions
    6. 6.5 Logarithmic Properties
    7. 6.6 Exponential and Logarithmic Equations
    8. 6.7 Exponential and Logarithmic Models
    9. 6.8 Fitting Exponential Models to Data
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 Systems of Equations and Inequalities
    1. Introduction to Systems of Equations and Inequalities
    2. 7.1 Systems of Linear Equations: Two Variables
    3. 7.2 Systems of Linear Equations: Three Variables
    4. 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables
    5. 7.4 Partial Fractions
    6. 7.5 Matrices and Matrix Operations
    7. 7.6 Solving Systems with Gaussian Elimination
    8. 7.7 Solving Systems with Inverses
    9. 7.8 Solving Systems with Cramer's Rule
    10. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Analytic Geometry
    1. Introduction to Analytic Geometry
    2. 8.1 The Ellipse
    3. 8.2 The Hyperbola
    4. 8.3 The Parabola
    5. 8.4 Rotation of Axes
    6. 8.5 Conic Sections in Polar Coordinates
    7. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Sequences, Probability, and Counting Theory
    1. Introduction to Sequences, Probability and Counting Theory
    2. 9.1 Sequences and Their Notations
    3. 9.2 Arithmetic Sequences
    4. 9.3 Geometric Sequences
    5. 9.4 Series and Their Notations
    6. 9.5 Counting Principles
    7. 9.6 Binomial Theorem
    8. 9.7 Probability
    9. Chapter Review
      1. Key Terms
      2. Key Equations
      3. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  11. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
  12. Index

Try It

1.1 Real Numbers: Algebra Essentials

1.
  1. 11 1 11 1
  2. 3 1 3 1
  3. 4 1 4 1
2.
  1. 4 (or 4.0), terminating;
  2. 0. 615384 ¯ , 0. 615384 ¯ , repeating;
  3. –0.85, terminating
3.
  1. rational and repeating;
  2. rational and terminating;
  3. irrational;
  4. rational and terminating;
  5. irrational
4.
  1. positive, irrational; right
  2. negative, rational; left
  3. positive, rational; right
  4. negative, irrational; left
  5. positive, rational; right
5.
N W I Q Q'
a. 35 7 35 7 X X
b. 0 X X X
c. 169 169 X X X X
d. 24 24 X
e. 4.763763763... X
6.
  1. 10
  2. 2
  3. 4.5
  4. 25
  5. 26
7.
  1. 11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;
  2. 33, distributive property;
  3. 26, distributive property;
  4. 4 9 , 4 9 , commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;
  5. 0, distributive property, inverse property of addition, identity property of addition
8.

Constants Variables
a. 2πr( r+h ) 2πr( r+h ) 2,π 2,π r,h r,h
b. 2(L + W) 2 L, W
c. 4 y 3 +y 4 y 3 +y 4 y y
9.
  1. 5;
  2. 11;
  3. 9;
  4. 26
10.
  1. 4;
  2. 11;
  3. 121 3 π 121 3 π ;
  4. 1728;
  5. 3
11.

1,152 cm2

12.
  1. −2y−2zor −2( y+z ); −2y−2zor −2( y+z );
  2. 2 t −1; 2 t −1;
  3. 3pq−4p+q; 3pq−4p+q;
  4. 7r−2s+6 7r−2s+6
13.

A=P( 1+rt ) A=P( 1+rt )

1.2 Exponents and Scientific Notation

1.
  1. k 15 k 15
  2. ( 2 y ) 5 ( 2 y ) 5
  3. t 14 t 14
2.
  1. s 7 s 7
  2. ( −3 ) 5 ( −3 ) 5
  3. ( e f 2 ) 2 ( e f 2 ) 2
3.
  1. ( 3y ) 24 ( 3y ) 24
  2. t 35 t 35
  3. ( g ) 16 ( g ) 16
4.
  1. 1 1
  2. 1 2 1 2
  3. 1 1
  4. 1 1
5.
  1. 1 ( −3t ) 6 1 ( −3t ) 6
  2. 1 f 3 1 f 3
  3. 2 5 k 3 2 5 k 3
6.
  1. t −5 = 1 t 5 t −5 = 1 t 5
  2. 1 25 1 25
7.
  1. g 10 h 15 g 10 h 15
  2. 125 t 3 125 t 3
  3. −27 y 15 −27 y 15
  4. 1 a 18 b 21 1 a 18 b 21
  5. r 12 s 8 r 12 s 8
8.
  1. b 15 c 3 b 15 c 3
  2. 625 u 32 625 u 32
  3. −1 w 105 −1 w 105
  4. q 24 p 32 q 24 p 32
  5. 1 c 20 d 12 1 c 20 d 12
9.
  1. v 6 8 u 3 v 6 8 u 3
  2. 1 x 3 1 x 3
  3. e 4 f 4 e 4 f 4
  4. 27r s 27r s
  5. 1 1
  6. 16 h 10 49 16 h 10 49
10.
  1. $1.52× 10 5 $1.52× 10 5
  2. 7.158× 10 9 7.158× 10 9
  3. $8.55× 10 13 $8.55× 10 13
  4. 3.34× 10 −9 3.34× 10 −9
  5. 7.15× 10 −8 7.15× 10 −8
11.
  1. 703,000 703,000
  2. −816,000,000,000 −816,000,000,000
  3. −0.00000000000039 −0.00000000000039
  4. 0.000008 0.000008
12.
  1. 8.475× 10 6 8.475× 10 6
  2. 8× 10 8 8× 10 8
  3. 2.976× 10 13 2.976× 10 13
  4. 4.3× 10 6 4.3× 10 6
  5. 1.24× 10 15 1.24× 10 15
13.

Number of cells: 3× 10 13 ; 3× 10 13 ; length of a cell: 8× 10 −6 8× 10 −6 m; total length: 2.4× 10 8 2.4× 10 8 m or 240,000,000 240,000,000 m.

1.3 Radicals and Rational Exponents

1.
  1. 15 15
  2. 3 3
  3. 4 4
  4. 17 17
2.

5| x || y | 2yz . 5| x || y | 2yz . Notice the absolute value signs around x and y? That’s because their value must be positive!

3.

10| x | 10| x |

4.

x 2 3 y 2 . x 2 3 y 2 . We do not need the absolute value signs for y 2 y 2 because that term will always be nonnegative.

5.

b 4 3ab b 4 3ab

6.

13 5 13 5

7.

0 0

8.

6 6 6 6

9.

14−7 3 14−7 3

10.
  1. −6 −6
  2. 6 6
  3. 88 9 3 88 9 3
11.

( 9 ) 5 = 3 5 =243 ( 9 ) 5 = 3 5 =243

12.

x (5y) 9 2 x (5y) 9 2

13.

28 x 23 15 28 x 23 15

1.4 Polynomials

1.

The degree is 6, the leading term is x 6 , x 6 , and the leading coefficient is −1. −1.

2.

2 x 3 +7 x 2 −4x−3 2 x 3 +7 x 2 −4x−3

3.

−11 x 3 x 2 +7x−9 −11 x 3 x 2 +7x−9

4.

3 x 4 −10 x 3 −8 x 2 +21x+14 3 x 4 −10 x 3 −8 x 2 +21x+14

5.

3 x 2 +16x−35 3 x 2 +16x−35

6.

16 x 2 −8x+1 16 x 2 −8x+1

7.

4 x 2 −49 4 x 2 −49

8.

6 x 2 +21xy−29x−7y+9 6 x 2 +21xy−29x−7y+9

1.5 Factoring Polynomials

1.

( b 2 a)(x+6) ( b 2 a)(x+6)

2.

(x−6)(x−1) (x−6)(x−1)

3.
  1. (2x+3)(x+3) (2x+3)(x+3)
  2. ( 3x−1 )( 2x+1 ) ( 3x−1 )( 2x+1 )
4.

(7x−1) 2 (7x−1) 2

5.

(9y+10)(9y10) (9y+10)(9y10)

6.

(6a+b)(36 a 2 −6ab+ b 2 ) (6a+b)(36 a 2 −6ab+ b 2 )

7.

(10x1)( 100 x 2 +10x+1 ) (10x1)( 100 x 2 +10x+1 )

8.

(5a−1) 1 4 (17a−2) (5a−1) 1 4 (17a−2)

1.6 Rational Expressions

1.

1 x+6 1 x+6

2.

(x+5)(x+6) (x+2)(x+4) (x+5)(x+6) (x+2)(x+4)

3.

1 1

4.

2(x−7) (x+5)(x−3) 2(x−7) (x+5)(x−3)

5.

x 2 y 2 x y 2 x 2 y 2 x y 2

1.1 Section Exercises

1.

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

3.

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

5.

−6 −6

7.

−2 −2

9.

−9 −9

11.

9

13.

-2

15.

4

17.

0

19.

9

21.

25

23.

−6 −6

25.

17

27.

4

29.

14 14

31.

−66 −66

33.

–12 –12

35.

–44 –44

37.

–2 –2

39.

−14y11 −14y11

41.

−4b+1 −4b+1

43.

43z3 43z3

45.

9y+45 9y+45

47.

−6b+6 −6b+6

49.

16x 3 16x 3

51.

9x 9x

53.

1 2 ( 4010 )+5 1 2 ( 4010 )+5

55.

irrational number

57.

g+4002( 600 )=1200 g+4002( 600 )=1200

59.

inverse property of addition

61.

68.4

63.

true

65.

irrational

67.

rational

1.2 Section Exercises

1.

No, the two expressions are not the same. An exponent tells how many times you multiply the base. So 2 3 2 3 is the same as 2×2×2, 2×2×2, which is 8. 3 2 3 2 is the same as 3×3, 3×3, which is 9.

3.

It is a method of writing very small and very large numbers.

5.

81

7.

243

9.

1 16 1 16

11.

1 11 1 11

13.

1

15.

4 9 4 9

17.

12 40 12 40

19.

1 7 9 1 7 9

21.

3.14× 10 5 3.14× 10 5

23.

16,000,000,000

25.

a 4 a 4

27.

b 6 c 8 b 6 c 8

29.

a b 2 d 3 a b 2 d 3

31.

m 4 m 4

33.

q 5 p 6 q 5 p 6

35.

y 21 x 14 y 21 x 14

37.

25 25

39.

72 a 2 72 a 2

41.

c 3 b 9 c 3 b 9

43.

y 81 z 6 y 81 z 6

45.

0.00135 m

47.

1.0995× 10 12 1.0995× 10 12

49.

0.00000000003397 in.

51.

12,230,590,464 m 66 m 66

53.

a 14 1296 a 14 1296

55.

n a 9 c n a 9 c

57.

1 a 6 b 6 c 6 1 a 6 b 6 c 6

59.

0.000000000000000000000000000000000662606957

1.3 Section Exercises

1.

When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.

3.

The principal square root is the nonnegative root of the number.

5.

16

7.

10

9.

14

11.

7 2 7 2

13.

9 5 5 9 5 5

15.

25

17.

2 2

19.

2 6 2 6

21.

5 6 5 6

23.

6 35 6 35

25.

2 15 2 15

27.

6 10 19 6 10 19

29.

1+ 17 2 1+ 17 2

31.

7 2 3 7 2 3

33.

15 5 15 5

35.

20 x 2 20 x 2

37.

7 p 7 p

39.

17 m 2 m 17 m 2 m

41.

2b a 2b a

43.

15x 7 15x 7

45.

5 y 4 2 5 y 4 2

47.

4 7d 7d 4 7d 7d

49.

2 2 +2 6x 1−3x 2 2 +2 6x 1−3x

51.

w 2w w 2w

53.

3 x 3x 2 3 x 3x 2

55.

5 n 5 5 5 n 5 5

57.

9 m 19m 9 m 19m

59.

2 3d 2 3d

61.

3 2 x 2 4 2 3 2 x 2 4 2

63.

6z 2 3 6z 2 3

65.

500 feet

67.

−5 2 −6 7 −5 2 −6 7

69.

mnc a 9 cmn mnc a 9 cmn

71.

2 2 x+ 2 4 2 2 x+ 2 4

73.

3 3 3 3

1.4 Section Exercises

1.

The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.

3.

Use the distributive property, multiply, combine like terms, and simplify.

5.

2

7.

8

9.

2

11.

4 x 2 +3x+19 4 x 2 +3x+19

13.

3 w 2 +30w+21 3 w 2 +30w+21

15.

11 b 4 −9 b 3 +12 b 2 −7b+8 11 b 4 −9 b 3 +12 b 2 −7b+8

17.

24 x 2 −4x−8 24 x 2 −4x−8

19.

24 b 4 −48 b 2 +24 24 b 4 −48 b 2 +24

21.

99 v 2 −202v+99 99 v 2 −202v+99

23.

8 n 3 −4 n 2 +72n−36 8 n 3 −4 n 2 +72n−36

25.

9 y 2 −42y+49 9 y 2 −42y+49

27.

16 p 2 +72p+81 16 p 2 +72p+81

29.

9 y 2 −36y+36 9 y 2 −36y+36

31.

16 c 2 −1 16 c 2 −1

33.

225 n 2 −36 225 n 2 −36

35.

−16 m 2 +16 −16 m 2 +16

37.

121 q 2 −100 121 q 2 −100

39.

16 t 4 +4 t 3 −32 t 2 t+7 16 t 4 +4 t 3 −32 t 2 t+7

41.

y 3 −6 y 2 y+18 y 3 −6 y 2 y+18

43.

3 p 3 p 2 −12p+10 3 p 3 p 2 −12p+10

45.

a 2 b 2 a 2 b 2

47.

16 t 2 −40tu+25 u 2 16 t 2 −40tu+25 u 2

49.

4 t 2 + x 2 +4t−5txx 4 t 2 + x 2 +4t−5txx

51.

24 r 2 +22rd−7 d 2 24 r 2 +22rd−7 d 2

53.

32 x 2 −4x−3 32 x 2 −4x−3 m2

55.

32 t 3 100 t 2 +40t+38 32 t 3 100 t 2 +40t+38

57.

a 4 +4 a 3 c−16a c 3 −16 c 4 a 4 +4 a 3 c−16a c 3 −16 c 4

1.5 Section Exercises

1.

The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, 4 x 2 4 x 2 and −9 y 2 −9 y 2 don’t have a common factor, but the whole polynomial is still factorable: 4 x 2 −9 y 2 =( 2x+3y )( 2x−3y ). 4 x 2 −9 y 2 =( 2x+3y )( 2x−3y ).

3.

Divide the x x term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

5.

7m 7m

7.

10 m 3 10 m 3

9.

y y

11.

( 2a−3 )( a+6 ) ( 2a−3 )( a+6 )

13.

( 3n−11 )( 2n+1 ) ( 3n−11 )( 2n+1 )

15.

( p+1 )( 2p−7 ) ( p+1 )( 2p−7 )

17.

( 5h+3 )( 2h−3 ) ( 5h+3 )( 2h−3 )

19.

( 9d−1 )( d−8 ) ( 9d−1 )( d−8 )

21.

( 12t+13 )( t−1 ) ( 12t+13 )( t−1 )

23.

(4x+10)(4x10) (4x+10)(4x10)

25.

(11p+13)(11p13) (11p+13)(11p13)

27.

(19d+9)(19d9) (19d+9)(19d9)

29.

(12b+5c)(12b5c) (12b+5c)(12b5c)

31.

( 7n+12 ) 2 ( 7n+12 ) 2

33.

( 15y+4 ) 2 ( 15y+4 ) 2

35.

(5p12) 2 (5p12) 2

37.

(x+6)( x 2 6x+36) (x+6)( x 2 6x+36)

39.

(5a+7)(25 a 2 35a+49) (5a+7)(25 a 2 35a+49)

41.

(4x5)(16 x 2 +20x+25) (4x5)(16 x 2 +20x+25)

43.

(5r+12s)(25 r 2 60rs+144 s 2 ) (5r+12s)(25 r 2 60rs+144 s 2 )

45.

( 2c+3 ) 1 4 ( −7c15 ) ( 2c+3 ) 1 4 ( −7c15 )

47.

( x+2 ) 2 5 ( 19x+10 ) ( x+2 ) 2 5 ( 19x+10 )

49.

( 2z9 ) 3 2 ( 27z99 ) ( 2z9 ) 3 2 ( 27z99 )

51.

( 14x−3 )( 7x+9 ) ( 14x−3 )( 7x+9 )

53.

( 3x+5 )( 3x−5 ) ( 3x+5 )( 3x−5 )

55.

(2x+5) 2 (2x5) 2 (2x+5) 2 (2x5) 2

57.

(4 z 2 +49 a 2 )(2z+7a)(2z7a) (4 z 2 +49 a 2 )(2z+7a)(2z7a)

59.

1 ( 4x+9 )( 4x−9 )( 2x+3 ) 1 ( 4x+9 )( 4x−9 )( 2x+3 )

1.6 Section Exercises

1.

You can factor the numerator and denominator to see if any of the terms can cancel one another out.

3.

True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.

5.

y+5 y+6 y+5 y+6

7.

3b+3 3b+3

9.

x+4 2x+2 x+4 2x+2

11.

a+3 a3 a+3 a3

13.

3n8 7n3 3n8 7n3

15.

c6 c+6 c6 c+6

17.

1 1

19.

d 2 25 25 d 2 1 d 2 25 25 d 2 1

21.

t+5 t+3 t+5 t+3

23.

6x5 6x+5 6x5 6x+5

25.

p+6 4p+3 p+6 4p+3

27.

2d+9 d+11 2d+9 d+11

29.

12b+5 3b−1 12b+5 3b−1

31.

4y−1 y+4 4y−1 y+4

33.

10x+4y xy 10x+4y xy

35.

9a7 a 2 2a3 9a7 a 2 2a3

37.

2 y 2 y+9 y 2 y2 2 y 2 y+9 y 2 y2

39.

5 z 2 +z+5 z 2 z2 5 z 2 +z+5 z 2 z2

41.

x+2xy+y x+xy+y+1 x+2xy+y x+xy+y+1

43.

2b+7a a b 2 2b+7a a b 2

45.

18+ab 4b 18+ab 4b

47.

ab ab

49.

3 c 2 +3c2 2 c 2 +5c+2 3 c 2 +3c2 2 c 2 +5c+2

51.

15x+7 x−1 15x+7 x−1

53.

x+9 x−9 x+9 x−9

55.

1 y+2 1 y+2

57.

4 4

Review Exercises

1.

−5 −5

3.

53

5.

y=24 y=24

7.

32m 32m

9.

whole

11.

irrational

13.

16 16

15.

3 a 6 3 a 6

17.

x 3 32 y 3 x 3 32 y 3

19.

a a

21.

1.634× 10 7 1.634× 10 7

23.

14

25.

5 3 5 3

27.

4 2 5 4 2 5

29.

7 2 50 7 2 50

31.

10 3 10 3

33.

−3 −3

35.

3 x 3 +4 x 2 +6 3 x 3 +4 x 2 +6

37.

5 x 2 x+3 5 x 2 x+3

39.

k 2 3k18 k 2 3k18

41.

x 3 + x 2 +x+1 x 3 + x 2 +x+1

43.

3 a 2 +5ab2 b 2 3 a 2 +5ab2 b 2

45.

9p 9p

47.

4 a 2 4 a 2

49.

(4a3)(2a+9) (4a3)(2a+9)

51.

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

53.

(2h3k) 2 (2h3k) 2

55.

(p+6)( p 2 6p+36) (p+6)( p 2 6p+36)

57.

(4q3p)(16 q 2 +12pq+9 p 2 ) (4q3p)(16 q 2 +12pq+9 p 2 )

59.

( p+3 ) 1 3 ( −5p24 ) ( p+3 ) 1 3 ( −5p24 )

61.

x+3 x4 x+3 x4

63.

1 2 1 2

65.

m+2 m3 m+2 m3

67.

6x+10y xy 6x+10y xy

69.

1 6 1 6

Practice Test

1.

rational

3.

x=–2 x=–2

5.

3,141,500

7.

16 16

9.

9

11.

2x 2x

13.

21

15.

3 x 4 3 x 4

17.

21 6 21 6

19.

13 q 3 4 q 2 5q 13 q 3 4 q 2 5q

21.

n 3 6 n 2 +12n8 n 3 6 n 2 +12n8

23.

(4x+9)(4x9) (4x+9)(4x9)

25.

(3c11)(9 c 2 +33c+121) (3c11)(9 c 2 +33c+121)

27.

4z3 2z1 4z3 2z1

29.

3a+2b 3b 3a+2b 3b

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