Special Products, Factoring, Basic Operations of Algebraic Expressions

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2. O M G PREVIOUS NEXT VISION A premier university in CALABARZON, offering academic programs and related services designed to respond to the requirements of the Philippines and the global economy, particularly in Asian Countrie s. TABLE OF CONTENTS

3. V G O PREVIOUS NEXT MISSION The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, industrial technologies, teacher education, medicine, law, arts and sciences, information technologies and other related fields. It shall also undertake research and extension services and provide progressive leadership in its areas of specialization. TABLE OF CONTENTS

4. V O M PREVIOUS NEXT GOALS In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness. TABLE OF CONTENTS

6. FOREWORD This Teacher’s Visual Presentation Hand-out entitled “Workbook in Solving Algebraic Expression for Second Year High School” is part of the requirements in Educational Technology 2 under the revised curriculum for Bachelor in Elementary Education based on CHED Memorandum Order (CMO)-30, Series of 2004. Educational Technology 2 is a three (3)-unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. PREVIOUS NEXT TABLE OF CONTENTS

9. PREVIOUS NEXT ACKNOWLEDGEMENT The authors wish to acknowledge the following persons who gave them the inspiration and the strength to write this module: The Education Faculty of Laguna State Polytechnic University whose insights inspired the writers to finished this module; Prof. Lydia R. Chavez, Dean of College of Education for appreciating and checking our workbook. Mr. For Ian Sandoval, Module Adviser for assisting us in finishing our workbook. Mrs. Delia Mercado, Module Consultant for checking and giving pieces of advice in making our workbook. PREVIOUS NEXT TABLE OF CONTENTS

10. Dr. Corazon N. San Agustin, an Educational Technology professor for being the first one who teach us to make a module. Friends who helped to finished this module. The authors’ families who inspired them and ignited their desire to pursue their passion for writing; and Lastly, to the Lord God Almighty who is the source of enlightenment and inspiration. THE AUTHORS PREVIOUS NEXT TABLE OF CONTENTS

11. INTRODUCTION This workbook is composed of activities in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring. The workbook is designed to give the learner an opportunity to develop himself in solving mathematical problems in algebra most especially in algebraic expression. The exercises in understanding and analyzing different terminologies and concepts in algebraic expression, solving algebraic expression using fundamental operations, solving algebraic expression using synthetic methods, and simple types of factoring are for the student’s self improvement. The exercises were designed to give the learner ample exercises to develop skill in solving algebraic expressions and mathematical problems in algebra. PREVIOUS NEXT TABLE OF CONTENTS

12. GENERAL OBJECTIVES In this workbook entitled “Workbook in Solving Algebraic Expression for Second Year High School Students” the students are expected to: 1. Differentiate concept and terminologies in algebraic expression. 2. Measure proficiency in analyzing the function of terminologies in algebraic expression. 3. Avoid guessing an answer in true or false. 4. Define different terminologies in algebraic expression. 5. Analyze the standards in answering fill in the blanks test. 6. Explore the knowledge of the students in analyzing the concepts and terminologies in algebraic expression. PREVIOUS NEXT TABLE OF CONTENTS

13. 7. Recognize the different terms of a polynomial. 8. Write a monomial, binomial and trinomial equation. 9. Specify if the equation is a monomial, binomial or trinomial. 10. Define different terms of polynomial. 11. Compare monomial to binomial, binomial to trinomial. 12. Improve the abilities in comparing monomial to binomial and binomial to trinomial. 13. Write different equation of a polynomial in a monomial, binomial and trinomial. 14. Identify different terms of polynomials. 15. Increased proficiency in comparing monomial, binomial and trinomial PREVIOUS NEXT TABLE OF CONTENTS

14. 16. Recall the different degree of polynomial. 17. Have confidence to their self to find the correct answer. 18. Improve the abilities in matching an equation to each degree of polynomials. 19. Identify degree of polynomials. 20. Select the best answer in identifying the degree of polynomial. 21. Have patient in answering multiple choice test. PREVIOUS NEXT TABLE OF CONTENTS

15. TABLE OF CONTENTS Vision, Mission, Goals and Objectives Foreword Acknowledgement Introduction General Objectives PREVIOUS NEXT

16. PREVIOUS NEXT Chapter I Understanding and Analyzing Different Terminologies in Algebraic Expression Pre Test I Activity 1 Activity 2 Activity 3 Activity 4 Activity 5 Activity 6 Activity 7

17. PREVIOUS NEXT Chapter II Solving Algebraic Expression Using Fundamental Operations Post Test I Activity 10 Pre Test II Activity 11 Activity 14 Activity 12 Activity 13 Activity 9 Activity 8

18. PREVIOUS NEXT Activity 18 Activity 19 Activity 20 Activity 21 Post Test II Activity 15 Activity 17 Activity 16

19. PREVIOUS NEXT Activity 24 Activity 25 Activity 26 Activity 27 Activity 28 Chapter III Using Synthetic Method in Solving Algebraic Expression Activity 23 Activity 22 Pre Test III

20. PREVIOUS NEXT Activity 32 Activity 33 Activity 34 Activity 35 Activity 36 Post Test III Activity 31 Activity 30 Activity 29

21. PREVIOUS NEXT Chapter IV Simple Types of Factoring of Algebraic Expression Pre Test IV Activity 37 Activity 38 Activity 39 Activity 40 Activity 41 Activity 42 Activity 43

22. PREVIOUS NEXT Post Test IV Activity 44 Activity 45 Activity 46 Activity 47 Activity 48 Activity 49 Activity 50 Activity 51 Activity 52 Activity 53 Activity 54

23. About the Author References PREVIOUS NEXT Final

30. Answers QUESTIONS QUESTIONS QUESTIONS QUESTIONS A. 1.B 2.B 3.B 4.B 5.B B. 1. e 2. b 3. a 4. c 5. d C. 1. constant 2.Literal coefficient 3. monomial 4. variable 5. polynomials D . 1. B 2. A 3. B 4. C 5. C

31. QUESTIONS QUESTIONS QUESTIONS QUESTIONS QUESTIONS G . 1. c 2. a 3. e 4. d 5. b H . 1. c 2.c 3.c 4.c 5.c F . 1. binomial 2. trinomial 3. monomial 4. binomial 5. trinomial E . 1. c 2. a 3. b 4. d 5. e I. 1. 8 th degree 2. 9 th degree 3. 11 th degree 4. 9 th degree 5. 6 th degree

37. Previous Next Answers __________6. It is a positive or negative integer, written in the upper right of letters or symbols. __________7. It is polynomial contains of two terms. __________8. It is a terms which differ only in their constant coefficient. __________9. It is an algebraic expression involves non-negative powers or exponents containing numbers or variables. It contains of one or more terms. __________10. It is a polynomial contains of three terms.

43. Activity 6 Name:____________________Score:_____________Date:____________ Year and Section:____________________Teacher: ___________________ Objectives: 1. To identify different terms of polynomials; 2. To increase proficiency in comparing monomial, binomial and trinomial; and 3. To improve the abilities in comparing monomial to binomial and binomial to trinomial. Instruction: Identify the number of terms of the given polynomials. Write your answer in the space provided before each number. ______________1. 6x² - 8 ______________2. 5x² + 35xy + 25y² ______________3. 9xy ______________4. 8x² + 10x ______________5. 7x² + 5xy + 9y² ______________6. 25xy + 14y ______________7. 10ab ______________8. 81x² + 6xy – 14y ______________9. 49x² + 16y² ______________10. 36a² - 25b⁴ Previous Next Answers TABLE OF CONTENTS

53. A. Instruction: Identify the terms and terminologies in each number. Encircle the letter of your answer. 1. It is a letter or symbol coefficient containing nonnegative power or exponent. a. Terms b. Coefficient c. Exponent 2. It is any letter or symbol that is used to represent any element of a given polynomial. a. Algebraic Expression b. Variables c. Polynomials 3. It is a positive or negative integer, written in the upper right of letters any or symbols. a. Exponent b. Integers c. Monomial 4. Terms which differ only in their constant coefficient is called___________. a. Coefficient b. Literal Coefficient c. Like Terms 5. It is a polynomial containing three terms. a. Monomial b. Binomial c. Trinomial Previous Next Answers

54. 6. It is a number in a given polynomial. a. Constant b. Variable c. Exponent 7. Algebraic Expression involves non-negative power or exponent containing numbers or variables. a. Polynomial b. Numerical Coefficient c. Literal Coefficient 8. It is a number or a constant with variables and containing non-negative powers or exponents. a. Coefficient b. Polynomial c. Variable 9. It is a factor of product of a polynomial. a. Terms b. Degree c. Factor 10. It is a polynomial contains one term. a. Monomial b. Binomial c. Trinomial Previous Next Answers

60. INSTRUCTION: Write your solution in performing the given operations. 1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) 2. (3x – 8y + 6z) + ( 7y – 2x + 4z) 3. (5x³ + 2y²) + ( 7x³ - y²) 4. (6 – y + 3x) + (-8x + 2y + 10) 5. (7x + 4y) + (5x + 8y) 6. (5x² + 4y) + (7x² + 5y) 7. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y) 8. (3x + 4xy – 6y) + (4xy – 3y + 2x) 9. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²) 10. (5a² + 3ab + 6c) + (8a² + 3ab + 4c) Previous Next Solutions

61. 11. (-5x² – 4x + 2y) – (6x² - x + 3) 12. (2a³ + a² + 4a – 3) – (4a³ - 8a² + 2a + 6) 13. (16a + 9b) – (8a + 2b) 14. (-16a + 9b) – (8a – 7b) 15. (x³ - 3x² + 7x + 2) – (5x³ + x² - 10x + 24) 16. (x + y)(2x + 3y)(5x + 4y) 17. (2m 2 )(4m) 18. 3x 3 (4y 2 ) 19. (5a + 7b – 8c)(8a + 4c) 20. (9u + 5v – 2z)(5u + 2v – 2u) Previous Next Solutions

62. 21. (88x – 44y) + (55x + 22y) 22. (37b + 49ab² - 28a³) + ( 34a³ - 32ab² - 25b) 23. (59x² + 49y) + (74x² + 54y) 24. 13x(85z) 25. (73x + 45xy – 66y) + (64xy – 93y + 82x) 26. 34m²p(86op) 27. (13x³ +14y + 24xy²) + (32x³ + 84xy² + 26y) 28. 18j²(17j⁸k⁶) 29. 14h²l⁵(-36t²) 30. 59i⁶l²(61u³v³) Previous Next Solutions

63. 31. 58xyz(34xz) 32. -14f²(62huv) 33. 28xy²(18x²) 34. 92a²b²c(57a³b²c²) 35. (x 2 + 7x + 10) ÷ (x – 5) 36. (2 3 a 4 b) ÷ (3 2 c) 37. (x 2 – 9x – 10) ÷ (x + 1) 38. (a 3 – 1)(a – 1) 39. (12t 4 – 25t 3 + 18t 2 + 7t – 25) ÷ (3t – 4) 40. (73x + 45xy – 66y) + (64xy – 93y + 82x) Previous Next Solutions

64. Answers Pre Test 31 - 40 Pre Test 21 - 30 Pre Test 11-20 Pre Test 1 - 10 A. 1. 14a 2 – 10b + 5c 2. x – y + 10z 3. 12x 3 + y 2 4. -5x + y + 16 5. 12x + 12y 6. 12x 2 + 9y 7. 6x 3 + 12xy 2 + 6y 8.5x + 8xy – 9y 9. 10x 5 + 5xy 3 + 4y 2 10.13a 2 + 6ab + 10c B 11.-11x 2 – 3x + 2y + 3 12. -2a 3 – 7a 2 + 6a + 3 13. 8a + 7b 14. -24a + 16b 15. -4x 3 – 4x 2 + 17x + 22 16. 10x 3 + 33x 2 y + 35xy 2 + 12y 3 17. 8m 3 18. 12x 3 y 2 19. 40a 2 + 56ab – 44ac + 28bc – 32c 2 20. 27u 2 + 33uv – 6uz + 10v 2 – 4vz C 21. 113x – 22y 22. 6a 3 + 7ab 2 + 12b 23. 133x 2 + 103y 24. 1105xz 25. 155x + 109xy – 159y 26. 2924 m 2 op 2 27.45x 3 + 40y + 108xyz 28.306j 10 k 6 29. -504h 2 l 5 t 2 30.3599i 6 l 3 u 3 v 3 D 31. 1972 x 2 yz 2 32. -868 f 2 huv 33. 504x 3 y 2 34. 5244a 5 b 4 c 3 35. x + 10 r. 70 36. 8a 4 b/9C 37. x – 10 38. a 4 – a 3 – a + 1 39. 4t 3 – 3t 2 + 2t + 5 r. -5 40. 155x + 109xy – 159

66. _____1. (6a² – 4b + 3c) + ( 8a² - 6b + 2c) _____2. (3x – 8y + 6z) + ( 7y – 2x + 4z) _____3. (5x³ + 2y²) + ( 7x³ - y²) _____4. (6 – y + 3x) + (-8x + 2y + 10) _____5. (7x + 4y) + (5x + 8y) _____6. (8x + 7xy + 3y) + (6x – 3xy + 4y) + (7x + 4xy – 6y) _____7. (4x + 6y + 6) + (3x – 4y – 2) _____8. (4x – 6y + 6z) + (3x – 4y +2z) _____9. (2a + ab + c) + (3c + 4a + 2ab) _____10. (2a + 4b) + ( 3a – 5b ) + ( -6a + 4b) Previous Next Answers

67. Answers Questions 1. s 2. p 3. l 4. t 5. q 6. m 7. o 8. h 9. k 10. g

69. 6. (3b + 4ab² - 2a³) + ( 3a³ - 3ab² - 2b) 7. (5x² + 4y) + (7x² + 5y) 8. (3x³ + 4y + 4xy²) + (3x³ + 8xy² + 2y) 9. (3x + 4xy – 6y) + (4xy – 3y + 2x) 10. (8x⁵ - 3xy³ + 2y²) + (2x⁵ - 2xy³ + 2y²) 11. (5a² + 3ab + 6c) + (8a² + 3ab + 4c) 12. (6a³ + 4ab² - 8c) + (-8c +7a³ + ab²) 13. (3m + 25n – 8) ­+ (6n – 8 + 8m) 14. (8a + 7b) + (2a + 2c) + (5c – d) 15(5x + 2z) + (-2z + 5x) Previous Next Answers

70. Answers Questions 1- 5 Questions 6 - 15 1. 8a 2 + 8ab – 4c 2. 7x 2 + 5xy – 7y 3. 11a 3 – ab 2 – c 4. 3a – 3ab – 10b 5. 13x – 2y 6. a 3 + ab 2 + b 7. 12x 2 + 9y 8. 6x 3 + 12xy 2 +6y 9. 8xy – 2y 10. 10x 5 – 5xy 3 + 4y 2 11. 13a 2 + 6ab + 10c 12. 13a 3 + 5ab 2 – 16c 13. 11m + 31n - 16 14. 10a + 7b + 7c – d 15. 10x

72. Answers Questions 1. 2y 2 – 7x + 4y 2. 13t – 5x – 2u 3. 7a 3 + ab 2 – 8c 4. -6a + 4ab – 2c 5. -2a + 2x 6. 12t 2 + 2t – y and 12t 2 – 8t + 5y 7. -4a 3 – 12b 2 – 2c and -4a 3 – 5b 2 - 2c 8. -20j e – 8r 2 + 10x 3 and -6j e – 8r 2 + 10x 3 9. -4g 3 + 12 10. 5h 3 – 4x and 6h 3 -4x

74. Answers Questions 1. 4x 2 – 6x + 15 2. 3a 2 – 5a – 2 3. -8a – 14b + 7c 4. -4a + 5b + c 5. -11x 2 – 3x + 2y – 3 6. -2a 3 + 7a 2 + 2a – 9 7. 8a + 7b 8. -24a + 16b 9. -4x 3 – 4x 2 + 17x – 22 10. -7x 5 + 16x 3 – 2x 2 + 27

76. ___________ 6. (-5x + 7y – z) – (6x – 7y + 2z) is equal to 11x + 14y – 3z. ___________ 7. In equation (-11x³ - 5x² - 7x -6) – (-9x³ - 6x² + 9x + 3) the third term is16x. ___________ 8. The difference of 16xy – 7xy is 9xy. ___________ 9. In (-4x³ + 6y² - 3z) – (-5x³ - 3y² - 2z), the second equation will become positive. ___________ 10.The difference of 3ab – 7ab is a positive. Answers Previous Next

77. Answers Questions 1 - 5 Questions 6 - 10 1. + 2. + 3. + 4. - 5. + 6. - 7. + 8. + 9. + 10. -

79. Answers Questions 1. –l 2 + 9m + 10y 2. 8x + 2t – 6u 3. 3a 3 – ab 2 + 8c 4. 6a 2 – ab + 2c 5. -10a + 12x 6. 24t 2 – 6t + 4y 7. -16a 3 – 11b 2 + 4c 8. 15j e + 3r 2 – 2x 3 and 30j e + r 2 + 3x 3 9. 12g 3 + 10 10. 16h 3 – 3x and 5h 3 + 5x

81. 8. 3x 3 (4y 2 ) 9. (5a + 7b – 8c)(8a + 4c) 10. (9u + 5v – 2z)(5u + 2v – 2u) 11. (-5x 2 y 3 w)(2x + y) 12. (4x + 2y)(5x 3 + 2x 2 – y) 13. (6a 3 + b 2 )(4a 3 + b – y) 14. (2t 2 + 3t)(4t 2 ­ – 3t 2 –t) 15. (4x 2 – y 3 )( 4x 3 – y 2 + 6) Previous Next Answers

82. Answers Questions 1 - 7 Questions 8- 15 1. 20xy 2 – 10y – 8xyz 2 – 6z 2 2. -9a 5 b 3 cd 2 – 9ab 3. -12bc – 3c 2 – 32b – 8c 4. 6x 4 5. 16u 2 v 2 w 6. 10x 3 + 35x 2 y + 35xy 2 + 12y 3 7. 8m 3 8. 12x 3 y 2 9. 40a 2 + 56ab – 44ac + 28bc – 32c 2 10. 27u 2 + 33uv – 6uz +10x 2 – 4vz 11. -10x 3 y 3 w – 5x 2 y 2 w 12. 20x 4 + 8x 3 – 4xy + 10x 3 y + 4x 2 y – 2y 2 13. 24a 5 + 6a 3 b – 6a 3 y + 4a 3 b + b 3 – b 2 y 14. 4t 4 + t 3 -3t 2 15. 16x 5 – 4x 2 y + 24x 2 – 4x 3 y 3 + y 5 – 6y 3

84. Across 1. (2xy)(9x²)(7y) 4. (5u²)(5u) 5. (9w)(5) 7. (zmn)(z³m²n) 8 (3x²)(3x²y) 9. (26a²)(2a²) Down 1. (6u²)(3u) 2. 2(19)(3) 3. (yzw)(yz) 4. 2m³z² (m²z²) 6. 2(7)(3) 8. 3a²(8a)(4a) Previous Next

85. Answers Questions Across 1. 126x 3 y 2 4. 25u 3 5. 45w 7. z 4 m 3 n 2 8. 9x 4 y 9. 52a 2 Down 1. 18u 3 2. 114 3. y 2 z 2 w 4. 2m 4 z 4 6. 42 8. 96a 4

88. Answers Questions 1 - 7 Questions 8 - 15 1. a4 2. c5 3. f7 4. c6 5. h8 6. d1 7. a3 8. g5 9. b5 10. d2 11. a1 12. b2 13. b6 14. a7 15. e8

90. Answers Questions 1. x – 5 2. y + 1 3. 4 4. x 5. X + 12 r. 70 6. 8a 4 b/9c 7. x – 10 8. a + 1 9. 4t 3 – 3t 2 + 2t + 5 r. -5 10. 8v – 5x

92. 8. (2a 2 b 2 ) ÷ (a 2 b 2 ) 9. (4x 2 y 3 – 24xy 4 ) ÷ (2xy 2 ) 10. (12x 3 y 4 + 18x 4 y 2 – 36xy 3 ) ÷ (3x 2 y 2 ) 11. (7x³y² - 14x⁵y³ + 28x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²) 12. 4e² ÷ 2e 13. (2y² – 5y – 6) ÷ (2y – 1) 14. (2x²- 5x – 12) ÷ (2x + 3) 15. (3a n + b m ) ÷ (a n b m ) Previous Next Answers

93. Answers Questions 1 - 7 Questions 8- 15

95. Answers Questions

99. C. Multiply the following Algebraic Expressions. 11. 6x²(25xy) 12. 42c²(21t) 13. 19x(36xy) 14. 34m²p(86op) 15. 13x(85z) 16. 18j²(17j⁸k⁶) 17. 14h²l⁵(-36t²) 18. 59i⁶l²(61u³v³) 19. 58xyz(34xz) 20. -14f²(62huv) 21. 28xy²(18x²) 22. 92a²b²c(57a³b²c²) 23. 51x(14y)(71z) 24. 76uv(23xyz) 25. 24c(-125n²)(-96c²) Previous Next Solutions

100. D. Divide the following Algebraic Expressions. 26. (x⁵ ) ÷ (x ² ) 27. (-4 ²x ) ÷ (2 ³x ) 28. (16x 8 ) ÷ (4x 3 ) 29. (10m 2 – 4m 2 ) ÷ (3m + 3m) 30. (10x 3 – 24x + 6) ÷ (x-4) 31. (23x 3 – 44x 2 y + 65xy 2 + 62y 3 ) ÷ (6x 2 - 12xy +24y 2 ) 32. (90xy 2 – 60x 3 ) ÷ (10x) 33. (12a 2 b 2 ) ÷ (6a 2 b 2 ) 34. (14x 2 y 3 – 24xy 4 ) ÷ (5xy 2 ) 35. (12x 3 y 4 + 18x 4 y 2 – 36xy 3 ) ÷ (12x 2 y 2 ) 36. (28x³y² - 14x⁵y³ + 35x⁸y⁵ - 21x⁵y⁶) ÷ (7x³y²) 37. 20e² ÷ 4e 38. (2y² – 5y – 6) ÷ (2y – 1) 39. (22x²- 16x – 12) ÷ (4x + 6) 40. (21a n + b m ) ÷ (7a n b) Previous Next Solutions

101. Answers Post Test A A. 1. 10a 2 + 5a + 6ab + 4c 2. 28x 2 + 26xy – 16y 3. 117a 3 – 8ab 2 – 9c 4. 45a – 36ab – 111b 5. 143x – 22y 6. 6a 3 + 17ab 2 + 8b 7. 133x 2 + 103y 8. 45x 3 + 108xy 2 + 40y 9. 155x + 109xy – 159y 10. 30x 5 – 25xy 3 + 24y 2

102. Answers Post Test B B. 1. -13x – 3y + 50z 2. 148x 3 – 6y 2 + 118z 3. 26x – 3y – 5z 4. 60x 6 + 112y 5. 10a + 20c 6. 28x + 110y – 26z 7. 38x 3 + 10x 2 + 96x - 107 8. -56xy 9. 37x 3 + 124y 2 + 44z 10. -58ab

103. Answers Post Test C 11. 150x 3 y 12.882c 2 t 13. 684x 2 y 14. 2924m 2 op 2 15. 1105xz 16.306j 10 k 2 17. -504h 2 l 5 t 2 18. 5599i 6 l 2 u 3 v 3 19. 1972x 2 yz 2 20. -868f 2 huv 21.504x 3 y 2 22. 5244a 5 b 4 c 3 23. 50694xyz 24. 1748 vxyz 25. 288,oooc 3 n 3

104. Answers Post Test D

107. 11. (f +2) (f – 8) 12. (w + 4) (w + 11) 13. (s + 5) (s + 6) 14. (c + 10) (c – 3) 15. (a + 8) (a + 9) 16. (i + 25) (i – 3) 17. (i + 25) (i – 3) 18. (m + 5) (m – 6) 19. (h + 3) (h + 5) 20. (l + 6) (l + 9) Previous Next Solutions

109. Answers 1. f⁴ - 4fc² + 4c² 2. x ² + 26x + 169 3. 256a 4 + 32a 2 + b 2 4. 4p 2 + 8pq + 4q 2 5. 4a 2m + 12a m z + 9q 2 6. 81y 4 + 90xy 3 + 25x 2 y 2 7. 279h 2x + 324h x 0 g + 360 g 8. a 2 + 2a - 24 9. x 2 – 6x - 27 10. m 2 + 13m + 40 11. f 2 – 6f - 16 12. w 2 + 15w + 44 13. s 2 + 11s + 30 14. c 2 + 7c - 30 15. a 2 + 17a + 72 16. i 2 + 21i - 75 17. i 2 + 21i - 75 18. m 2 – m - 30 19. h 2 + 8h + 15 20. l 2 + 15l + 54 21. a 3 x 2 – 6a 2 x 3 y – 12ax 3 y 2 – 8x 3 y 3 22. x 3 y 6 + 3x 2 y 3 wz 2 + 3xy 3 w 2 y 4 + w 3 z 6 23. 1029x 6 + 147x 4 y 4 + 21x 2 y 8 + y 12 24. 4a 2 + 20ab + 25b 2 25. 121a 6 + 88a 3 x 2 + 64x 4 26. 4x 2 + 24x + 36 27. 180x 4 y 4 -216x 2 y 8 + 252x 3 y 4 28. 9ax 3 + a 2 xy 2 + a 3 xy 29. 7abcd 2 – 63a 2 b 2 – 9abcd 3 30. 3x 5 + 4x 4 – 6x 3 31. 48x 3 y + 16x 2 y + 48xy 2 32. 5x 5 + 10x 4 + 5x 3 33. x 8 y 4 34. a 4 c 2e e 2m 35. 441t 6 w 6 Pre Test 21 - 35 Pre Test 11-20 Pre Test 1 - 10

111. Answers 1. 25 2x 2. 16y 6 3. x 8 y 4 4. a 4 c 2e e 2m 5. k 20 m 6n 6. 16j 2n h 2x+2 7. 100m 2 8. 16x 2 y 2 z 2 9. 625m 2n 10. 4 4 + 2n Questions

113. Answers 1. V 2. A 3. R 4. I 5. A 6. B 7. L 8. E 9. S Questions

115. 8. (3a 4 b 3 ) 2 9. (53x 2 ) 2 10. (13x 2 y 2 ) 2 11. (4n x+1 ) 2 12. (5ab 3 ) 2 13. (21t 3 w 3 ) 2 14. (3b a+2 m 2 w 2 ) 2 15. (8l o v e ) 2 Previous Next Answers

116. Answers 1. 49x 6 2. u 2 v 4 3. 100x 2 4. 64y 2 5.x 2 y 2 6. 36m 12x 7. 169a 2x b 4y c 10z 8. 9a 8 b 6 9. 2809x 4 10. 169x 4 y 4 11. 8n 2x + 2n 12. 25a 2 b 6 13. 441t 6 w 6 14. 9b 2a+4 m 4 w 4 15. 64l 20 v 2e Questions 1 - 7 Questions 8 - 15

118. __________6. The product of the third term of the equation 4c(5a 2 + 2c 2 – 5d + 3b) is -20cd. __________7. In 2 x + 1 (4 x+1 + y x ), the first term of the product has an exponent of 2x. __________8. 3(4x + 2y + 3x 2 – y 2 ) have the product of 9x 2 – 3y 2 + 12x +6y. __________9. In 45x 2 y 2 z 2 (2 x 2 y 2 – 4x 2 y – 3yz 2 ) the third term of the product is 135x 2 y 3 z 4 . Show your solution in the given space and encircle the third term of the product. ________10. 5j 2 (10ex + 2r 2 – 14i 2 + 13cx) have the product of 50ej 2 x + 10j 2 r 2 + 70i 2 j 2 + 65cx. Previous Next Answers

119. Answers 1. a 2. A 3. a 4. A 5. a 6. A 7. a 8. A 9. a 10. a Questions 1 - 5 Questions 6 - 10

121. Answers 1. xy 2 + x 3 y + 6x 2. 4a 3 – 7a 2 – 2a 3. 6x 3 + 8x 2 + 18x 4. 6 r2 st + 60r 3 t 5. a 2 b 2 c – a 2 bc + ab 2 c – 3abc 6. 9ax 3 + a 2 xy 2 + a 3 xy 7. 7abcd 2 – 63a 2 b 2 – 7abcd 3 8. 3x 5 + 12x 4 – 6x 3 9. 48x 3 y + 16x 2 y + 48xy 2 10. 5x 5 + 10x 4 + 5x 3 Questions

123. Answers 1. 56x 3 y 2 + 378x 3 + 14x 6 2. 2y 3 + 8y 2 - 42 3. 63d 3 p + 189d 2 p 4. 720p 3 q 2 – 15 p 2 qx 2 5. -28q 2 h – 49hy + 42hr 6. 40t 2x + 24x 3x – 40 x 7. 180x 4 y 4 – 216x 2 y 8 + 252x 3 y 4 8. 66e 6x j 2 + 22e 3 j 4t – 66e 3 j 2 Questions

125. Answers 1. 16a 2 + 8ab + b 2 2. 4x 2 + 12xy + 9y 2 3. 16u 2 + 24uv + 9v 2 4. 64a 2 + 48au + 9u 2 5. 25a 2 – 10 ab + b 2 6. 4a 2 + 20 ab + 25b 2 7. 25t 4 + 50dt 2 + 25d 2 8. 144e 6 – 24e 3 j 4 +j 8 9. 16y 4 + 32y 2 z 3 + 16z 6 10. 121a 6 + 88a 3 + 16x 4 Questions

128. Answers 1. y 3 – 18y +81 2. 4x 3 + 24x +36 3. x 4 + 2x 2 + 1 4. y 4 – 8y 3 + 16y 2 5. x 2 + 6x + 9 6. 9b 4 + 6b 3 + b 2 7. 4x 2 4x + 1 8. 4x 2 – 12xy + 9y 2 9. 4x 4 + 24x 3 + 36x 10. 729x 4 + 54x 2 y + y 4 11. y 4 – 26y 3 – 169y 2 12. x 4 + 8x 2 + 16x 13. 4x 2 – 40x + 100 14. 4x 2 + 32x + 64 15. x 6 – 84 4 + 16x 2 Questions 1 – 7 Questions 8 - 15

129. Activity 30 Name: __________________________Score: _____________Date:______________ Year and Section:____________________Teacher: ___________________________ Objectives: 1. To help the students to enhance their skills in squaring binomial. 2. To have the student a mastery in squaring binomial. 3. To have more patient in squaring a binomial. INSTRUCTION: Solve the following binomial and show your complete solution. Encircle your answer. 1. (5y – 1) 2 6. (5a 3 + x 2 ) 2 2. (2c + d) 2 7. (y – 2) 2 3. (x 2 + 2y) 2 8. (2xy – 4x) 2 4. (5at – 1) 2 9. (8x – 2 ) 2 5. (3x 2 + 2x 2 ) 2 10. (3x 2 + 2y) 2 Previous Next TABLE OF CONTENTS Answers

130. Answers 1. 25y 2 – 10y + 1 2. 4c 2 + 4cd + d 2 3. x 4 + 4x 2 y + 4y 2 4. 25a 2 t 2 – 10at + 1 5. 9x 4 +12x 4 + 4x 4 or 25x 4 6. 25a 6 + 10a 3 x 2 + x 4 7. y 2 – 4y + 4 8. 4x 2 y 2 – 16x 3 y – 16x 3 9. 64x 2 – 32x + 4 10. 9x 4 + 12x 2 y + 4y 2 Questions

132. 8. (12c 2 – 6x 2 ) 3 9. (3b 3 – 7y) 3 10. (6e 2 + 3j) 3 11. (9a 3 – 7m) 3 12. (4d 2 + 3f) 3 13. (3q 2 – 4k) 3 14. (6k 2 – 5y) 3 15. (8x – 12y) 3 Previous Next Answers

133. Answers 1. x 3 + 3x 2 y + 3xy 2 + y 3 2. 8x 3 + 48x 2 y + 96xy 2 + 64y 3 3. 27x 9 + 135x 6 y + 225x 3 y 2 + 125y 3 4. x 3 - 3x 2 y + 3xy 2 – y 3 5. 64a 3 – 96a 2 y + 48ay 2 – 8y 3 6. 343m 3 + 441m 2 n + 189mn 2 + 27n 3 7. 512b 2 + 768b 2 y + 384by 2 + 64y 3 8. 1728c 6 – 2592c 4 x 2 + 1296c 2 x 4 – 216x 6 9. 27b 9 – 189b 6 y + 441b 3 y 2 – 343y 3 10. 216e 6 + 324e 4 j + 162e 2 j 2 + 27j 3 11. 729a 9 – 1701a 6 m + 1323a 3 m 2 – 343m 3 12. 64d 6 + 144d 4 f + 108d 2 f 2 + 27f 3 13. 27q 6 – 108q 4 k + 144k 2 q – 64k 3 14. 216k 6 – 540k 4 y + 450k 2 y 2 - 125y 3 15. 512x 3 – 2304x 2 y + 3456xy 2 – 1728y 3 Questions 1 - 7 Questions 8 - 15

135. Answers 1. 8x 2 – 36x 2 y + 54xy 2 – 27y 3 2. x 2 – 6x 2 + 12x - 8 3. 8x 3 + 24ax 2 + 24a 2 x + 8a 3 4. 125x 3 – 225x 2 y + 135xy 2 – 27y 3 5. 8a 3 + 12a 2 b + 6ab 2 – b 3 6. 8y 3 + 12y 2 z + 6yz 2 – z 3 7. x 3 – 15x 2 + 75x - 125 8. 8x 3 + 84x 2 y + 294xy 2 + 343y 3 9. 8a 3 y 6 – 48a 3 y 5 – 96a 3 y 4 – 64a 3 y 3 10. c 6 – 3c 4 d 2 + 3c 2 d 4 – d 6 Questions

137. Answers 1. 27x 3 + 108x 2 y + 144xy 2 + 64y 3 2. 343x 6 + 147x 4 y 4 – 21x 2 y 8 + y 2 3. 64f 3 – 384f 2 y + 768fy 2 – 512y 3 4. 64y 9 + 144y 8 + 108y 7 + 27y 6 5. x 3 y 6 + 3x 2 y 4 wz 2 + 3xy 2 w 2 z 4 + w 3 z 6 6. 27w 3 + 108w 2 z + 144wz 2 + 64z 3 7. y 9 – 24y 6 + 192y 3 - 512 8. 729l 3 + 1944l 2 t + 1728lt 2 + 512t 3 9. 8o 9 + 24o 6 x 4 + 24o 3 x 8 + 8x 12 10. a 3 x 3 – 6a 2 x 3 y + 12ax 3 y 2 – 8x 3 y Questions

139. 8. (j 2 + 6) (j 2 + 8) 9. (e 3 + 2) (e 3 – 4) 10. (r 4 – 3) (r 4 + 5) 11. (3x + 8)(7x + 9) 12. (2x + 4)(4x + 6) 13. (5x + 2)(3x + 4) 14. (6x + 3)(4x + 2) 15. (2x + 4)(8x + 5) Previous Next Answers

140. Answers 1. a 2 + 109 + 16 2. l 2 + 15l + 54 3. e 2 + 12e + 35 4. t 2 + 8t + 12 5. h 2 + 8h + 15 6. x 2 + 6x + 8 7. m 2 – m – 30 8. j 4 + 14j 2 + 48 9. e 6 – 2e 3 – 8 10. r 8 + 2r – 15 11. 21x 2 + 83x + 72 12. 8x 2 + 28x + 24 13. 15x 2 + 26x + 8 14. 24x 2 + 24x + 6 15. 16x 2 + 42x + 20 Questions 1 - 7 Questions 8 - 15

142. 8. (w + 4) (w + 11) 9. (j + 5) (j – 3) 10. (x + 19) (x – 6) 11. (3x + 5) (2x + 35) 12. (3x 2 + 3) (3x 2 + 25) 13. (4a + 14) (6a + 39) 14. (5r + 7) (8r + 3) 15. (9q 2 + 2)(2q 2 – 5) Previous Next Answers

143. Answers 1. x 2 – 17x - 60 2. y 2 – y – 2 3. k 2 + 35 k + 150 4. a 2 + 2a – 24 5. x 2 – 6x – 27 6. m 2 + 13m + 40 7. f 2 – 6f - 16 8. w 2 + 15w + 44 9. j 2 + 2y – 15 10. x 2 + 13x - 114 11. 6x 2 + 115x + 175 12. 9x 4 + 84x 2 + 75 13. 24a 2 + 240a + 546 14. 40r 2 + 71r + 21 15. 18q 4 – 41q 2 - 10 Questions 1 – 7 Questions 8 - 15

145. Answers 1. i 2 + 22i - 75 2. i 2 + 22i - 75 3. 0 2 + 11o - 26 4. x 2 + 4x - 5 5. a 2 + 17a + 72 6. a 2 – 2a – 99 7. p 2 + 9p + 20 8. s 2 + 11s + 30 9. c 2 + 7c - 30 10. q 4 + 3q 2 - 10 Questions

151. Answers 1. e 2 r 6 2. 25y 4 3. 144d 2 4. 49j 2 y 2 5. y 2 x 2 6. 49k 8x 7. 4w 29 y 4h z 6z 8. 144r 10 t 12 9. 676m 6a 10. 169k 2 l 4 t 12 11. u 2 – 20u + 100 12. 4x 14y + 12x 7y +9 13. 25x 2a + 20xa + 4 14. f 4 - 4cf 2 + 4c 2 15. x 2 + 26x + 169 16. 256a 2 + 32a 2 b + b 2 17. 4p 2 + 8pq + 4q 2 18. 4a 2m + 12a m z + 9z 2 19. 81y 4 + 90xy 3 + 25x 2 y 2 20. 729h 2x + 324h x o g + 36o 2g Questions A

152. Answers 1. 12a 3 x 2 – 175a 2 bx 2 y + 7 935ab 2 xy 2 – 12 167b 3 y3 2. 8x 3 – 72x 2 + 216x - 216 3. 8f 3 x 3 + 24f 2 hx 2 + 24fh 2 x + 8h 3 4. 125c 3 – 300c 2 + 240c - 64 5. 343a 3 + 294a 2 k + 84ak 2 + 8k 3 6. 512y 3k – 192y 2k z – 24y k z 2 – z 3 7. 8x 6 – 36x 4 – 54x 2 - 27 8. 125k 3 – 600k 2 l + 960kl 2 + 512l 3 9. 343a 3 x 6 – 294a 3 x 4 y + 84a 3 x 2 y 2 – 8a 3 y 3 10. 27h 3 x 3 – 189h 2 x 2 y + 441hxy 2 + 343y 3 Questions B

153. Answers 1. a 2 f 2 – a 4 y + 6a 2 2. 6a 2 m – 9am – 10m 3. 8x 4 + 4ax 2 + 32x 4. 6r 2 st + 60r 3 t + 9rs 5. m 2 n 2 o – m 2 no + mno 2 – 3mno 6. 9k 3 x + k 2 x 2 y 2 + k 3 xy 7. 6abcd 2 – 14a 2 b 2 – 10abcd 3 8. 5x 7 – 5x 6 9. 28x 4 z + 8xyz + 24xz 2 10. 8z 7 + 25x 6 + 7x 5 11. 60x 3 y 2 + 204x 3 + 12x 5 12. s 2 – 4s - 21 13. m 2 – 16m + 512 14. x 2 – 3x - 10 15. t 2 + 30t + 209 Questions C_1 - 15

154. Answers 16. k 2 – 13k - 90 17. q 2 + 6q + 8 18. y 2 + 10y + 21 19. u 2 + 13u - 30 20. x 4 – 2x 2 – 8 21. w 6 + 13w 3 + 40 22. 12l 2 + 34l + 14 23. 6x 4 + 24x 2 + 24 24. 12y 2 + 146y + 495 25. 20t 2 + 52t + 24 26. 6q 4 – 16q - 9 27. 55v 2 + 21v + 2 28. 16u 2a + 12u a + 2 29. 21b 2 – 48b + 12 30. 648x 2 + 21x - 2 Questions C_1 - 15

156. A. Instruction: Tell whether if the common factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor __________1. The factor of 2x² - 6x + 8 is 2(x²– 3x + 4). __________2. The factor of 5x + 30 is 5(x + 6). __________3. The factor of 24x³ - 64y³ is 8(3x³ + 8y³). __________4. The factor of 625x³ - 100y² is 25(25x³ + 5y²). __________5. The factor of 2x³ + 4x² - 10x is 2(x³ + 2x² - 5x). B. Instruction: Match the polynomial in column A to its proper and common factor in column B . Write the letter of your answer in the space provided before each number. A B _____1. 3x + 9y a. 5 (x + 6) _____2. 2x³ + 4x² - 10x b. 2x (x² - 2x – 3) _____3. 6a³b + 3a²b² - 18ab³ c. 2x (x² + 2x – 5) _____4. 5x + 30 d. 3 (x + 3y) _____5. 2x³ - 4x² - 6x e. 3 (3a³b + a²b² - 6ab³) PREVIOUS NEXT ANSWERS

157. C. Instruction: Factor the following algebraic expression. Get their common factor. Write your answer in the space provided. 1. 6c 4 – 8c³ - 2c² 2. 2b³ - 4b² - 8b + 10 3. 3y⁶ - 12y³ - 5y 4. 3ax² - 6a²x + 9a³x 5. 18x² - 24xy + 3y² D. Instruction: Tell whether if the factor of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of m² - 144 is (m + 7) (m + 7). _____2. The factor of b²x² - y² is (b + y) (x – y). _____3. The factor of 25 - p² is (5 + p) (5 – p). _____4. The factor of 64x²y² - x² is (8xy + y) (8xy – x). _____5. The factor of c² - d⁴ is (c + d²) (c - d²). PREVIOUS NEXT ANSWERS

158. E. Instruction: Tell whether if the factor by grouping of the following polynomial is correct. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of ax + ay + bx + by is (a + b) (x + y). _____2. The factor of 2x +8y – 3px -12py is (2 – 3p) (x + 4y). _____3. The factor of 3x – 3y + 4ay – 4ax is (3 – 4a) (x – y). _____4. The factor of x³ + 7x² + 2x ² 14 is (x² + 2) ( x + 7). _____5. The factor of 3x² + xy -12x -4y is (x – 4) (3x + y). F. Instruction: Match the polynomials in column A to its proper factor of grouping in column B . Write your answer in the space provided before each number. A B _____1. 15x⁴ - 15x² + 5x² a. 2a³b² (a² + 4ab - 2b²) _____2. 2a⁵b² + 8a⁴b³ -4a³b⁴ b. (4x – 5) (x + 3) _____3. a³ -2a² + 5a – 10 c. 5x² (x² - 3x + 1) _____4. 3xy + 21x -2y – 14 d. (a – 2) (a² + 5) _____5. 5x² + 11x + 2 e. (x – 4y) (2x + 3y) PREVIOUS NEXT ANSWERS

159. G. Instruction: Factor the following algebraic expressions by grouping. Write your answer in the space provided. 1. 27x³ + 108x² + 144x + 64 2. 4b² + 12bc + 9c² - 25d 3. 36x² - 9y² + 24yz- 16z² 4. ax² -4a + 3x² - 12 36x² - 9y² + 24yz – 16z² H. Instruction: Match polynomials in column A to its correct factoring which is the difference of two squares in column B . Write your answer in the space provided before each number. A B _____1. x² - 9 a. (x⁴ + y⁴) (x² + y²) (x + y) (x – y) _____2. 4x² - 36y⁶ b. 4xy (2x + 3y) (2x - 3y) _____3. 49x⁴ - 36y⁴ c. (x + 3) (x – 3) _____4. x⁸ - y⁸ d. (7x² + 6y²) (7x² - 6y²) _____5. (t + 4)² - 9 e. (t + 7) (t + 1) PREVIOUS NEXT ANSWERS

161. K. Instruction: Match polynomials in column A to its correct factor which is a perfect trinomial square in column B . A B _____1. 4x² + 4x + 1 a. (2x + 3)² _____2. 25y² - 40y + 16 b. (2x + 1)² _____3. x² - 8x + 16 c. (x – 4)² _____4. a² + 14a + 49 d. (a + 7)² _____5. 4x² + 12x + 9 e. (5y – 4)² L. Instruction: Factor the following polynomials by a perfect trinomial square. Write you answer in the space provided. 1. x² + 12x + 36 2. x² + 12xy + 9y² 3. x² - 4x + 4 4. x² + 8x + 16 5. 36a² - 48a + 16 PREVIOUS NEXT ANSWERS

162. M. Instruction: Tell whether if the factor of the following equations is a factor of general quadratic trinomial. Write A if the factor is correct and B if the factor is incorrect and write the correct factor. _____1. The factor of 8p² + 24p + 18 is (2p + 3) (4p + 6). _____2. The factor of 15x² + 41x + 28 is (3 + 4) (5x + 7). _____3. The factor of 12b² + 17b – 5 is (2b + 1) ( 6b – 5) _____4. The factor of 24m² + 50mn – 9 is (4m + 3) (6m – 3). _____5. The factor of 6y² + 7y - 20 is (3y + 10) (2y – 2). N. Instruction: Match the polynomials in column A to its correct factor which is in the general equation in column B . A B _____1. (4x – 5) (x + 3) a. 3x² + 17x + 20 _____2. (x + 5) (x + 5) b. x² + 10x + 25 _____3. (p – 3) (p + 2) c. 2x² - 10 x + 12 _____4. (2x – 6) (x – 2) d. p² - p – 6 _____5. (x + 4) (3x + 5) e. 2x² - 10x + 12 PREVIOUS NEXT ANSWERS

163. O. Instruction: Factoring the sum and difference of cubes of the following polynomials. Write the letter of your answer in the space provided. 1. x³ - 8 2. 27x³ + 1 3. x³y⁶ - 64 4. 8x³ + 27 5. x³ + 1 PREVIOUS NEXT ANSWERS

164. A. 1. A 2. A 3. A 4. B 25(25x³ - 5y²) 5. A Answers B. 1. D 2. C 3. E 4. A 5. B C. 1. 2c 2 (3c 2 – 4c - )1 2. 2(b 3 – 2b 2 – 4b + 5 3. y(3y 5 – 12y 2 – 5) 4. 3ax(x – 2a + 3a 2 ) 5. 3(6x 2 – 8xy + y 2 ) D. 1.B (m + 12) (m – 12) 2. B (bx – y) (bx + y) 3. A 4. B (8xy – x) (8xy +x 5. A Questions A Questions C Questions B Questions D E. 1. A 2. A 3. B (3 + 4a) ( x – y) 4. A 5. A F. 1. C 2. A 3. D 4. E 5. B G. 1. 2. 3. 4. 5. H. 1. C 2. B 3. D 4. A 5. E Questions H Questions G Questions F Questions E

165. I. 1. (9a+16b 2 )(9a-16b 2 2.(5+13z)(5 -13z) 3. (11-10xy)(11+10xy) 4. (5m–6n)(5m+6n) 5. (8xy 2 –1) (8xy 2 +1) O. 1. (x-2) (x² - 2x + 4) 2. (3x + 1) (9x² +3x + 1) 3. (xy - 8) (x 2 y 5 -8xy+ 8) 4. (2x + 3) (4x 3 +6x + 9) 5. (x + 1) (x 2 + x + 1) N. 1. E 2. B 3. D 4. C 5. A J. 1. 6x 2. 16 3. a 2 4. 25 5. 40ab M. 1. A 2. A 3. B (4b - 1) ( 3b + 5) 4. B (6m - 1) (4m + 9) 5. B (3y - 4) (2y + 5). K. 1. B 2. E 3. C 4. D 5. A L. 1. (x+6) 2 2.(x+3) 2 3. (x – 2) 2 4. (x+4) 2 5. (6a – 4) 2 Questions I Questions J Questions K Questions L Questions O Questions M Questions N

167. Answers 1. A 2. A 3. B 8(3x 3 – 8y 3 ) 4. B 25(25x 3 – 4y 2 ) 5. A 6. B 8x(2x – 3y) 7.B 3a(2a – 3b) 8. B 6ab(2a – 3a 2 ) 9. B 3a(3y + a – 2y 2 ) 10. B 2(n 2 – 3n + 2) Questions

169. Answers 1. H 2. F 3. J 4. D 5. C 6. B 7. I 8. A 9. G 10. E Questions

171. Answers 1. 2(ab + 4a 2 b 2 c 2 – 8a 3 b 3 c 3 2. 2ay(5ay 2 + 2) 3. 2c(c 2 – 2c – 3) 4. 11m(1 + 2m) 5. 12a(a 2 – 2a – 4) 6. 2c(3c 3 – 4c 2 – c) 7. 2(b 3 - 2b 2 – 4b + 5) 8. 3y(y 5 – 4y 2 – 5) 9. 3ax(x – 2a + 3a 2) 10. 3(6x 2 – 8xy + y 2 ) Questions

173. Answers 1. A 2. A 3. A 4. A 5. A 6. B (2x + y)(a - 2b)(a + 2b) 7. B (x + y + z) (x + y - z). 8. B (m + n) (x + y) (x – y) 9. A 10. B (3a 2 b + 5ab) (3a 2 b – 1). Questions

175. Answers 1. C 2. J 3. E 4. H 5. B 6. G 7. F 8. A 9. D 10. I Questions

178. Answers 1. B (m + 7) (m - 7) 2. B (bx + y) (xx – y) 3. A 4. B (8xy + x) (8xy – x) 5. A 6. A 7. A 8. A 9. A 10. A Questions

180. Answers 1. C 2. J 3. G 4. A 5. H 6. B 7. I 8. F 9. D 10. E Questions