Brackets Factors and Equations

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Presentation transcript:

Brackets Factors and Equations Exercises 1 and 2

Oral Examples: Expand p(q + r) p(q - r) -p(q + r) -p(q - r)

Oral Examples: Expand 5(2 + y) 5(2 - y) -5(2 + y) -5(2 - y)

Oral Examples: Expand 5(3x + 4y) 5(3x - 4y) -5(3x + 4y) -5(2 - y)

Exercise 1: Expand 1. 2(x + 3) 2. 2(x - 3) -2(x + 3) 4. -2(x - 3)

Exercise 1: Expand 1. 2(x + 3) = 2x + 6 2. 2(x - 3) = 2x - 6

Exercise 1: Expand 5. 3(2 + y) 3(2 - y) -3(2 + y) 8. -3(2 - y)

Exercise 1: Expand 5. 3(2 + y) = 6 + 3y 3(2 - y) = 6 – 3y

Expand 9. 3(x + 4) 10. -3(x + 4) 11. 3(x - 4) 12. -3(x - 4)

Expand 9. 3(x + 4) = 3x + 12 10. -3(x + 4) = -3x - 12

Exercise 1: Expand 13. 4(3 + y) 14. -4(3 + y) 15. 4(3 - y)

Exercise 1: Expand 13. 4(3 + y) = 12 + 4y 14. -4(3 + y) = -12 – 4y

Exercise 1: Expand 17. 4(x + 2) 18. 4(x - 2) 19. -4(x + 2)

Exercise 1: Expand 17. 4(x + 2) = 4x + 8 18. 4(x - 2) = 4x - 8

Exercise 1: Expand 21. 2(x + 4) 22. 2(x - 4) 23. -2(x + 4)

Exercise 1: Expand 21. 2(x + 4) = 2x + 8 22. 2(x - 4) = 2x - 8

Exercise 1: Expand 25. 5(x + y) 26. -5(x + y) 27. 5(x - y)

Exercise 1: Expand 25. 5(x + y) = 5x + 5y 26. -5(x + y) = -5x – 5y

Exercise1: Expand 29. 2(3x + 5y) 30. -2(3x + 5y) 31. 2(3x - 5y)

Exercise1: Expand 29. 2(3x + 5y) = 6x + 10y 30. -2(3x + 5y) = -6x -10y

Exercise 1: Expand 33. 3(4x + 5y) 34. 3(4x - 5y) 35. -3(4x + 5y)

Exercise 1: Expand 33. 3(4x + 5y) =12x + 15y 34. 3(4x - 5y) = 12x -15y

Exercise 1: Expand 37. 4(2x + 5y) 38. 4(2x - 5y) 39. -4(2x + 5y)

Exercise 1: Expand 37. 4(2x + 5y) = 8x + 20y 38. 4(2x - 5y) = 8x – 20y

Exercise 2 1. x (x + 1) 2. x (x - 2) 3. x (x + 3) 4. x (x - 4) 5. y (1 + y) 6. y (2 - y)

Exercise 2 1. x (x + 1) = x2 + x 2. x (x - 2) = x2 - 2x 5. y (1 + y) = y + y2 6. y (2 – y) = 2y – y2

Exercise 2 7. y (3 + y) 8. y (4 - y) 9. x (x + y) 10. x (x - y) 11. y (x + y) 12. y (x - y)

Exercise 2 7. y (3 + y) = 3y + y2 8. y (4 - y) = 4y- y2 9. x (x + y) = x2 + xy 10. x (x - y) = x2 - xy 11. y (x + y) = xy + y2 12. y (x - y) = xy + y2

Exercise 2 13. 2x (x + 4) 14. 2x (3 + y) 15. 2x (3x + 4y) 16. 2xy (3x + 4y) 17. 3y (x - 5) 18. 3y (4 - y)

Exercise 2 13. 2x (x + 4) = 2x2 + 8x 14. 2x (3 + y) = 6x + 2xy 16. 2xy (3x + 4y) = 6x2y + 8xy2 17. 3y (x - 5) = 3xy – 15y 18. 3y (4 - y) = 12y – 12y2

Exercise 2 19. 3y (4x - 5y) 20. 3xy (4x - 5y) 21. 4x (x + 2) 23. 4x (5x + 2y) 24. 4xy (5x + 2y)

Exercise 2 19. 3y (4x - 5y) = 12xy – 15y2 20. 3xy (4x - 5y) = 12x2y – 15xy2 21. 4x (x + 2) = 4x2 +8x 22. 4x (5 + y) = 20x + 4xy 23. 4x (5x + 2y) = 20x2 + 8xy 24. 4xy (5x + 2y) = 20x2y + 8xy2

Exercise 2 25. 5y ( x - 3) 26. 5y (2 - y) 27. 5y (2 - 3y) 29. x (x + 4) + 2(x + 4) 30. y (y + 1) + 3(y + 1)

Exercise 2 25. 5y ( x - 3) = 5xy – 15y 26. 5y (2 - y) = 10y – 5y2 29. x (x + 4) + 2(x + 4) = x2 + 6x + 8 30. y (y + 1) + 3(y + 1) = y2 + 4y + 3

Exercise 2 31. x (x + 2) + (x + 2) 32. y (y + 3) + 4(y + 3)

Exercise 2 31. x (x + 2) + (x + 2) 32. y (y + 3) + 4(y + 3)

37. x (x - 2) + (x - 2) 38. y (y - 3) + 4(y - 3) 39. x (x - 3) + 2(x - 3) 40. y (y - 4) + (y - 4) 41. x (x + 4) - 2(x + 4) 42. y (y + 1) - 3(y + 1)

43. x (x + 2) - (x + 2) 44. y (y + 3) - 4(y + 3) 45. x (x + 3) - 2(x + 3) 46. y (y + 4) - (y + 4) 47. x (x - 4) - 2(x - 4) 48. y (y - 1) - 3(y - 1)

49. x (x - 2) - (x - 2) 50. y (y - 3) - 4(y - 3) 51. x (x - 3) - 2(x - 3) 52. y (y - 4) - (y - 4) 53. 3x (x + 2) + 4(x + 2) 54. 3x (x - 2) + 4(x - 2)

55. 3x (x + 2) - 4(x + 2) 56. 3x (x - 2) - 4(x - 2) 57. 2y (y + 4) + 3(y + 4) 58. 2y (y - 4) + 3(y - 4) 59. 2y (y + 4) - 3(y + 4) 60. 2y (y - 4) - 3(y - 4)

61. 2x (x + 3) + (x + 3) 62. 2x (x - 3) + (x - 3) 63. 2x (x + 3) - (x + 3) 64. 2x (x - 3) - (x - 3)

Exercise 3 1. 2x + 6y = 2 ( ) 2. 3x - 6y = 3 ( ) 3. 8x + 2y = 2 ( )

Factorise 7. 30 + 5y = 5 ( ) 8. 6 - 30y = 6 ( ) 9. 4x + 6y = 2 ( )

Factorise 13. 8 + 12y = 4 ( ) 14. 20 - 24y = 4 ( ) 15. 12x + 18y - 30z = 6 ( ) 16. 18x - 24y + 30z = 6 ( )