1. Brackets Factors and Equations
Exercises 1 and 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

25. 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)

26. 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

27. 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)

28. 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

29. 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)

30. 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

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

32. 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

33. 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)

34. 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

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

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

37. 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)

38. 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)

39. 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)

40. 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)

41. 61. 2x (x + 3) + (x + 3)
62. 2x (x - 3) + (x - 3)
63. 2x (x + 3) - (x + 3)
64. 2x (x - 3) - (x - 3)

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

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

44. Factorise
y = 4 ( )
y = 4 ( )
x + 18y - 30z = 6 ( )
x - 24y + 30z = 6 ( )