1. Expressions & Equations Properties And Like Terms

2. Commutative and Associative Properties

5. The Associative Property is particularly useful when you are combining integers. Example: -15 + 9 + (-4)= -15 + (-4) + 9=Changing it this way allows for the -19 + 9 = negatives to be added together first. -10

6. Associative Property of Multiplication: The order in which the terms of a product are grouped does not change the product.

7. 1Identify the property of -5 + 3 = 3 + (-5) ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAssociative Property of Multiplication

8. 2Identify the property of a + (b + c) = (a + c) + b ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAssociative Property of Multiplication

9. 3Identify the property of (3 x -4) x 8 = 3 x (-4 x 8) ACommutative Property of Addition BCommutative Property of Multiplication CAssociative Property of Addition DAsociative Property of Multiplication

10. Discuss why using the associative property would be useful with the following problems: 1. 4 + 3 + (-4) 2. -9 x 3 x 0 3. -5 x 7 x -2 4. -8 + 1 + (-6)

11. Combining Like Terms

13. Examples: LIKE TERMS NOT LIKE TERMS 6x and 2x 6x 2 and 2x 5y and 8y 5x and 8y 4x 2 and 7x 2 4x 2 y and 7xy 2

14. 4 Identify all of the terms like 2x A5x B3x 2 C5y D12y E2

15. 5 Identify all of the terms like 8y A9y B4y 2 C7y D8 E-18x

16. 6 Identify all of the terms like 8xy A8x B3x 2 y C39xy D4y E-8xy

17. 7 Identify all of the terms like 2y A51w B2x C3y D2w E-10y

18. 8 Identify all of the terms like 14x 2 A-5x B8x 2 C13y 2 Dx E-x 2

19. Coefficient Variable Exponent

20. If two or more like terms are being added or subtracted, they can be combined.

21. Sometimes there are constant terms that can be combined. 9 + 2f + 6 = 2f + 15 Sometimes there will be both coeffients and constants to be combined. 3g + 7 + 8g - 2 11g + 5 Notice that the sign before a given term goes with the number.

22. Begin to see operation signs as part of the terms. -2x + 3 – 4xy + 10x + 7 -2xy -2x +3 -4xy +10x +7 -2xy

23. Try These: Write them in your notebook. Circle each term including the operation sign. 1.) 2b +6g(3) + 4f + 9f 2b +18g +4f +9f = 2.) 9j + 3 + 24h + 6 + 7h + 3 3.) 7a + 4 + 2a -19 + 8c -12 + 5c 4.) 8x + 56xy + 5y

24. 98x + 3x = 11x A True B False

25. 107x + 7y = 14xy A True B False

26. 11 2x + 3x = 5x A True B False

27. 12 9x + 5y = 14xy A True B False

28. 13 6x + 2x = 8x 2 A True B False

29. 14 -15y + 7y = -8y A True B False

30. 15 -6 + y + 8 = 2y A True B False

31. 16 -7y + 9y = 2y A True B False

32. 179x + 4 + 2x = A15x B11x + 4 C13x + 2x D9x + 6x

33. 1812x + 3x + 7 - 5 A15x + 7 - 5 B13x C17x D15x + 2

34. 19-4x - 6 + 2x - 14 A-22x B-2x - 20 C-6x +20 D22x

35. The Distributive Property and Factoring

36. An Area Model Imagine that you have two rooms next to each other. Both are 4 feet long. One is 7 feet wide and the other is 3 feet wide. 4 7 3 How could you express the area of those two rooms together?

37. 4 7 +3 Either way, the area is 40 feet 2 : You could add 7 + 3 and then multiply by 4 4(7+3)= 4(10)= 40 OR You could multiply 4 by 7, then 4 by 3 and add them 4(7) + 4(3) = 28 + 12 = 40

38. An Area Model Imagine that you have two rooms next to each other. Both are 4 yards long. One is 3 yards wide and you don't know how wide the other is. 4 x 3 How could you express the area of those two rooms together?

39. 4 x + 3 You cannot add x and 3 because they aren't like terms, so you can only do it by multiplying 4 by x and 4 by 3 and adding 4(x) + 4(3)= 4x + 12 The area of the two rooms is 4x + 12 (Note: 4x cannot be combined with 12)

41. Write an expression equivalent to: 5(y + 4) 5(y) + 5(4) 5y + 20 6(x + 2)3(x + 4) 4(x - 5) 7(x - 1) Remember to distribute the 5 to the y and the 4

42. Be careful with your signs!

43. The numbers are turned to their opposites. Remove to see answer. Try these: -(9x + 3) = -(-5x + 1) = -(2x - 4) = -(-x - 6) =

44. 20 4(2 + 5) = 4(2) + 5 A True B False

45. 21 8(x + 9) = 8(x) + 8(9) A True B False

46. 22 -4(x + 6) = -4 + 4(6) A True B False

47. 23 3(x - 4) = 3(x) - 3(4) A True B False

48. 24Use the distributive property to rewrite the expression without parentheses 3(x + 4) A3x + 4 B3x + 12 Cx + 12 D7x

49. 25Use the distributive property to rewrite the expression without parentheses 5(x + 7) Ax + 35 B5x + 7 C5x + 35 D40x

50. 26Use the distributive property to rewrite the expression without parentheses (x + 5)2 A2x + 5 B2x + 10 Cx + 10 D12x

51. 27Use the distributive property to rewrite the expression without parentheses 3(x - 4) A3x - 4 Bx - 12 C3x - 12 D9x

52. 28Use the distributive property to rewrite the expression without parentheses 2(w - 6) A2w - 6 Bw - 12 C2w - 12 D10w

53. 29Use the distributive property to rewrite the expression without parentheses -4(x - 9) A-4x - 36 Bx - 36 C4x - 36 D-4x + 36

54. 30Use the distributive property to rewrite the expression without parentheses 5.2(x - 9.3) A-5.2x - 48.36 B5.2x - 48.36 C-5.2x + 48.36 D-48.36x

55. 31Use the distributive property to rewrite the expression without parentheses A B C D

58. Try these: Factor the following expressions: 1.) 6b + 9c = 2.) -2h - 10j = 3.) 4a + 20ab + 12abc =

59. 32Factor the following: 4p + 24q A4 (p + 24q) B2 (2p + 12q) C4(p + 6q) D2 (2p + 24q)

60. 33Factor the following: 5g + 15h A3(g + 5h) B5(g + 3h) C5(g + 15h) D5g (1 + 3h)

61. 34Factor the following: 3r + 9rt + 15rx A3(r+ 3rt + 5rx) B3r(1 + 3t + 5x) C3r (3t + 5x) D3 (r + 9rt + 15rx)

62. 35Factor the following: 2v+7v+14v A7(2v + v + 2v) B7v(2 + 1 + 2) C7v (1 + 2) Dv(2 + 7 + 14)

63. 36Factor the following: -6a - 15ab - 18abc A-3a(2 + 5b + 6bc) B3a(2+ 5b + 6bc) C-3(2a - 5b - 6bc) D-3a (2 -5b - 6bc)

64. -What divides into the expression: -5n - 20mn - 10np

65. -If a regular pentagon has a perimeter of 10x + 25, what does each side equal?