1. Algebraic Expressions 2x + 3y - 7
What are the Terms?

2. Algebraic Expressions 2x + 3y - 7
Terms

3. Algebraic Expressions 2x + 3y - 7
What are the coefficients?

4. Algebraic Expressions 2x + 3y - 7
Coefficients

5. Algebraic Expressions 2x + 3y - 7
What is the constant?

6. Algebraic Expressions 2x + 3y - 7
Constant

7. Algebraic Expressions 2x + 3y - 7
What are the operators?

8. Algebraic Expressions 2x + 3y - 7
Operator

9. Algebraic Expressions Polynomial: monomial → x, 2xy, 4, 3x²y, … single term binomial → x+1, 2xy+x, 3x²y+4, …two terms trinomial → 2x+3y+7, 3x²y+xy+4x, …three terms polynomial → …four or more terms Caution: polynomials do not contain division by a variable! Example: 3x/y + 4 is not a polynomial.

10. Evaluating Algebraic Expressions

11. Evaluate the following algebraic expression using
x=9, y=1
x-(x-(x-y³))

12. Answer: 8

13. Simplifying Algebraic Expressions

14. Simplify the following algebraic expression:
-3p + 6p

15. Answer: 3p

16. Simplify the following algebraic expression:
7x - x

17. Answer: 6x

18. Simplify the following algebraic expression:
-10v + 6w

19. Answer: -10v + 6w

20. Simplify the following algebraic expression:
b b

21. Answer: -b + 3

22. Simplify the following algebraic expression:
10x-w+4y-3x+36-38x-47+32x+2w-3y

23. Answer: w+x+y-11

24. Simplify the following algebraic expression using the distributive property:

25. Answer: v

26. Simplify the following algebraic expression using the distributive property:
(3 - 7k) ∙ (-2)

27. Answer: k

28. Simplify the following algebraic expression using the distributive property:
7n(6n + 3)

29. Answer: 42n² + 21n

30. Simplify the following algebraic expression using the distributive property:

31. Answer: b

32. Simplify the following algebraic expression using the distributive property:
3n(n² - 6n + 5)

33. Answer: 3n³ - 18n² + 15n

34. Simplify the following algebraic expression using the distributive property:
2k³(2k² + 5k - 4)

35. Answer: 4k⁵ +10k⁴ - 8k³

36. Simplify the following algebraic expression using the distributive property:
9v²(u² + uv - 5v²)

37. Answer: 9v²u² +9v³u – 45v⁴

38. Simplify the following algebraic expression using the distributive property:
3x(5x+2) - 14(2x²-x+1)

39. Answer: -13x² + 20x - 14

40. Simplify the following algebraic expression using the distributive property:
x(x+2) - 3(x+2)

41. Answer: x² - x - 6

42. Expand and simplify using the FOIL method:
(x-3)(x+2)

43. Answer: x² - x - 6

44. Factor the following algebraic expression:
x² + 4x + 4

45. Answer: (x+2)·(x+2) or (x+2)2

46. Simplify completely: y5
y-3 ( )½

47. Answer: y4

48. Simplify completely:
3x² - 6 9

49. Answer: x² - 2 3

50. Simplify completely:
a³ - a
a⁴ - a²

51. Answer: 1 a

52. Simplify completely:
18 – 36x
2 – 4x

53. Answer: 9

54. Simplify completely: 3x
4x – 4
9x²
x - 1

55. Answer: 1/12x

56. Write the following as a single fraction:3x x -

57. Answer: 24x2 – 11 40x

58. Write the following as a single fraction:

59. Answer: 2 – x 2x2+2x

60. Write the following as a single fraction:
a³ - a a³
a² a⁴ -

61. Answer: 7a - 1 7a

62. Write the following as a single fraction:
z² z² -

63. Answer: 1 z⁴ + z² -

64. Write the following as a single fraction:3x x -

65. Answer: 24x2 – 11 40x