1. Algebra 1 Notes: Lesson 1-5: The Distributive Property

2. Vocabulary
Closure Property

3. Vocabulary
Closure Property If you combine any two elements of a set and the result is also included in the set, then the set is closed.
Distributive Property

4. Vocabulary
Closure Property If you combine any two elements of a set and the result is also included in the set, then the set is closed.
Distributive Property
a(b + c) = ab + ac (b + c)a = ba + ca
a(b – c) = ab – ac (b – c)a = ba – ca

5. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) =

6. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) =

7. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) = 8(10)

8. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) = 8(10) +

9. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) = 8(10) + 8(4)

10. Example 1
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) = 8(10) + 8(4) =
= 112

11. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 =

12. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 =

13. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 = 126

14. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 = 126 –

15. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 = 126 – 36

16. Example 2
Rewrite (12 – 3)6 using the Distributive Property. Then evaluate.
(12 – 3)6 = 126 – 36
= 72 – 18
= 54

17. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) =

18. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) =

19. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2)

20. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) +

21. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x)

22. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) –

23. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)

24. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2

25. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2 +

26. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2 + 12x

27. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2 + 12x –

28. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2 + 12x – 3

29. Example 3
Rewrite 3(2x2 + 4x – 1) using the Distributive Property. Then evaluate.
3(2x2 + 4x – 1) = (3)(2x2) + (3)(4x) – (3)(1)
= 6x2 + 12x – 3

30. Vocabulary
Term

31. Vocabulary
Term y, p3, 4a, 5g2h
Separated by + or -
Like Terms

32. Vocabulary Term y, p3, 4a, 5g2h Like Terms 3a2 and 5a2
Have EXACT same variables
Coefficient

33. Vocabulary Term y, p3, 4a, 5g2h Like Terms 3a2 and 5a2
Coefficient numbers multiplied by the variable(s)

34. Vocabulary Term y, p3, 4a, 5g2h Like Terms 3a2 and 5a2
Coefficient xy, m

35. Vocabulary Term y, p3, 4a, 5g2h Like Terms 3a2 and 5a2
Coefficient xy, 1m

36. Example 4
Simplify each expression.
15x + 18x

37. Example 4
Simplify each expression.
15x + 18x

38. Example 4
Simplify each expression.
a) 15x + 18x
33x

39. Example 4
Simplify each expression.
a) 15x + 18x
33x

40. Example 4
Simplify each expression.
15x + 18x
33x
b) 10n + 3n2 + 9n2

41. Example 4
Simplify each expression.
15x + 18x
33x
b) 10n + 3n2 + 9n2

42. Example 4 Simplify each expression. 15x + 18x 33x b) 10n + 3n2 + 9n2

43. Example 4 Simplify each expression. 15x + 18x 33x b) 10n + 3n2 + 9n2

44. Example 4 Simplify each expression. 15x + 18x 33x b) 10n + 3n2 + 9n2

45. Let’s Use the Distributive Property
15  99

46. Use Distributive Property
15  ( 100 – 1 )

47. Use Distributive Property
15  ( 100 – 1 ) 15  100 – 15  1

48. Use Distributive Property
15  ( 100 – 1 ) 15  100 – 15  1 1,500 – 15

49. Use Distributive Property
15  ( 100 – 1 ) 15  100 – 15  1 1,500 – 15 1,485

50. Assignments
Pgs Evens, Evens