1. The Distributive Property

2. A (B + C) = AB + AC -A (B + C) = -AB - AC The distributive property says that a number next to the parentheses can be multiplied by each number inside the parentheses.

3. Example 5(3)+5(4) =15+20 =35 5 (3 + 4)= 4(-1)+4(3) =-4+12 =8 4 (-1+ 3)=

4. Example 3(5)+3(6) =15+18 =33 3 (5 + 6)= 2(-1)+2(5) =-2+10 =8 2 (-1 + 5)=

5. 3 (x + 2) x11 x11 x11 3(x)+3(2)= 3x+6= Example

6. 2 (x 2 + 2x - 2) 2(x 2 )+2(2x)= 2x 2 +4x= Example 2(2)- x2x2 x2x2 x x x x -4

7. Two practice problems 1. = 3 (2x 2 ) – 3(10x) + 3(7) 2. = 6x 2 – 30x + 21 1. = m (6x 2 ) + m(4x) – m(12) 2. = 6x 2 m + 4xm – 12m 3 (2x 2 – 10x + 7) = m (6x 2 + 4x – 12) =

8. Notes When multiplying by a negative number, use the distributive property and follow the rules for multiplying integers + + = + or - - = + (same signs = positive) - + = - or + - = - (opposite signs = negative)

9. Example -3(2x)+-3(4) =-6x+-12 -3 (2x + 4)= -2(-1x) ̶ -2(7) =2x ̶ -14 =2x + 14 -2 (-x – 7)=

10. Example -(-4x)+-(2) =4x+-2 - (-4x + 2)= -12(x) ̶ -12(4) =-12x ̶ -48 =-12x + 48 -12 (x – 4)=

11. Practice Activity

12. DISTRIBUTIVE PROPERTY Whiteboard Race! 1.We are in teams of 3 or 4. 2.I will give you a problem and EVERYONE will work it out silently on their boards for 30 seconds. 3.When I say “team time”, you have an additional minute to compare problems with your teammates 4.A team will only get a point if everyone has the answer correct. 5.When I say boards up, all boards go up. Any team who does not have all boards up with correct answers cannot score a point.

13. Problem 1 2 (x + 3)

14. 2x + 6

15. Problem 2 3 (4 + 5x)

16. 12 + 15x

17. Problem 3 -4(2x – 7)

18. -8x + 28

19. Problem 4 -2(8 + 4x)

20. -16x – 8

21. Problem 5 - (3x – 5)

22. -3x + 5

23. Problem 6 - (8 + 12x)

24. -8 – 12x

25. Problem 7 9 + 5(4x + 4)

26. 20x + 29

27. Problem 8 2x + 3(5 + 4x)

28. 15 + 14x

29. Problem 9 2x + 3 – (x + 5)

30. x – 2

31. Problem 10 3x – (2x + 5) + 8

32. x + 3

33. Problem 11 4x – 2(3x – 3)

34. -2x + 6

35. Problem 12 7x + 3 – (6x + 5)

36. x – 2

37. Problem 13 a (2x + 3)

38. 2xa + 3a