The document discusses the distributive property and combining like terms in algebra. It defines key terms such as terms, coefficients, and like terms. It then explains the distributive property using examples of distributing a number over terms in parentheses. Finally, it provides practice problems for students to work through using the distributive property to combine like terms.

1. The Distributive Property &
Combining Like Terms
CHAPTER 2.5

2. Vocabulary:
terms: parts of an expression that are added
together
coefficient: number part of a term with a
variable part
like terms: have identical variable parts
constant term: a term that has no variable

3. Example 3 Identify parts of an expression
Identify the terms, like terms, coefficients, and
constant terms of the expression 3x – 4 – 6x + 2.
SOLUTION
Write the expression as a sum: 3x + ( – 4 ) + (– 6x ) + 2
Terms: 3x, – 4, – 6x, 2
Like terms: 3x and – 6x; – 4 and 2
Coefficients: 3, – 6
Constant terms: – 4, 2

4. The Distributive Property
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.

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

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

7. Example
3 (x + 2) = 3(x) + 3(2)
= 3x + 6
x 1 1
x 1 1
x 1 1

8. Example
2 (x2 + 2x - 2) = 2(x2) + 2(2x) - 2(2)
= 2x2 + 4x - 4
x -1
x 2
x -1
x -1
x 2
x -1

9. Two practice problems
3 (2x2 – 10x + 7) =
1. = 3 (2x2) – 3(10x) + 3(7)
2. = 6x2 – 30x + 21
m (6x2 + 4x – 12) =
1. = m (6x2) + m(4x) – m(12)
2. = 6x2m + 4xm – 12m

10. 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)

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

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

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

14. Problem 1
2 (x + 3)

15. 2 (x + 3)
2x + 6

16. Problem 2
3 (4 + 5x)

17. 3 (4 + 5x)
12 + 15x

18. Problem 3
-4(2x – 7)

19. -4(2x – 7)
-8x + 28

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

21. -2(8 + 4x)
-16x – 8

22. Problem 5
- (3x – 5)

23. - (3x – 5)
-3x + 5

24. Problem 6
- (8 + 12x)

25. - (8 + 12x)
-8 – 12x

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

27. 9 + 5(4x + 4)
20x + 29

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

29. 2x + 3(5 + 4x)
15 + 14x

30. Problem 9
2x + 3 – (x + 5)

31. 2x + 3 – (x + 5)
x–2

32. Problem 10
3x – (2x + 5) + 8

33. 3x – (2x + 5) + 8
x+3

34. Problem 11
4x – 2(3x – 3)

35. 4x – 2(3x – 3)
-2x + 6

36. Problem 12
7x + 3 – (6x + 5)

37. 7x + 3 – (6x + 5)
x–2

38. Problem 13
a (2x + 3)

39. a (2x + 3)
2xa + 3a

40. THE END!
NOW YOU’RE AT BAT.
YOU ARE SITTING
SILENTLY WHILE I
HAND OUT THE
WORKSHEET.