Chapter 2.5 covers the distributive property and combining like terms, defining key vocabulary such as terms, coefficients, and constant terms. It provides examples and practice problems demonstrating how to apply the distributive property in mathematical expressions. The document also includes instructions for a team-based activity to reinforce these concepts.

1. CHAPTER 2.5
The Distributive Property &
Combining Like Terms

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: 6x–( )4)3x –(+ + + 2
Terms: 6x,–3x, 4,– 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) + 5(4)
= 15 + 20
= 35
5 (3 + 4) =
4(-1) + 4(3)
= -4 + 12
= 8
4 (-1+ 3) =

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

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

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

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

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

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

13. DISTRIBUTIVE PROPERTY
Whiteboard Races!!!
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. NOW YOU’RE AT BAT.
YOU ARE SITTING
SILENTLY WHILE I
HAND OUT THE
WORKSHEET.
THE END!