1. Title of Notes: Combining Like Terms & Distributive Property
Pg. 25 & 26

2. A term is a…
number,
variable, or
a product / quotient of numbers and variables.
Examples 5 m
2x2

3. A coefficient is…

4. Like Terms are…
terms with the same variable AND exponent.
Note -
To simplify expressions with like terms, simply combine the like terms.

5. Are these like terms? 13k, 22k Yes, the variables are the same.
5ab, 4ba
Yes, the order of the variables doesn’t matter.
x3y, xy3
No, the exponents are on different variables.

7. 5a and a are like terms
and
are like terms
The above expression simplifies to:

8. Try These! simplify the expressions
10k k – 1
3y + 8 – y
-13p p – 9

9. Try These! simplify the expressions
10k k – 1 = 16k + 4
3y + 8 – y = 2y +8
-13p p – 9 = -7p – 2

10. Try These! simplify the expressions
-12y y – 1
9g + 15 – g + 2g
r + 8r

11. Try These! simplify the expressions
-12y y – 1 = -9y - 9
9g + 15 – g + 2g = 10g - 15
r + 8r = 2r - 10

12. Distributive Property –
Multiply each number inside the parentheses by the number outside the parentheses, and then add the like terms .
a(b+c) = ab + ac OR
(b+c)a = ab + ac

13. Example 1
2(6 + 4) =
2(6) + 2(4)
12 + 8 20

14. Example 2
5(x + 3) =
5(x) + 5(3)
5x + 15

15. Example 3
3(x - 1) =
3(x) + 3(-1)
3x - 3

16. Example 4
-2(y - 5) =
-2(y) + -2(-5)
-2y + 10

17. Example 5
x(y - 5) =
x(y) + x(-5)
xy – 5x

18. Try These!
8(y - 3) =
-7(x + 5) =
-1(3 – 8) =

19. Try These!
8(y - 3) = 8y - 24
-7(x + 5) = -7x - 35
-1(3 – 8) = 5