1. The Distributive Property
and
Like Terms

2. Review
4 is the coefficient of x
3 is the
coefficient of

3. LIKE Terms Like terms are terms in an expression that have the
- same variable
- raised to the same power

4. LIKE Terms 5x and 3x are like terms 4 and 2 are also like terms
7x2 and x2 are also like terms

5. LIKE Terms
5x and 7x2 are NOT like terms
WHY????

6. LIKE TERMS NOT like terms 3b and 5b 3b and 5c 7x2 and 5x2 7x2 and 7y2
14c and 8c
7c3 and 5c3
NOT like terms
3b and 5c
7x2 and 7y2
12x2 and 7x
18a and 18b
LIKE TERMS
same variable
raised to the same power

7. Like Terms?? 8a and 12a 8b and 5c 7a and 7b 5c2 and 7c2 8x2 and 12x2
12g and g2
c and 8c
18b5 and 2b2
5ab and 7bc
7c3 and 5c3
8b and 5c
5c2 and 7c2
3x2 and 7z2
10x2 and 8x2
5xy and 6x
18a and 18b
5a and 8a
8x3 and 12c3

8. What do we do with LIKE TERMS?
We can add the coefficients together.
(We can subtract also)
Be careful - the coefficient changes but the variable and power do NOT change.

9. Combine Like Terms 8a + 12a = 20a 8x2 + 12x2 = 20x2 c + 8c = 9c
18b5 - 2b5 = 16b5
5b + 7b = 12b
7c3 + 5c3 = 12c3
coefficient changes the variable and power do NOT change.

10. Combine Like Terms 5c2 + 7c2= 12c2 10z2 + 8z2 = 18z2 5y + 6y = 11y
5a + 8a = 13a
10x3 – 3x3= 7x3
a + 6a = 7a
coefficient changes the variable and power do NOT change.

11. Combine Like Terms 8a + a = 8x2 + 6x2 = 5c + 12c = 18x5 – 2x5 =
15w - 7w =
9c3 + 3c3 =
coefficient changes the variable and power do NOT change.

12. Combine Like Terms 5y2 + 7y2= 2r2 + 3r2 = 8y - y = 11a + 8a =
12x3 – 5x3=
12a + a =
coefficient changes the variable and power do NOT change.

13. The Distributive Property
The product of 4 and (2+3x):
4(2+3x)
4●2 + 4 ● 3x
8 + 12x
Sharing what is Outside the parentheses with EVERYTHING INSIDE the parentheses.

14. Example using the distributive property

15. Example using the distributive property

16. The Distributive Property
The product of 5 and (a + 12):
5(a + 12)
5●a + 5 ● 12
5a + 60
Sharing what is Outside the parentheses with EVERYTHING INSIDE the parentheses.

17. Example using the distributive property

18. Another Example

19. Another Example

20. Another Example

21. Another Example

22. Another Example

23. Simplify

24. Simplify

25. Simplify

26. Simplify

27. Simplify

28. Another Example

29. Simplify

30. Another Example

31. Simplify

32. Simplify

33. Simplify

34. Simplify