Combining Like Terms and Distributive Property

1. Combining Like Terms and Distributive Property Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

2. Basic Information • When you are combining like terms, find terms with common variables (raised to the same power) then add the coefficients • Make sure you use the distributive property to get rid of any parenthesis before combining like terms • When an expression is completely simplified, you will only have one of each term from the original expression (ex. 4x +2y – 5)

3. Like Terms Let’s try to pick out the “like terms” from the list below.

4. Like Terms 4x and -2x are like terms because they both have an x.

5. Like Terms 8xy and -7xy are like terms because they both have an xy.

6. Like Terms 3y2 and 5y2 are like terms because they both have an x.

7. Like Terms 2y and y are like terms because they both have a y.

8. Combining Like Terms Let’s take a look at an example problem.

9. Combining Like Terms One strategy to solve this problem is to box things that are like terms. Since both 3x and -4x have an x, they are considered “like terms”.

10. Combining Like Terms Next, circle the next term that is not like the first. Circle any other terms that are “like terms” for this. 2 is a constant (it does not have a variable) and it is the only term left.

11. Combining Like Terms Now you can combine the coefficients for each set of like terms.

12. Combining Like Terms This is the simplified version of the expression after you combine like terms.

13. Combining Like Terms Let’s try something a little bit more difficult. Group your like terms together before simplifying. 4y and 2y are like terms because they each have a y. -5x and -7x are like terms because they each have an x. 2 and 6 are like terms because they are each constants (no variable with them).

14. Combining Like Terms Sometimes, you’ll have the same variable raised to different powers. THESE ARE NOT LIKE TERMS!

15. Combining Like Terms Let’s find our like terms. These are like terms because they both have an x2.

16. Combining Like Terms Let’s find our like terms. These are like terms because they both have an x.

17. Combining Like Terms Let’s find our like terms. -8 doesn’t have any other like terms because it is the only constant.

18. Combining Like Terms Now combine all your like terms to simplify the expression.

19. Distributive Property The distributive property is used to simplify expressions with parenthesis. You multiply the term on the outside of the parenthesis by each term on the inside of the parenthesis. Let’s take a look at an example.

20. Distributive Property For this problem, you need to multiply 3 by each term on the inside of the parenthesis. You will use this same method for each set of parenthesis in an expression or equation.

21. Distributive Property Take each set of parenthesis separately and then combine like terms to find the simplified expression.

22. Distributive Property If you have an expression with just a negative sign in front of the parenthesis, assume it is -1 and distribute.

23. Follow-Up Questions Answer the following questions on loose leaf and hand them in to your teacher.

24. Follow-Up Questions 1. 2. 3. 4. 5.

25. Follow-Up Questions 6. 7. 8. 9. 10.