1. Algebraic Properties Identifying & Applying Them

2. Key Vocabulary Combining Like Terms Commutative Property Associative Property Distributive Property

3. Combining Like Terms 2x² - 4x + 5x² + 3 To ‘Combine Like Terms’ it is essential to recall the definition of ‘terms’ & ‘coefficients.’ Terms: P arts of the expression separated by addition or subtraction. Ex: 2x; 4y; 5x; 3 Coefficients: The numbers in front of the variables. Ex: 2, 4, & 5

4. Combining Like Terms 2x² + 5x² - 4x + 3 1 st : Find each term with the same variable to the same power! Ex: 2x² & 5x² 4x 3 2 nd : Simplify using the coefficients and operations. Ex: 2x² + 5x² = 7x² 4x = 4x 3 = 3 3 rd : Unlike terms cannot be combined. 2x² cannot be added or subtracted with 4x or with 3 7x² - 4x + 3

5. Combining Like Terms

6. x + x + x is the same as 3x x + y + y is the same as x + 2y 4y – yis the same as 3y

7. Combining like terms is essential to apply the algebraic properties.

8. A way to remember: Keep ‘order’ in the community! COMMUTATIVE PROPERTY (Ordering) WordsNumbers You can add or multiply numbers in any order. 18 + 9 = 9 + 18 15  2 = 2  15

9. Examples of Applying the Commutative Property 5x + 2y + 4 = 2y + 4 + 5x 3 x 4 = 4 x 3 4x + 9 = 9 + 4x *All of the terms on one side of the equal sign are on the other side of the equal sign just in a different order.*

10. A way to remember! Be careful of the group you associate with! ASSOCIATIVE PROPERTY (Grouping) WordsNumbers ONLY when you are adding or multiplying, you can group any of the numbers together. (17 + 2) + 9 = 17 + (2 + 9) (12  2)  4 = 12  (2  4)

11. Examples of Applying the Associative Property All of the terms on each side of the equal sign are the same. The order is the same.

12. The Commutative and Associative Properties do not apply to subtraction or division. Caution!

13. DISTRIBUTIVE PROPERTY WordsNumbers To multiply a number by a sum, multiply by each number in the sum and then add. 6  (10 + 4) = (6  10) + (6  4) \ / \ / = 60 + 24 \ / = 84 Distributive Property

14. A way to remember! Distribute evenly to everyone.

15. 6(x + 7) (6· x) + (6 · 7) \/ \/ 6x + 42 Use the Distributive Property. There are no like terms, so it stays the same. Multiply.

16. A way to remember! Distribute evenly to everyone. 24 + 6x (24 ÷ 6) + (6x ÷ 6) \ / \ / (4 + x) 6(4 + x) Factor out the GCF of each term. … in this case 6.. Place the quotients in parenthesis. Place the GCF in front of the parenthesis of quotients.

17. Let’s Practice! 1. 4x + 7 2. 6n + 9 3. 24x 4. 33n 5. 3x 6. 4x + 3 7. 36y + x 8. 8x + 4y 9. 27x + 18y 10. 6x + 4 1. 3x + 7 + x 2. 4n + 2n + 9 3. 4(6x) 4. (3 · n) · 11 5. x + x + x 6. 3(x + 1) + x 7. (14y + x) + 22y 8. 4(2x + y) 9. 27x + 18y 10. 4(x + 1) + 2x