1. Identifying & Applying Them
Algebraic Properties
Identifying & Applying Them

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

3. 2x² - 4x + 5x² + 3 Combining Like Terms
To ‘Combine Like Terms’ it is essential to recall the definition of
‘terms’ & ‘coefficients.’
Terms: Parts 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
Combining Like Terms

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

5. Combining Like Terms

6. x + x + x is the same as 3x x + y + y is the same as x + 2y 4y – y is the same as 3y
Combining Like Terms

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

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

9. Examples of Applying the Commutative Property
5x + 2y + 4 = 2y x 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.*
Examples of Applying the Commutative Property

10. A way to remember! Be careful of the group you associate with!
ASSOCIATIVE PROPERTY (Grouping)
Words
Numbers
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)
A way to remember! Be careful of the group you associate with!

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.
Examples of Applying the Associative Property

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

13. Distributive Property
Words
Numbers
To multiply a number by a sum, multiply by each number in the sum and then add.
6  (10 + 4) = (6  10) + (6  4)
\ / \ / =
\ / =
Distributive Property

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

15. A way to remember! Distribute evenly to everyone.
6(x + 7)
(6· x) + (6 · 7)
\/ \/ 6x
Use the Distributive Property.
Multiply.
There are no like terms, so it stays the same.
A way to remember! Distribute evenly to everyone.

16. A way to remember! Distribute evenly to everyone.
24 + 6x
(24 ÷ 6) + (6x ÷ 6)
\ / \ /
( 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. .
A way to remember! Distribute evenly to everyone.

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