Algebraic Properties Identifying Applying Them Combining Like Terms

Algebraic Properties Identifying & Applying Them

Combining Like Terms Commutative Property Associative Property Distributive Property Key Vocabulary

2 x² - 4 x + 5 x² + 3 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: 2 x; 4 y; 5 x; 3 Coefficients: The numbers in front of the variables. Ex: 2, 4, & 5 Combining Like Terms

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

Combining Like Terms

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

Combining like terms is essential to apply the algebraic properties.

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

5 x + 2 y + 4 = 2 y + 4 + 5 x 3 x 4=4 x 3 4 x + 9 = 9 + 4 x *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

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

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

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

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

A way to remember! Distribute evenly to everyone.

6(x + 7) (6· x) + (6 · 7) / / 6 x + 42 Use the Distributive Property. Multiply. There are no like terms, so it stays the same. A way to remember! Distribute evenly to everyone.

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

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