Algebraic PropertiesIdentifying & Applying Them

Key Vocabulary

Combining Like Terms

Commutative Property

Associative Property

Distributive Property

Combining Like Terms

2x² - 4x + 5x² + 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: 2x; 4y; 5x; 3

Coefficients: The numbers in front of the variables.Ex: 2, 4, & 5

Combining Like Terms

2x² + 5x² - 4x + 3

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1st: Find each term with the same variable to the same power!Ex: 2x² & 5x²

4x3

2nd: Simplify using the coefficients and operations.Ex: 2x² + 5x² = 7x²

4x = 4x3 = 3

3rd: Unlike terms cannot be combined.2x² cannot be added or subtracted with 4x or with 3

7x² - 4x + 3

Combining Like Terms

Combining Like Terms

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 is essential to apply

the algebraic properties.

A way to remember:Keep ‘order’ in the community!

COMMUTATIVE PROPERTY (Ordering)

Words Numbers

You can add or multiply numbers in any order.

18 + 9 = 9 + 1815 2 = 2 15

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.*

A way to remember!Be careful of the group you associate with!

ASSOCIATIVE PROPERTY (Grouping)

Words NumbersONLY 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)

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.

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

Caution!

DISTRIBUTIVE PROPERTYWords 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) \ / \ / = 60 + 24 \ / = 84

Distributive Property

A way to remember!Distribute evenly to everyone.

A way to remember!Distribute evenly to everyone.

6(x + 7)

6(x + 7)

(6· x) + (6 · 7) \/ \/ 6x + 42

Use the Distributive Property.

There are no like terms, so it stays the same.

Multiply.

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.

Let’s Practice!

1. 4x + 72. 6n + 93. 24x4. 33n5. 3x6. 4x + 37. 36y + x8. 8x + 4y9. 27x + 18y10. 6x + 4

1. 3x + 7 + x2. 4n + 2n + 93. 4(6x)4. (3 · n) · 115. x + x + x6. 3(x + 1) + x7. (14y + x) + 22y8. 4(2x + y)9. 27x + 18y10. 4(x + 1) + 2x