1. Factoring and Expanding Linear Expressions .
Students will use the distributive property to expand algebraic expressions and they will factor algebraic expressions.
Factor: a number that divides evenly into another number.
Greatest Common Factor (GCF): the largest number common to two or more terms.

2. Greatest Common Factor (GCF)
What is the greatest number that is a factor of all three of these numbers?
**List the factors of each number.
6: 1, 2, 3, and 6
9: 1, 3, and 9
12: 1, 2, 3, 4, 6, and 12

3. Factoring and Expanding Linear Expressions
You can use number properties, such as the distributive property, to help you expand or factor expressions.
Example: Expand the expression 0.4(5x + 8).
Step 1: Apply the distributive property.
0.4(5x + 8) = (0.4 ∙ 5x) + (0.4 ∙ 8)
Step 2: Simplify the expression.
2.0x + 3.2

4. Your turn!
Expand the expression -5(2x – 6)

5. Greatest Common Factor of Algebraic Expressions
Factoring an expression means finding the GCF of all the terms and then dividing each term by that factor.
Factored expressions use parentheses or other grouping symbols to show what has been factored out.
So, factoring an expression is the opposite of expanding it!

6. What factors do these terms have in common?
Factor Expressions
List the factors of:
27a: 1, 3, 9, 27, and a
45ab: 1, 3, 5, 9, 15, 45, a, and b
What factors do these terms have in common?

7. FactorExpressions Example: Factor 4 + 8m completely.
Step 1: Identify the GCF of the terms 4 and 8m
4: 1, 2, and 4
8m: 1, 2, 4, 8, and m
The greatest numerical factor common to both 4 and 8m is 4. There is no variable factor in common.
Step 2: Use the distributive property to factor the expression. (Take out the GCF and rewrite the expression)
4 + 8m = 4(1 + 2m)

8. Your Turn!
Factor 12n – 3mn completely.

9. One More!
Factor 9x + 15y completely. Show your work!!