1. Algebraic Expressions

2. Unit 7 – Expanding and Factoring Algebraic Expressions

3. Vocabulary
Factor (verb) - To express as a product of two or more factors
Distributive Property - A property of real numbers that states that the product of the sum or difference of two numbers is the same as the sum or difference of their products.
Example: Multiplication over addition
2(15 + 4) = 2 × × 4
Multiplication over subtraction
3(5 – 8) = 3 × 5 – 3 × 8

4. Expanding Algebraic Expressions Bar Model Example
Expand each expression.
3(f + 2) 3(f + 2) means 3 groups of (f + 2) 3f + 6

5. Expanding Algebraic Expressions Distributive Property Example
Expand each expression.
3(f + 2)
3f + 6

6. Expanding Algebraic Expressions Bar Model Example
Expand each expression.
4(g + 4)
4(g + 4) means 4 groups of (g + 4)
4g + 16

7. Expanding Algebraic Expressions Distributive Property Example
Expand each expression.
4(g + 4)
4g +16

8. Expanding Algebraic Expressions Practice
Expand each expression
2(p + 7)
2p + 14
6(7m + 9)
42m + 54
9(d - 4) 9d
3(9y – 6)
27y - 18

9. Factoring Algebraic Expressions Example
Factor each expression.
6d + 10
1st – find the greatest common factor of 6d and 10
GCF = 2
2nd – divide each term by the GCF
6d ÷ 2 = 3d
10 ÷ 2 = 5
3rd – use the GCF and the quotients to rewrite the expression
2(3d + 5)

10. Factoring Algebraic Expressions Example
Factor each expression.
8t + 28
1st – find the greatest common factor of 8t and 28
GCF = 4
2nd – divide each term by the GCF
8t ÷ 4 = 2t
28 ÷ 4 = 7
3rd – use the GCF and the quotients to rewrite the expression
4(2t + 7)

11. Factoring Algebraic Expressions Example
Factor each expression.
9i - 27
1st – find the greatest common factor of 9i and 27
GCF = 9
2nd – divide each term by the GCF
9i ÷ 9 = i
27 ÷ 9 = 3
3rd – use the GCF and the quotients to rewrite the expression
9(i - 3)

12. Factoring Algebraic Expressions Practice
Factor each expression
24g + 8
8(3g + 1)
45h + 5
5(9h + 1)
21b - 7
7(3b - 1)
56z – 14
14(4z - 1)

13. Expanding and Factoring Algebraic Expressions Mixed Practice
State whether each pair of expressions is equivalent
6(2u + 3) and 6u + 18
12u and 6u + 18 no
3(2h - 5) and 6h -15
6h - 15 and 6h - 15
yes
22s and 2(11s + 9)
2(11s + 9) and 2(11s + 9)
yes
6h and 3(2h - 5)
3(2h + 5) and 3(2h - 5) no

14. Simplifying and Factoring Algebraic Expressions Practice
Simplify each expression. Then Factor the expression
9g g + 7
13g + 26
13(g + 2)
9(6a + 7) – 6 – 3a
54a + 63 – 6 – 3a
51a + 57
3(17a + 19)