1. Warm Up
Find the GCF of each set of numbers.
1. 12 and , 45 and 30
2. 18 and , 24 and 30
5. 72, 80 and 96 2 15 6 2 8

2. Learn factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

3. Vocabulary
term
coefficient
equivalent expressions

4. The terms of an expression are the parts of the expression that are added or subtracted. The terms of the expressions 140+4x are 140 and 4x.
In the term 4x, 4 is called the coefficient. A coefficient is the number that is multiplied by a variable in a algebraic expression.
You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

5. Equivalent expressions are expressions that have the same value for all the values of the variables. The expressions 15x+18 and 3(5x+6) are equivalent expressions since 15x+18=3(5x+6) for every value of x.

6. The greatest common factor (GCF) is the largest
common factor of two or more given numbers.
Remember!

7. Additional Example 1: Factoring Numerical Expressions
Factor the sum of terms as a product of the GCF and a sum.
27+39
27+39
The terms are 27 and 39
The GCF of the terms is 3
Rewrite each term as a product with GCF
3(9+13)
Apply the distributive law

8. Check It Out: Example 1
Factor the sum of terms as a product of the GCF and a sum.
15+45
27+39
The terms are 15 and 45
The GCF of the terms is 15
Rewrite each term as a product with GCF
15(1+3)
Apply the Distributive property

9. Additional Example 2: Factoring Algebraic Expressions
Factor the sum of terms as a product of the GCF and a sum.
12b + 28
12b + 28
The terms are 12b and 28
2.2.3.b+2.2.7
The GCF of the terms is 2.2
Rewrite each term as a product with GCF
4.3b + 4.7
4(3b+7)
Apply the Distributive law

10. Check It Out: Example 2
Factor the sum of terms as a product of the GCF and a sum.
16b+32
16b+32
The terms are 16b and 32 b
The GCF of the terms is
Rewrite each term as a product with GCF
16.b+16.2
16(b+2)
Apply the distributive property

11. There are many other ways to write equivalent expressions for each of the expressions in Example 3.
Helpful Hint

12. Additional Example 3: Writing Equivalent Expressions
Write four equivalent expressions for each given expression. A
9+15
The terms are 9 and 15
Rewrite each term as a product with GCF
3(3+5)
Apply the Distributive property
3(5+3)
Apply the Commutative property
3(8)
Add

13. Continued: Example 3
B. 25m-5m
25m-5m
The terms are 25m and 1m
Rewrite each term as a product with common factor 5m
5.5m-1.5m
(5-1)5m
Apply the Distributive property
4.5m
Subtract
20m
Multiply

14. Continued: Example 3
C. 2(4p+2)
2(4p+2)
2.4p+2.2
Apply the Distributive property
8p+4
Multiply
4+8p
Apply the Commutative property
4+23p
Write the coefficient of 8 as 23

15. Check It Out: Example 3
Write four equivalent expressions for each given expression.
3(9p+3)
3(9p+3)
3.9p+3.3
Apply the Distributive property
27p+9
Multiply
9+27p
Apply the Commutative property
9+33p
Write the coefficient of 27 as 33

16. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

17. Lesson Quiz
Factor the sum of terms as a product of the GCF and a sum
15(3+1)
8(3+5)
3. 16y + 36
4(4y+9) s
30(3+2s)

18. Continued: Lesson Quiz
Write four equivalent expressions for each given expression.
2(10-4); 4(5-2); 4.3; 12
6. 9z + 12
3(3z+4); 3(4+3z); 32z+12; 12+9z

19. Lesson Quizzes Lesson Quiz for Student Response Systems
1. Factor the sum of terms as a product of the GCF and a sum
60+30
A. 60(1+2)
B. 90
C. 30(2)
D. 30(2+1)

20. Continued: Lesson Quiz for Student Response Systems
2. Factor the sum of terms as a product of the GCF and a sum
13+39r
A. 13(1+3r)
B. 13(1+3)
C. 13(3r)
D. 42r

21. Continued: Lesson Quiz for Student Response Systems
3. Which expression is not equivalent to 12-3?
A. 3(4-1)
B. 3(22-1) C
D. 3(1-3)

22. Continued: Lesson Quiz for Student Response Systems
4. Which expression is not equivalent to 8z+12?
A. 8z+4.3
B. 4(2z+3)
C. 4(2z+12)
D. 4(3+2z)