1. I CAN factor numerical expressions. I CAN factor algebraic expressions
I CAN factor numerical expressions. I CAN factor algebraic expressions. I CAN write equivalent numerical and algebraic expressions.

2. Vocabulary
term
coefficient
equivalent expressions

3. The terms of an expression are the parts of the expression that are added or subtracted. The terms of the expression x 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 an algebraic expression.
You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

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

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

6. Example 1: Factoring Numerical Expressions
B. Factor the sum of terms as a product of the GCF and a sum.
35+15
The terms are 35 and 15
The GCF of the terms is 5
5∙7+5∙3
Rewrite each term as a product with GCF
5(7+3)
Apply the distributive property

7. You Try! Example 1
Factor the sum of terms as a product of the GCF and a sum. A B
4∙5+4∙14
14∙1+14∙3
14(1+3)
4(5+14)

8. Example 2: Factoring Algebraic Expressions
A. Factor the sum of terms as a product of the GCF and a sum.
The terms are 12b and 28
12b + 28
The GCF of the terms is 4
4∙3b + 4∙7
Rewrite each term as a product with GCF
4(3b+7)
Apply the distributive property

9. Example 2: Factoring Algebraic Expressions
B. Factor the sum of terms as a product of the GCF and a sum.
16b+32
The terms are 16b and 32
The GCF of the terms is 16
Rewrite each term as a product with GCF
16∙b+16∙2
16(b+2)
Apply the distributive property

10. You Try! Example 1
Factor the sum of terms as a product of the GCF and a sum.
B. 40y30y
A. 12b+28
10y∙410y∙3
4∙3b+4∙7
4(3b+7)
10y(43)

11. Reflection
CAN YOU factor numerical and algebraic expressions?

12. 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)

13. HOMEWORK
p. 158: 1-12, 19-21, 25-27

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

15. 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.

16. Example 3: Writing Equivalent Expressions
Write four equivalent expressions for each given expression. A
Rewrite each term as a product with GCF
3∙3+3∙5
3(3+5)
Apply the Distributive property
3(5+3)
Apply the Commutative property
3(8)
Add

17. Continued: Example 3
B. 25m-5m
Rewrite each term as a product with GCF
5m∙5-5m∙1
5m(5-1)
Apply the Distributive property
5m∙4
Subtract
20m
Multiply

18. Continued: Example 3
C. 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

19. You Try! Example 3
Write four equivalent expressions for each given expression.
A. 3(9p+3)
B. 8+24
3∙9p+3∙3
8∙1+8∙3
8(1+3)
27p+9
9+27p
8(3+1)
9+33p
8(4)

20. Reflection
CAN YOU write equivalent numerical and algebraic expressions?

21. Lesson Quiz
Write four equivalent expressions for each given expression.
2(10-4); 4(5-2); 4∙3; 12
2. 9z + 12
3(3z+4); 3(4+3z); 32z+12; 12+9z

22. HOMEWORK
HOMEWORK
p. 158: , 31-36
p. 158: , 31-36