5-13C Factoring and Expanding
Linear Expressions
Name
Objective
To apply Properties of Operations as strategies to factor and expand linear
expressions with rational coefficients
The formula for the perimeter of a rectangle is 2l ! 2w. Write this expression
in factored form.
! An expression is written in factored form when it is written as
a product of two or more factors. You can use the Properties of
Operations to factor an expression.
2l ! 2w " 2 • l ! 2 • w
Write each term as a product.
" 2(l ! w)
Use the Distributive Property to
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
factor out the GCF of the terms.
Remember
The Distributive Property says
that a(b ! c) " a • b ! a • c.
The greatest common factor
(GCF) is the greatest number
that is a factor of two or more
numbers.
Notice that 2l ! 2w and 2(l ! w) are different, but equivalent,
forms of the same expression.
So, in factored form, the formula for the perimeter of a rectangle is 2(l ! w).
! You can also write an expression that is factored in expanded form.
In expanded form, each term of the expression is separated by
addition or subtraction.
Write 23(6x ! 24y # 18) in expanded form.
2
2
2
3 • 6x ! 3 • 24y # 3 • 18
4x ! 16y # 12
Use the Distributive Property.
Simplify.
So, in expanded form, the expression 23 (6x ! 24y # 18) is 4x ! 16y # 12.
Example
Write 1.3p # 5.2q ! 3.9 in factored form.
1.3 • p # 1.3 • 4q ! 1.3 • 3
1.3(p # 4q ! 3)
Write each term as a product using a common factor.
Use the Distributive Property.
Use the Properties of Operations to factor or expand the expression.
1. Write 10(3a # 2b ! 5) in expanded form.
2. Write 0.4(6s ! 5t ! 2) in expanded form.
3. Write 5m # 120n # 25 in factored form.
4. Write 43 x # 14 y ! 43 in factored form.
5. Discuss and Write When working with expressions, are expanding
and factoring inverse operations? Explain.
Use after online Common Core Lesson 5-13B.
Chapter 5, Lesson 13C
1
5-13C Factoring and Expanding
Linear Expressions
Name
Use the Properties of Operations to expand the expression.
6. 12 (2n ! 8)
9. 0.6(5f # 8g ! 2)
7. #1(4m ! 7n # 8)
10. 14(4x ! 2y # 3z)
8. #1.2(12f ! 5g # 16)
11. #12(3a # 6b # c)
12. #5r ! 30s # 25
13. 57 x ! 47 y # 17
14. #1.3s # 2.1t # 3.2
15. 65p # 20q # 15
16. 0.02m ! 0.12n # 0.14
17. 8x ! 4y # 8
18. 45 a ! 53 b ! 25
19. #2c # 24d ! 16
20. 75x ! 200y # 125z ! 50
Find the perimeter of the figure. Write the expression for perimeter in both
expanded and factored forms.
21. The width of a rectangle is 3a ! 9. Its length
is 6b.
22. A triangle has sides of length 6s ! 3t ! 1,
5s # 4t ! 8, and 3s # 6t ! 12.
23. One side of a triangle has a length of
15x ! 3y # 6. Another side is 13 that length.
The third side has a length of 8x ! 4y ! 4.
24. The width of a rectangle is 12m # 4n ! 6. Its
length is 4 less than 5 times its width.
WHAT’S THE ERROR?
25. Vicky factored the expression #4q ! 2r # 1 as #1(4q # 2r).
Is this correct? Explain why or why not using the Properties
of Operations.
2
Chapter 5, Lesson 13C
Use after online Common Core Lesson 5-13B.
Copyright © by William H. Sadlier, Inc. Permission to duplicate classroom quantities granted to users of Fundamentals of Algebra.
Use the Properties of Operations to factor the expression.