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→ → Factoring/Distributive property

With this worksheet generator, you can make customizable worksheets for the distributive property and factoring. These worksheets are especially meant for and courses (grades 6-9).

The generator includes only very simple problems with linear expressions. We hope to add more problem types later.

Each worksheet is randomly generated and thus unique. The and is placed on the second page of the file.

You can generate the worksheets — both are easy to print. To get the PDF worksheet, simply push the button titled " " or " ". To get the worksheet in html format, push the button " " or " ". This has the advantage that you can save the worksheet directly from your browser (choose File → Save) and then in Word or other word processing program.

Sometimes the generated worksheet is not exactly what you want. Just try again! To get a different worksheet using the same options:


Simplify expressions such as 2(x + 3) using the distributive property; no negative numbers
   

Simplify expressions such as 2(x + 3 + y) using the distributive property; no negative numbers
   

Simplify expressions such as −5(2x − 3) using the distributive property
   

Simplify expressions such as −5(2x − 3 + y) using the distributive property
   

Factor expressions such as 2x + 6 using the distributive property; no negative numbers
   

Factor expressions such as 15x + 30 + 25y using the distributive property; no negative numbers
   

Factor linear expressions such as −6x + 3 using the distributive property
   

Factor linear expressions such as −24x − 8 + 16y using the distributive property
   



+ 6) = 2 + 12
+ − 5) = 3 + 6 − 15
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Key to Algebra workbook series

Key to Algebra Workbooks

Key to Algebra offers a unique, proven way to introduce algebra to your students. New concepts are explained in simple language, and examples are easy to follow. Word problems relate algebra to familiar situations, helping students to understand abstract concepts. Students develop understanding by solving equations and inequalities intuitively before formal solutions are introduced. Students begin their study of algebra in Books 1-4 using only integers. Books 5-7 introduce rational numbers and expressions. Books 8-10 extend coverage to the real number system.

FACTORING LINEAR EXPRESSIONS

The following steps will be useful to factor linear expressions. 

Step 1 : 

Find the largest common divisor for all the terms in the expression

Step 2 : 

Divide each term of the expression by the largest common divisor.

Step 3: 

Write the quotients inside the parenthesis. 

Step 4 : 

Write the largest common divisor and the parenthesis together using multiplication. 

Example 1 : 

Solution : 

Find the largest common divisors for 4x and 8. 

The largest common divisor for 4x and 8 is 4. 

Divide 4x and 8 by 4

4x/4  =  x

8/4  =  2

Write the quotients x and 2 inside the parenthesis and multiply by the largest common divisor 4.

Example 2 : 

16a + 64b - 4c

Find the largest common divisors for 16a, 64b and 4c. 

The largest common divisor for   16a, 64b and 4c is 4. 

Divide  16a, 64b and 4c by 4 

16a/4  =  4a

64b/4  =  16b

4c/4  =  c

Write the quotients 4a, 16b and c inside the parenthesis and multiply by the largest common divisor 4.

4(4a + 16b - c)

Example 3 : 

36x  - 16

Find the largest common divisors for  36x  and 16. 

The largest common divisor for  36x  and 16 is 4.

Divide  36x  and - 16 by 4.

36x/4  =  9x

-16/4  =  -4

Write the quotients 9x and -4 inside the parenthesis and multiply by the largest common divisor 4.

Example 4 : 

Find the largest common divisors for 35 and 21a.

The largest common divisor for 35 and 21a  is 7.

Divide each term by 7

35/7  =  5

21a/7  =  3a

Write the quotients  5 and  3a  inside the parenthesis and multiply by the largest common divisor 7.

35 + 21a  =  7(5 + 3a)

Example 5 : 

Factor : 

4a - 8b + 5ax - 10bx

Since we have four terms, we can group them into two terms

=  4a - 8b + 5ax - 10bx

Common divisor for first two terms, that is 4a and 8b is 4

Common divisor for third and fourth terms, that is 5ax and 10bx is 5x.

Divide first two terms by 4

4a/4  =  1a

- 8b/4  =  -2b

Divide third and fourth terms by 5x

5ax/5x  =  a

-10bx/5x  =  -2b

=  4(a - 2b) + 5x (a - 2b)

=  (a - 2b) (4 + 5x)

homework practice factor linear expressions

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