homework practice factor linear expressions

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)

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to   [email protected]

We always appreciate your feedback.

© All rights reserved. onlinemath4all.com

• Sat Math Practice
• SAT Math Worksheets
• PEMDAS Rule
• BODMAS rule
• GEMDAS Order of Operations
• Math Calculators
• Transformations of Functions
• Order of rotational symmetry
• Lines of symmetry
• Compound Angles
• Quantitative Aptitude Tricks
• Trigonometric ratio table
• Word Problems
• Times Table Shortcuts
• 10th CBSE solution
• PSAT Math Preparation
• Privacy Policy
• Laws of Exponents

Recent Articles

SAT Math Videos (Part 2 - No Calculator)

May 25, 24 05:35 AM

SAT Math Videos (Part 1 - No Calculator)

May 25, 24 05:07 AM

Simplifying Algebraic Expressions with Fractional Coefficients

May 17, 24 08:12 AM

• Number Charts
• Multiplication
• Long division
• Basic operations
• Telling time
• Place value
• Roman numerals
• Fractions & related
• Add, subtract, multiply,   and divide fractions
• Mixed numbers vs. fractions
• Equivalent fractions
• Prime factorization & factors
• Fraction Calculator
• Decimals & Percent
• Add, subtract, multiply,   and divide decimals
• Fractions to decimals
• Percents to decimals
• Percentage of a number
• Percent word problems
• Classify triangles
• Classify quadrilaterals
• Circle worksheets
• Area & perimeter of rectangles
• Area of triangles & polygons
• Coordinate grid, including   moves & reflections
• Volume & surface area
• Pre-algebra
• Square Roots
• Order of operations
• Scientific notation
• Proportions
• Ratio word problems
• Write expressions
• Evaluate expressions
• Simplify expressions
• Linear equations
• Linear inequalities
• Graphing & slope
• Equation calculator
• Equation editor
• Elementary Math Games
• Addition and subtraction
• Math facts practice
• The four operations
• Factoring and number theory
• Geometry topics
• Middle/High School
• Statistics & Graphs
• Probability
• Trigonometry
• Logic and proof
• For all levels
• Favorite math puzzles
• Favorite challenging puzzles
• Math in real world
• Problem solving & projects
• For gifted children
• Math history
• Math games and fun websites
• Interactive math tutorials
• Math help & online tutoring
• Assessment, review & test prep
• Online math curricula

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.

Curriculum  /  Math  /  7th Grade  /  Unit 3: Numerical and Algebraic Expressions  /  Lesson 8

Numerical and Algebraic Expressions

Lesson 8 of 11

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).

Common Core Standards

Core standards.

The core standards covered in this lesson

Expressions and Equations

7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Foundational Standards

The foundational standards covered in this lesson

6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

The Number System

7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Look for and make use of structure in expressions (MP.7).
• Analyze student work to understand different approaches in simplifying expressions.
• Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

Suggestions for teachers to help them teach this lesson

The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

A student simplified the expression below as part of their homework. Review their work and check for any mistakes. For each line in their work, explain what they did to get their next step.

Homework Problem:

$${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$$

Student’s Work:

Step 1:  $${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$$

Step 2:  $${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$$

Step 3:  $${\left ( -\frac{5}{3}-1 \right )x+0}$$

Step 4:  $${-\frac{8}{3}x}$$

Guiding Questions

Find the perimeter of the parallelogram.

An expression is given.

$${-2y+\frac{3}{2}x+\frac{7}{4}}$$

Which are equivalent to the given expression? Select each correct answer.

Math Spring Operational 2016 Grade 7 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC) . Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 10:59 a.m..

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Which expressions are equivalent to the expression $$n+\frac{5}{6}(m-n)-\frac{1}{3}m$$ ? Select all that apply.

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Have students swap work every now and then to check and correct each other’s work (without an answer key). 
• Kuta Software Free Algebra 1 Worksheets Basics - Combining Like Terms
• Utah Middle School Math Project Chapter 3 Expressions and Equations Student Workbook — pages 60 - 62, 64, 65
• PARCC Released Items Math Spring Operational 2016 Grade 7 Released Items — Problem 16
• PARCC Released Items Math Spring Operational 2015 Grade 7 End of Year Released Items — Problem 4

Topic A: Evaluating Numerical and Algebraic Expressions

Evaluate numerical expressions with rational numbers using the order of operations.

7.EE.A.1 7.NS.A.3

Write and evaluate expressions for mathematical and contextual situations.

Create a free account to access thousands of lesson plans.

Already have an account? Sign In

Topic B: Generating Equivalent Expressions

Expand and factor expressions using the distributive property and the greatest common factor.

Expand and factor expressions with negative rational numbers.

Add and simplify expressions by combining like terms.

Subtract and simplify expressions.

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).

Write and interpret expressions in different ways to shed new meaning on a context.

Topic C: Solving Multi-Step Problems using Expressions

Solve multi-step real-world problems with rational numbers.

7.EE.B.3 7.NS.A.3

Model real-world problems involving rational numbers using reasoned estimates.

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School information, what courses are you interested in, are you interested in onboarding professional learning for your teachers and instructional leaders, any other information you would like to provide about your school.

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free

• Notifications 0

• Add Friend ($5)

As a registered member you can:

• View all solutions for free
• Request more in-depth explanations for free
• Ask our tutors any math-related question for free
• Email your homework to your parent or tutor for free
• Grade 7 McGraw Hill Glencoe - Answer Keys

Explanation:

Factor each expression. If the expression cannot be factored, write cannot be factored. Use algebra tiles if needed.

\(3x + 6=\)

• Type below:

\(2x - 15=\)

\(12x + 30y=\)

The area of a rectangular dance floor is (4x - 8) square units. Factor 4x - 8 to find possible dimensions of the dance floor.

The area of a rectangular porch is (9x + 18) square units. Factor 9x + 18 to find possible dimensions of the porch. 

Six friends visited a museum to see the new holograms exhibit. The group paid for admission to the museum and $12 for parking. The total cost of the visit can be represented by the expression $6x + $12. What was the cost of the visit for one person?

The diagram represents a flower border that is 3 feet wide surrounding a rectangular sitting area. Write an expression in factored form that represents the area of the flower border.

Yes, email page to my online tutor. ( if you didn't add a tutor yet, you can add one here )

Thank you for doing your homework!

Submit Your Question