Add a student-friendly definition in the Binder Page editor.
Equivalent Expressions
Students identify and create expressions that have the same value for every permitted variable value by combining like terms, distributing, and factoring.
Find It. Learn It. Master It.
Beginner
15–20 minutes
Algebraic Expressions
Algebraic Expressions
Page 5 of 5
Inside Cover
Equivalent Expressions
At a Glance
Binder SectionAlgebraic Expressions
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
How can we prove that two expressions are equivalent?
Build Understanding
Equivalent expressions may look different but produce the same value for every allowed value of the variable. For example, 3(x + 4) and 3x + 12 are equivalent because of the distributive property.
Like terms have identical variable parts, including exponents. Combine their coefficients: 5x + 2x = 7x. The terms 4x and 4x² are not like terms and cannot be combined.
To simplify 2(3x − 5) + 4x, distribute first: 6x − 10 + 4x. Then combine like terms: 10x − 10.
Factoring reverses distribution. The expression 12x + 18 has a greatest common factor of 6, so it can be written as 6(2x + 3). Expanding the factored form checks the result.
You can test possible equivalence by substituting the same value into both expressions, but one matching value does not prove expressions are always equivalent. Algebraic properties provide the proof.
Common errors include combining unlike terms, changing an exponent when adding terms, forgetting to distribute a negative sign, and distributing to only one term.
Visual Model
4Thousands
3Hundreds
2Tens
7Ones
4,327 = 4,000 + 300 + 20 + 7
Goals
Learning Targets
- Equivalent expressions have the same value for all permitted variable values.
- Combine only like terms.
- Add or subtract coefficients; keep the variable part unchanged.
- Distribution multiplies every term inside grouping symbols.
- Factoring reverses distribution.
- Substitution can disprove equivalence, but one matching value does not prove it.
Click each word
Interactive Vocabulary
Add a student-friendly definition in the Binder Page editor.
Add a student-friendly definition in the Binder Page editor.
Add a student-friendly definition in the Binder Page editor.
Add a student-friendly definition in the Binder Page editor.
Reveal one step at a time
Worked Examples
Example 1
Combine like terms
1
4x+3+2x−5
2
Group 4x+2x and 3−5.
3
6x−2.
Example 2
Expand
1
3(2x−4)
2
Distribute 3 to both terms.
3
6x−12.
Ask and explain
Common Questions
Are 3x and 3x² like terms? No. Their exponents differ.
Why does 2x + 5x equal 7x rather than 7x²? Adding like terms combines coefficients; it does not multiply variables.
Are x + x and x² equivalent? No. x + x = 2x.
How can I check a factored expression? Distribute to return to the original expression.
Does one matching test value prove equivalence? No. Use properties to show equivalence for all values.
Notice and correct
Common Misconceptions
Combining unlike terms
Variable parts and exponents must match.
Changing signs while distributing a negative
Multiply every term, including its sign.
Learn Through Video
Watch, pause, and explain
Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.
Not Started
Build Your Skills
Practice until you can explain it
Move from a quick warm-up to guided practice, independent work, and deeper challenges.
0%
0 of 4 stages complete
Warm-Up
Guided
Independent
Challenge
1
Quick Start
Warm-Up
Simplify 3x+5x.
2
We Do
Guided Practice
Combine like terms: 6x + 4x. Answer: 10x.
Simplify 9y − 2 + 3y + 7. Answer: 12y + 5.
Expand 5(a − 3). Answer: 5a − 15.
Simplify 2(4x + 1) − 3x. Answer: 5x + 2.
Factor 15x + 20. Answer: 5(3x + 4).
Are 4(x + 2) and 4x + 8 equivalent? Answer: Yes.
Are 3x + 2x² and 5x³ equivalent? Answer: No; the terms are unlike.
3
You Do
Independent Practice
Factor 12x+18.
Are 4(x+2) and 4x+8 equivalent?
4
Stretch Your Thinking
Challenge & Real-World Practice
Write three visibly different expressions equivalent to 6x+12. Include an expanded form, a factored form, and a form containing like terms; prove each.
Practice Complete
Continue to My Math Journal →
Nice work!
You completed the Practice It learning path.
IXL
Equivalent Expressions Lesson
Open resourceWriting Algebraic Expressions
Open resourceIdentify Equivalent Expressions I
Open resourceIdentify Equivalent Expressions II
Open resourceEquivalent Expressions Involving Exponents
Open resourceKhan Academy
Equivalent Forms of Expressions
Open resourceEquivalent Expressions with Percent Problems
Open resourceCreate Equivalent Expressions by Factoring
Open resourceNegative Numbers and Distribution
Open resourceDeltaMath
Mixed Numbers—Equivalent Expressions
Open resourceFractions—Equivalent Expressions L2
Open resourceEquivalent Expressions—Decimal Multiplication
Open resourceEquivalent Expressions
Open resource
BUILD YOUR PERSONAL MATH LIBRARY
Save today’s lesson and grow your MathBinder
Collect lesson resources, revisit recent pages, build review packets, and watch your binder grow over time.
My Binder
0
Saved Items in My Binder
Start your collection
Today’s Lesson
0 resources collected
Printable Resources
Available Now
Choose a Printable ↓
Interactive Notebook Printables
Choose any notebook page below and select Print Blank Copy to complete it by hand.
- Lesson-specific pages
- Clean print layout
- Add to a physical binder
Your Collection
Recently Added
Your saved items will appear here.Build a binder you can use all year.
Binder Preview
My MathBinder
MathBinder
Find It. Learn It. Master It.
0 saved items
Number SystemRatiosAlgebraGeometry
Study Tools
Build a Review Packet
My Collected Lessons
Create a printable list of the lessons saved in this browser.
Favorite This Lesson
Save this page for quick access from your MathBinder dashboard.
Continue Learning
Move to another published lesson in this Binder Section.
Open Properties of Addition and Multiplication →Milestones
Your Binder Achievements
Finish Strong
Go to My Math Journal →
Learned. Watched. Practiced. Saved.
Now capture the most important idea in My Math Journal.
Parent Tip
Spend five minutes reviewing one saved lesson together each week. Ask your child to explain one example aloud.
MY PRIVATE MATH SPACE
My Math Journal
Capture your thinking, questions, and reflections. Everything is saved automatically on this device.
Saved on this device
Ready
Confidence Check
How confident do you feel?
Awesome! You’re ready to teach someone else!
Quick Reflection
Complete the thought
My Math Notes
0 words
What do you want to remember?
Learning Record
0 entries
My Journal History
Revisit reflections saved from other MathBinder lessons on this device.
Your journal history will grow as you reflect.
Complete this lesson’s journal to begin your learning record.
Your Math Journal is automatically saved on this device.
Clearing your browser data will erase your saved journal entries.
Show What You Know
Can you do this on your own?
Complete each question without hints. Your result is saved privately on this device.
5–8
Minutes
0 of 5 answered
0%
Before you begin, I can…
- I can identify like terms before combining them.
- I can distribute positive and negative factors.
- I can verify equivalence algebraically or with multiple inputs.
1
Question 1
3x+5x equals?
2
Question 2
3(2x−4) equals?
3
Question 3
Which terms are like?
4
Question 4
Factor 8x+12.
5
Question 5
Are 2(x+5) and 2x+10 equivalent?
Confidence Check
How confident do you feel?
Mastery Result
0%
Your Results
Recommended Next Step
Review and try again
Badge EarnedEquivalent Expressions Master
Lesson Complete
Great job on Equivalent Expressions!
You reviewed the lesson, practiced the skill, and completed the mastery check.