Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. But before we can talk about collecting like terms, we need to talk about like terms in general. What are they? **Like terms** are terms that share the same variable and exponent. You can also say that like terms are terms that like each other. Terms can be a single number, a variable, or a combination of numbers and variables multiplied with each other. If you think of the variable and exponent part of a term as the term's last name, then like terms are those terms that share the same last name and are thus part of the same family. If a term didn't have a variable attached to it, then that means it doesn't have a last name and is, therefore, related to all the other terms without last names, without variables attached. For example, 4*x*, 7*x*, and *x* are all like terms because they all share the same variables with the same exponents. 5*x*^2, 6*x*^2, 3*x*^2 are also all like terms. But, 4*x* and 3*x*^2 are not like terms. Why is this? Even though their variables are the same, their exponents are not the same. Yes, for them to be like terms, both the variables and the exponents must match.

If you saw a group of terms together, you would be able to identify like terms by looking at the variables and exponents of each term. This is the first step of collecting like terms on one side of an equation. Say, for example, we are trying to simplify the equation 4*x* + 5 + 3*x* - 2 = 0. If you see a problem asking you to simplify, remember that what it wants is for you to collect like terms together. To do this, we need to first identify which terms are like terms. What I recommend doing is to highlight the various like terms with different colors. I begin by highlighting the 4*x*. I continue reading my equation to see if there are other terms that are like 4*x*. I see a 3*x* with the same variable and exponent. That means that 3*x* is a like term to 4*x*. They both share the same last name of *x*. I keep reading the equation to see if there are more. Nope, that's it. Now I choose a different color highlighter, and I highlight the 5. I keep reading the equation to see if there are more terms that are like 5. Since I've already highlighted some terms, I can concentrate on reading only those terms that haven't been highlighted. Notice how I've included the negative. That negative tells me that the 2 is negative. It's very important to keep the right signs for the next step. I can go on to the next step now that I've highlighted all the terms on the one side of the equation.

The next step is to combine these like terms. So I look at my first highlight, and I notice that is a blue color. So I look for all the terms that are also highlighted in blue. I see, in addition to my 4*x*, a 3*x*. Combining these involves adding the number part together. So 4*x* + 3*x* = 7*x*. Now I need to add the rest. My next color highlight is purple. I see a 5 and a -2. Combining these I get 5 - 2 = 3. Do you see how important the negative sign is here? If we didn't pay attention to it and added the 2 instead of subtracting, our answer would be wrong.

Now that I've added all my like terms, I now need to write these in place of my like terms in my equation. To help me do this, I can rewrite my beginning equation so that the like terms are grouped together. So 4*x* + 5 + 3*x* - 2 = 0 becomes 4*x* + 3*x* + 5 - 2 = 0. I can replace the 4*x* + 3*x* with the 7*x*, and I can replace the 5 - 2 with a 3. So now my simplified equation is 7*x* + 3 = 0, and I am done collecting like terms.

Let's go over another example. Say the problem wants us to collect like terms for the equation 5*x*^2 + 8*x*^2 + 4*x*^2 + 1 = 0. How do we begin? We begin by first highlighting the 5*x*^2 using one color, say yellow. I continue reading the equation to see if there are other like terms to 5*x*^2. I see an 8*x*^2 and a 4*x*^2, so I highlight those the same color, yellow. Now I choose a different color, say pink, and I highlight the 1. I look at my equation and see that I've highlighted all my terms, so now I can go ahead and combine my like terms. Looking at my highlights, I see I have a group of 5*x*^2, 8*x*^2, and 4*x*^2 and I have a group of 1. The group of 1 is already combined, so I can leave that alone. Combining the group of 5*x*^2, 8*x*^2, and 4*x*^2 gives me 17*x*^2. Rewriting my equation with my combined like terms I get 17*x*^2 + 1 = 0, and I am done.

What have we learned? We've learned that **like terms** are terms that share the same variable and exponent. Terms can be a single number, a variable, or a combination of numbers and variables multiplied with each other. To identify like terms, we compare to see if the variable and exponent part of a term is identical to that of another term. To combine them, we add up the number part of each like term. To finish simplifying our equation, we rewrite the equation with our combined like terms in place of the individual terms.

Study this video lesson's information and prepare to:

- Characterize like terms
- Remember to use different colors to highlight like terms
- Combine like terms to simplify an equation

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
14 in chapter 8 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Algebra Terms Flashcards
- Go to High School Algebra: Algebraic Expressions and Equations

- Computer Science 336: Network Forensics
- Computer Science 220: Fundamentals of Routing and Switching
- Global Competency Fundamentals & Applications
- Introduction to the Principles of Project Management
- Praxis Elementary Education: Reading & Language Arts - Applied CKT (7902): Study Guide & Practice
- Intro to Approaches to Psychology
- Psychology, Physiology & Genetics
- Network Encryption Overview
- Networking Basics
- Traffic Analysis in Network Forensics
- TASC Test Score Information
- What is the TASC Test?
- Praxis Prep Product Comparison
- GED Prep Product Comparison
- CBEST/CSET Prep Product Comparison
- ASVAB Prep Product Comparison
- GACE Prep Product Comparison

- How to Write a Number in Standard Form
- Strategies for Teaching ELL Students
- Student Grouping Strategies for Reading Instruction
- What Is a Basal Reading Program?
- Financescapes: Definition & Impact on Global Cultural Flow
- Global Competence: Taking Action Domain
- Practical Application: Accounting Disciplines Infographic
- Using the Logical Volume Manager (LVM) in Linux
- Quiz & Worksheet - Pyemotes Herfsi Bite Care
- Quiz & Worksheet - Comparing Wild & Domestic Animals
- Quiz & Worksheet - 8 Blessings from Sermon on the Mount
- Quiz & Worksheet - John Kotter's Management & Leadership Theory
- Quiz & Worksheet - Text Structure Identification
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- CLEP Spanish Language - Levels 1 & 2: Study Guide & Test Prep
- Where the Red Fern Grows Study Guide
- College Composition Syllabus Resource & Lesson Plans
- Biology 104: Bioethics
- Arts Flashcards
- American Imperialism: Tutoring Solution
- Human Geography - Nonrenewable Resources: Help and Review
- Quiz & Worksheet - Types of Performance Appraisals
- Quiz & Worksheet - Graphical, Algebraic & Numerical Symmetry About the Origin
- Quiz & Worksheet - Murdock's Theories on Family & Culture
- Quiz & Worksheet - Geometric Probability
- Quiz & Worksheet - Dominant Ideologies

- What is Propaganda? - Definition, Techniques, Types & Examples
- Phytosterols: Definition, Function & Impact on Health
- Wisconsin Science Standards for First Grade
- Books for Guided Reading
- Colorado State Math Standards
- Pros & Cons of Homeschooling
- Fourth Grade South Carolina Science Standards
- Homeschooling in Texas
- 5th Grade Florida Science Standards
- What is the TExES PPR Exam?
- Positive Behavior Support Conferences
- Animal Farm Lesson Plan

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject