Combining Like Terms

Pic of Twins
Image Source:

People who are twins are a “Like Pair” because they have the exact same features.

An Algebra Equation we can write for this is :

T + T = 2T

Eg. One Twin + One Twin = 2 Twins.

In Algebra, when there are items that are the same thing, we can add them together to make a simpler expression.

Algebra Like Terms One
Image Copyright 2012 by Passy’s World


Introductory Videos About Like Terms

The following is a video taken of a PowerPoint presentation and has no sound, but does a great job of introducing the concept of “like terms”


Here is how a typical Like Terms Algebra problem is done:


Definition of Like Terms

“Like Terms” are terms that contain the same letter Variables raised to the exact same Powers.

( Only the first number “Coefficients” of the like terms are different).

3a and 2a are like terms because although they have different coefficient numbers, they have the exact same letter “a” in them.

The letters and powers in the items are always identical whenever we have “Like Terms”.

Algebra Like Terms Two
Image Copyright 2012 by Passy’s World

It is extremely important that the Exponent Index power values are identical on each letter.

If they are not identical, then we do not have Algebraic Like Terms.

Algebra Like Terms Four
Image Copyright 2012 by Passy’s World


Identifying Like Terms

It is important to fully examine each term very carefully.

Just like two cars might be nearly identical, we need to examine the two cars fully to notice that they are not exactly the same.

Algebra Like Terms Five
Image Copyright 2012 by Passy’s World

Here are some examples where you need to decide if the given items are “Like Terms”.

Algebra Like Terms Six
Image Copyright 2012 by Passy’s World

Here are the answers to the previous examples.

Algebra Like Terms Seven
Image Copyright 2012 by Passy’s World


Why We Combine Like Terms

Often in real life it is necessary to combine like items together to create a shorter list of items we can deal with.

For example, imagine that a mathematics class is on an excursion and need to order a take away food lunch.

It would be crazy to read out each individual order, one after each other, at the counter of the fast food restaurant.

Instead we would total up how many burgers, how many fries, how many drinks, etc that we needed for the whole group.

This type of summarizing process is exactly the same as combining like terms.

The following video might get really annoying after a while, but it definitely shows why we need to group items together into separate sub totals of each type when doing mathematics.


How to Combine Like Terms

We can add together items that are the same to make a simplified shorter list of items.

This is called “combining like terms” or “collecting like terms”.

Consider the following family take away order:

Two burgers, one fries, one drink, three more burgers, two more fries, and two more drinks.

This order needs to have the like items grouped together to make a shorter summarised list.

Algebra Like Terms Eight
Image Copyright 2012 by Passy’s World


Subtracting Like Terms

We can also subtract Like Terms.

The following Example shows how we do this.

Algebra Like Terms Ten
Image Copyright 2012 by Passy’s World

WARNING: Like Terms are only used for Adding and Subtracting terms.

We never use combining like terms for Multiplying and Dividing !

Multiplying and Dividing use a totally different method, and they must not be done using the grouping Like Terms method.

Algebra Like Terms Eleven
Image Copyright 2012 by Passy’s World


Videos About Combining Like Terms

This video is about Combining Like Terms with Professor Perez and Charlie (7 mins 30 secs long), but well worth watching.


If you are not getting the idea of like terms yet, then watching this coloured shapes video should help.


Video Examples for Like Terms Questions

This video shows how to identify like terms, and also how to combine them to make simplified answers.


The following video shows how to do several simplifying like terms questions.


Steps for Combining Like Terms

The steps for combining like terms are as follows.

Algebra Like Terms Nine
Image Copyright 2012 by Passy’s World


Like Terms Examples

The following examples show how to do some typical Like Terms simplification questions.

Algebra Like Terms Example 1
Image Copyright 2012 by Passy’s World


Algebra Like Terms Example 2
Image Copyright 2012 by Passy’s World


Algebra Like Terms Example 3
Image Copyright 2012 by Passy’s World


Algebra Like Terms Example 4
Image Copyright 2012 by Passy’s World


Algebra Like Terms Example 5
Image Copyright 2012 by Passy’s World


Matching Like Terms Game

Algebra Like Terms Game Two

In this game check what the “Target” value is, and then click on all squares that are Like Terms as fast as you can.

In the screen print above, the Target is a number, and so we need to click on all squares that contain ordinary numbers in them with no letters present.


Like Terms Invaders Game

Like Terms Game One

In this game you need to shoot at aliens that have the same term as on your bottom of screen shooter.

However, you also need to keep using the mouse to move and dodge Alien rockets firing at you.

Use the left button on the mouse to shoot.

Click the link below to play this fun game.


Combining Like Terms Millionaire Game

Algebra Like Terms Game Three

Click the link below to go to this game, and then click the “Play Game” box.


Like Terms Online Quiz

Click the link below to go to an Online Quiz on Like Terms.

Under each question, click on the blank line and a box will appear where you can type in your answer.

At the end of the quiz, you can click the “How did I do Charlie” button to check your answers.

For more great lessons, videos and quizzes on Algebra, check out the “Algebra2go” website at this link:


Related Items

Algebra Expressions
Algebra Terms Coefficients variables and Constants.
Algebra Substitution Using Positive Numbers.
Algebra Substitution Using Negative Numbers.
Basic Powers Exponents and Indices.
Substitution Using Powers Exponents and Indices.
Real World Algebra Formulas
Survivor Algebra – Class Activity

If you enjoyed this post, why not get a free subscription to our website.
You can then receive notifications of new pages directly to your email address.

Go to the subscribe area on the right hand sidebar, fill in your email address and then click the “Subscribe” button.

To find out exactly how free subscription works, click the following link:

How Free Subscription Works

If you would like to submit an idea for an article, or be a guest writer on our blog, then please email us at the hotmail address shown below.

Free Gift Header

If you are a subscriber to Passy’s World of Mathematics, and would like to receive a free PowerPoint version of this lesson valued at $4.99, but 100% free to you as a Subscriber, then email us at the following address:

Email address image

Please state in your email that you wish to obtain the free subscriber copy of the “Like Terms” PowerPoint.

Feel free to link to any of our Lessons, share them on social networking sites, or use them on Learning Management Systems in Schools.


Like Us on Facebook

Our Facebook page has many additional items which are not posted to this website.

These include items of mathematical interest, funny math pictures and cartoons, as well as occassional glimpses into the personal life of “Passy”.

Check it out at the following link:

While you are there, LIKE the page so you can receive our FB updates to your Facebook News Feed.


Help Passy’s World Grow

Each day Passy’s World provides hundreds of people with mathematics lessons free of charge.

Help us to maintain this free service and keep it growing.

Donate any amount from $2 upwards through PayPal by clicking the PayPal image below. Thank you!

PayPal does accept Credit Cards, but you will have to supply an email address and password so that PayPal can create a PayPal account for you to process the transaction through. There will be no processing fee charged to you by this action, as PayPal deducts a fee from your donation before it reaches Passy’s World.



This entry was posted in Algebra and tagged , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.