# Combining Like Terms

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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.

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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”.

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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.

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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.

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

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Here are the answers to the previous examples.

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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.

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Subtracting Like Terms

We can also subtract Like Terms.

The following Example shows how we do this.

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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.

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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.

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Like Terms Examples

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

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Matching Like Terms Game

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.

http://themathgames.com/our-games/like-terms-games/play-matching-action/

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

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

http://www.quia.com/rr/195128.html

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:

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