Combining Like Termsand

Solving Equations

A quick lesson in simple Algebra

Combining Like Terms

In Algebra, there is no better way to make your life easier than to learn how to simplify problems by combining like terms.

Ok, well, maybe not that easy. But just think, by combining like terms, you make problems shorter and simpler.

Ming Xia, “Easy Cheese” October 8, 2005 via Flickr, Creative Commons Attribution, Share Alike.

Which would you rather have

This problem:

Or, this one:

546273 xaaxaaa

842 aax

Which would you rather have

This problem:

Or, this one:

Believe it or not, they are the same problem, but I sure would rather deal with the second one.

546273 xaaxaaa

842 aax

So, what is a like term?

Like terms are terms that have the same variables in the same form or an equivalent form.

Blah, blah, blah. The people who write math books are too smart for their own good.

This just means that in like terms, the variable parts match.

Powerhouse Museum Collection, “Man [Eric Sheldon?] eating banana and reading sheet music” uploaded September 1, 2009 via Flickr, Public Domain.

On to an example

Simplify by adding like terms:

Our first step will always be to rewrite the problem with the variables in alphabetical order.

546273 xaaxaaa

546273 axaxaaa

Identify like terms

Now, starting with the first term, go through and put a circle around all of the terms that match it.

Notice how I included the sign in front of each term. This will be important later.

Now, do the next term with a different shape.

Identify and combine like terms

Etc. etc. until all terms are “identified”.

Now, I can put my shapes together. I’ll start with my red circles.

A 1st Grade review: “put together” means what?

Combine like terms

Then, do the same thing with your other shapes.

Now I can rearrange my pieces to get my answer.

842 aax

Combining Like Terms Part 2

Putting Apples with Apples and Oranges with Oranges

User “Fir0002”, “Sundown and cross section” January 22, 2009 via Wikimedia Commons, GNU Free Documentation License 1.2.

User “Neutrality”, “Citrus sinensis” December 11, 2005 via Wikimedia Commons, Public Domain.

Simplify by Adding Like Terms

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Look at that mess. Wow!! Remember, we want to “simplify” to make your

life easier! First we want to move the letters around so

that they are in the same order in each term.

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Now that the variables in our terms are all in order, let’s do something that may seem strange.

In case you don’t like the circles and squares from before, let’s do it differently.

Let’s say that every is an apple, and every is an orange. Makes sense since we are comparing apples and oranges.

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So, now we will get a different looking problem.

Now, what does that give me?

Now just put the nasty looking stuff back in for our apples and oranges.

2 3 10

5

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Solving Equations!!!