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How to Simplify a Multiplication Expression

How to Simplify a Multiplication Expression
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  • 0:01 A Multiplication Expression
  • 0:49 Simplifying
  • 1:54 Example 1
  • 3:13 Example 2
  • 5:22 Lesson Summary
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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.

In this video lesson, you will learn how to simplify a multiplication expression that has both numbers and variables in it. Learn what you need to watch for and how to write your simplified expression.

A Multiplication Expression

Look at this math problem: simplify 3x * 4x * 2. This is what we call a multiplication expression, a mathematical expression with multiplication. As you can see, all we have going on is multiplication.

You will see these kinds of problems in your math lessons and tests. These kinds of problems also test your problem solving skills. So, by learning how to solve these kinds of problems, not only will you become a better mathematician, but you will also be a better problem solver. As you can see, we have both numbers and variables. How do we combine the two?

Simplifying

Because we are multiplying, everything sort of comes together. Our numbers combine into one number and our like variables all merge together. Let's see how this is done. First, we can multiply all our numbers together. We get 3 * 4 * 2 = 12 * 2 = 24. Now we can merge our variables together. We have only xs to worry about. To merge these variables, we count how many xs we have. We have two of them. So, to merge our xs, we write x, and then we write a little superscript 2 to tell us that our x is to the second power, which also means that we're multiplying two xs together. Our simplified expression becomes this:

multiplication expression

Let's look at a couple more examples.

Example 1

Simplify 12x * 3y * y.

In this problem, we see we have numbers, xs and ys. So this tells us that we need to combine our numbers together, our xs together and our ys together. Combining our numbers together, we get 12 * 3 = 36. We only have one x, so we can go ahead and write an x. We have two ys, so we write a y to the second power to let us know that we have two ys that we are multiplying together. Our simplified form becomes this:

multiplication expression

There is a proper way of writing our simplified form. This proper way involves writing our variables in alphabetical order. As you can see, I've written my x first, followed by the y. Our number always comes first. This is the standard form. Your answers should always be in this form even if the problem gives you the variables in random order.

Example 2

Let's look at one more example. Simplify f * 4a * 2b * a * a * 3b.

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