Can you add?
How about subtract?
Is multiplying a piece of cake?
Does division come easy to you?
Then you're ready to simplify algebraic expressions.

At first glance, these expressions seem extremely complicated but theyre actually pretty simple. And you can make them even simpler. I'm going to show you how.

If I gave you the following expression and asked you to simplify it, what would you do?

3 + 6 - 15 x 2 + 45

First you would multiply 15 times 2. This will give you a product of 30. The you would add 3 and 6 to get 9. Then you would subtract 30 and get a difference of -21. Then you would add 45 and get a sum of 24.

Next, you need to find the product of 2 and 3 which is 6.

The final step is to divide 24 by 6 which gives you a quotient of 4.

Now you try it: You can check your answers below.

1) 4 - 6 + 8 x 4

2) 6 x 8 + 13 - 6 x 7

3) 4 + 8 x 3 ÷ 6
10 x2

The same process works for algebraic expressions. The only thing that you need to do is be able to recognize parts of the expression that have the same characteristics.

Let's start will a simple expression.

x + x + x + x + x + x = 6x

As you can see, you just count the number of x's that are in the expression.

Let's try another.

y + y + y + b + b

This time there are two different variables. You need to add the variables separately. First start with the y's.
There are three so the first part of the expression is 3y.

Next you add the b's. There are two so the second part of the expression is 2b.

You need to write the final expression as 3y + 2b.

What if you start with an expression that has variables with coefficients other than one? (Remember, the coefficient is the number in front of the variable.)

3a + 6b + 2a + 5b

This can be rewritten as a + a + a + b + b + b + b + b + b + a + a + b + b + b + b + b
You need to count the number of a's. There are five so the first part of the expression should be 5a.
You do the same with the b's. There are eleven so the second part of the expression should be 11b.
Together, the final answer is 5a + 11b.

What happens if you need to subtract?

For example:
4s + 6t + s - 3t
Again, this can be rewritten as s + s + s + s + t + t + t + t + t + t + s - t -t -t
Starting with the s's you get 5s. Next, if you look at the t's you start with six and you need to subtract three. The second part of the expression is 3t. Together the final answer is 5s + 3t.

This is not complete, I need your help. Please edit this page with any knowledge you have on this topic in your words, not someone elses.

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Here are some websites that you can visit to see other explanations.

D7. Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified;
e.g., 4m=m + m + m + m or a · 5 + 4= 5a + 4.