Operations - SSAT Middle Level: Quantitative

Combine like terms and by subtracting their coefficients; do not combine either with the 7.

You can only add like terms. Therefore, different variables are treated as different types of terms. Since and both end in the variable , they can be added together. The cannot be added to these numbers; however, because it has a different variable. The answer is:

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are and . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power.

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

Our last term is not like because the variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term.

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Now we have

Add the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer:

The associative property of addition allows us to group the numbers with the same variables together:

The like terms in this expression are:

• and
• 
• 

Terms with different variables cannot be grouped together.

As a result, the only way to simplify this expression is to add and .

First, group together your like variables:

The only like variables needing to be combined are the x-variables. You can do this in steps or all at once:

First, move the like terms to be next to each other:

Now, combine the x-variables and the y-variables:

Let's begin by moving the like terms toward each other. Notice the following: zy is the same as yz. (Recall the commutative property of multiplication.)

Now, all you have to do is combine the x-variables and the yz-terms:

Notice that you do not end up with any exponent changes. That would only happen if you multiplied those variables.

Remember, when you have exponents like this, you will treat each exponented variable as though it were its own "type." Likewise, pairs of variables are to be grouped together. Therefore, group the problem as follows:

Notice that the only thing to be combined are the terms.

Therefore, your answer will be:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

Then, all you need to do is to combine the terms:

Remember, for exponent problems, you group together different exponents and different combinations of variables as though each were a different type of variable. Therefore, you can group your problem as follows:

Now, just combine like terms:

You should begin by distributing through the whole group that it precedes:

Now, move your like variables next to each other:

Finally, combine the like terms:

Begin by distributing the to its entire group:

Next, group the like terms:

Finally, combine the like terms:

Begin by distributing the through the parentheses:

Next, move the like terms next to each other. Remember, treat like it is its own, separate variable.

Finally, combine like terms:

Combine like terms:

Combine like terms: