Operations - ISEE Upper Level Quantitative Reasoning

Combine like terms:

Combine like terms:

The first step in simplifying this expression is to get the binomial out of the parentheses. It's important to note you cannot further simplify this binomial first, since there are no like terms in it.

Since you have a minus sign in front of the binomial, you need to flip the sign of both terms inside the parentheses to get rid of the parentheses (similar to distributing a negative one across the binomial):

Now you are able to combine like terms, making sure that exponents on the variables match exactly before you combine. The first and fourth terms are like terms, and the second and third terms are like terms.

To combine those terms, keep the variables and exponents the same and add up the coefficients. The first term has a coefficient of and the fourth term has a coefficient of , so they add up to a total of . The second term has a coefficient of and the third term has a coefficient of , so they add up to a total of .

This brings you to the final, simplified answer:

First, rewrite the problem so that like terms are next to each other.

Next, evaluate the terms in parentheses.

Rewrite the expression in simplest form.

First we rewrite the problem so that like terms are together.

Next we can place like terms in parentheses and evaluate the parentheses.

Now we rewrite the equation in simplest form.

To simplify this expression, you need to combine like terms.

There are two terms with , one term with , and two terms without a variable.

This gives you the final answer:

Remember that when you subtract by a negative number, you are actually adding the inverse - thereby adding a positive number.

In this problem, you need to combine like terms. Be very careful when combining like terms, since a few terms differ only by a few exponents. You have two terms with , two terms with , and one term with .

This leads to the final answer:

On Gina's swim team, 40 percent of the swimmers also play one other sport competitively. Given that there are 20 people on her swim team, 8 people play one other sport because 40 percent of 20 is 8.

If 2 swimmers run cross country that leaves 6 swimmers who play a different sport.

Given that twice as many play soccer as those who play baseball, it follows that 4 play soccer and 2 play baseball.

Thus, 4 is the correct answer.

The sum of two supplementary angles is always 180 degrees; therefore:

Simplify the following expression:

We can solve this question in one step.

We need to add some variables, but we need to recall that we can only add variables with the same exponent. Thus, we can only add the $b^7$'s.

With this in mind, simply add the coefficients and keep the rest the same.

So our answer is

Simplify the following expression.

When adding variables, we can only add those with the same exponent. The others must remain unchanged.

That means that in this problem, we can only add the blue terms.

Because these terms are the only ones with the same exponents.

So, to add them, keep the exponents the same and add the coefficients (the numbers out in front).

Now, just rewrite it in standard form and you have our answer

When adding variables, we will look at the variables like objects.

So, in the problem

we can think of the variable b as books. So,

We can read it like this: We borrowed 3 books from the library yesterday. We go back to the library and borrow 5 more books. How many books have we borrowed altogether? We have borrowed 8 books. So,

We add variables the same way.

Simplify the following:

To combine the given expression, we need to realize that we can only combine terms with the same exponent.

In this case, all our terms have the same exponents, so we can add them up just like we would any integer.

To add up our terms, simply add up the coefficients and keep the exponent the same. (With this in mind we could eliminate any answer choices which do not have an exponent of two)

So, do the following:

\

So, we have our answer of 60 x squared

Simplify the following:

We can only add variables with the same exponents.

In this case, we have two "x to the sixth" terms.

So, we treat the first x to the sixth as

Then, we add it to

In order to simplify this expression, we will need to add like terms.

There is a lone positive three.

Combine all the terms.

The answer is:

Never divide fractions! Simply flip the fraction that follows the division symbol, and then multiply it by the first fraction. So this expression becomes:

$\frac{1}{3}$times $\frac{9}{1}$=\frac{9}{3}$=3