Operations in Expressions

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Basic Math › Operations in Expressions

Questions 1 - 10
1

Solve:

Explanation

Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

We want to solve what's in the parentheses first.

Now, do the division and the multiplication.

Therefore our equation becomes:

Finally, subtract.

2

Factor the following expression:

Explanation

When you factor an expression, you are separating it into its basic parts. When you multiply those parts back together, you should obtain the original expression.

The first step when factoring an expression is to see if all of the terms have something in common. In this case, , , and all have an which can be taken out:

The next step is to focus on what's in the parentheses. To factor an expression of form , we want to try to find factors , where and . We therefore need to look at the factors of to see if we can find two that add to :

We've found our factors! We can therefore factor what's inside the parentheses, , as . If we remember the we factored out to begin with, our final completely factored answer is:

3

Solve:

Explanation

Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

We want to solve what's in the parentheses first.

Now, do the division and the multiplication.

Therefore our equation becomes:

Finally, subtract.

4

Factor the following expression:

Explanation

When you factor an expression, you are separating it into its basic parts. When you multiply those parts back together, you should obtain the original expression.

The first step when factoring an expression is to see if all of the terms have something in common. In this case, , , and all have an which can be taken out:

The next step is to focus on what's in the parentheses. To factor an expression of form , we want to try to find factors , where and . We therefore need to look at the factors of to see if we can find two that add to :

We've found our factors! We can therefore factor what's inside the parentheses, , as . If we remember the we factored out to begin with, our final completely factored answer is:

5

Factor

Explanation

To factor an equation in the form , where and , you must find factors of that add up to .

List the factors of 36 and add them together:

Since , is the factor we need. Plug this factor in to get the final answer.

6

Factor

Explanation

To factor an equation in the form , where and , you must find factors of that add up to .

List the factors of 36 and add them together:

Since , is the factor we need. Plug this factor in to get the final answer.

7

Which of the following is equivalent to ?

Explanation

Since all of the answer choices look like , let's find in .

Then,

When you have an exponent being raised to an exponent, multiply the exponents together.

8

Simplify the following expression:

Explanation

The correct answer is due to the law of exponents. When solving this type of problem, it is easiest to focus on like terms (i.e. terms containing x or terms containing y).

First we can start by simplifying the 'x' terms. We start with which is equivalent to . We then are left with .

Now we can simplify the 'y' terms as follows: .

Last, the 'z' terms can be simplified as follows: .

This leaves us with the final simplified answer of .

9

Simplify:

Explanation

When dividing terms with the same bases, remember to subtract the exponents.

Keep in mind that when there is a negative exponent in the numerator, putting that term in the denominator will make the exponent positive.

10

Which of the following is equivalent to ?

Explanation

Since all of the answer choices look like , let's find in .

Then,

When you have an exponent being raised to an exponent, multiply the exponents together.

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