Algebra II : Expressions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #71 : Expressions

Simply: 

Possible Answers:

Correct answer:

Explanation:

In this form, the exponents are multiplied: .

In multiplication problems, the exponents are added.

In division problems, the exponents are subtracted.

It is important to know the difference.

Example Question #4662 : Algebra 1

Find the product: 

Possible Answers:

Correct answer:

Explanation:

 times  gives us , while  times 4 gives us . So it equals .

Example Question #4663 : Algebra 1

Distribute:

Possible Answers:

Correct answer:

Explanation:

Be sure to distribute the  along with its coefficient.

Example Question #1 : How To Add Trinomials

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

With this problem, you need to take the trinomials out of parentheses and combine like terms. Since the two trinomials are being added together, you can remove the parentheses without needing to change any signs:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms:

Example Question #1 : How To Add Trinomials

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative , those two terms will cancel out:

 

Example Question #2 : How To Multiply Trinomials

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

When multiplying these two trinomials, you'll need to use a modified form of FOIL, by which every term in the first trinomial gets multiplied by every term in the second trinomial. One way to do this is to use the grid method.

You can also solve it piece by piece the way it is set up. First, multiply each of the three terms in the first trinomail by . Second, multiply each of those three terms again, this time by . Finally multiply the three terms again by .

Finally, you can combine like terms after this multiplication to get your final simplified answer:

Example Question #4871 : Algebra 1

Evaluate the following to its simplest form:

Possible Answers:

None of the available answers

Correct answer:

Explanation:

First we will foil the first function before distributing.

We will then distribute out the

We will then distribute out the

Now the only like terms we have are  and , so our final answer is:

Example Question #72 : Expressions

Simplify the expression:

Possible Answers:

Correct answer:

Explanation:

 distributes to , multiplying to become , and  distributes to , multiplying to make .

Example Question #123 : Basic Single Variable Algebra

Divide the fractions.

Possible Answers:

Correct answer:

Explanation:

Dividing fractions is equal to multiplying by the reciprocal.

Cross-cancel the 30 with the 25, and the 22 with the 11.

Combine via multiplication and simplify.

Example Question #32 : Simplifying Expressions

Simplify the following expression.

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Distribute the outside term into the parentheses.

Simplify each distributed factor into one expression.

 

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