### All Algebra 1 Resources

## Example Questions

### Example Question #2 : How To Multiply Trinomials

**Evaluate the following:**

**Possible Answers:**

**Correct answer:**

In the problem above, we are given two trinomials that we need to multiply together. To solve this problem, we need to use the distributive property to multiply each term in the first set of parentheses to each term in the second set of parentheses. We will perform 9 multiplication steps total.

Let's start with the first term in the first set of parentheses, . We will multiply this term by all three terms in the second set of parentheses, as follows:

**remember, when you multiply together two of the same variable, you add together the value of their exponents**

and

Now, we will go through the same process for the second term in the first set of parentheses, :

and

and

Finally, we'll go through the same process for the last term of the first set of parentheses, :

and

and

Now, we add together all of the values we got in our mulitplication steps:

Finally, we combine like terms to get our simplified answer:

### Example Question #3 : How To Multiply Trinomials

Multiply:

**Possible Answers:**

**Correct answer:**

Multiply each term of the first trinomial throughout the second trinomial and add all the terms together.

Combine like terms. The and terms will cancel upon addition.

The answer is:

### Example Question #31 : Variables

Multiply:

**Possible Answers:**

**Correct answer:**

In order to solve, we will need to multiply each term of the first trinomial with all the terms of the second trinomial. Sum all the terms together.

Add all of the terms and combine like terms.

The answer is:

### Example Question #32 : Variables

Multiply:

**Possible Answers:**

**Correct answer:**

Multiply each term of the first trinomial with the terms of the second trinomial.

Combine like-terms.

The answer is:

### Example Question #2 : Simplifying Polynomials

Subtract the expressions below.

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

Since we are only adding and subtracting (there is no multiplication or division), we can remove the parentheses.

Regroup the expression so that like variables are together. Remember to carry positive and negative signs.

For all fractional terms, find the least common multiple in order to add and subtract the fractions.

Combine like terms and simplify.

### Example Question #1 : Simplifying Polynomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

First distribute the :

Then distribute the :

Finally combine like terms:

### Example Question #1 : How To Add Trinomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

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 #2 : How To Add Trinomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

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 #3 : How To Add Trinomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

To add these two trinomials, you will first begin by combining like terms. You have two terms with , two terms with , and two terms with no variable. For the two fractions with , you can immediately add because they have common denominators:

### Example Question #53 : Algebra

Add:

**Possible Answers:**

**Correct answer:**

To add trinomials, identify and group together the like-terms: . Next, factor out what is common between the like-terms:. Finally, add what is left inside the parentheses to obtain the final answer of .