# Algebra 1 : How to multiply trinomials

## Example Questions

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### Example Question #2 : Simplifying Polynomials

Multiply:

Explanation:

Set up this problem vertically like you would a normal multiplication problem without variables. Then, multiply the  term to each term in the trinomial. Next, multiply the term to each term in the trinomial (keep in mind your placeholder!).

Then combine the two, which yields:

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

Multiply the expressions:

Explanation:

You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern

,

where  and .

To find , you use the formula for perfect squares:

,

where  and .

Substituting above, the final answer is .

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

Evaluate the following:

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 #10 : Simplifying And Expanding Quadratics

Evaluate the following:

Explanation:

When multiplying this trinomial by this binomial, you'll need to use a modified form of FOIL, by which every term in the binomial gets multiplied by every term in the 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 trinomail by . Then multiply each of those three terms again, this time by .

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

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

Multiply:

Explanation:

Solving this is just like using FOIL on binomials, except we have nine calculations to perform instead of four (since that's the result of a 3x3 combination!):

First, calculate the combinations of the first term on the left:

Next, calculate the combinations of the middle term on the left:

Next, calculate the combinations of the third term on the left:

Lastly, combine the terms with compatible variables and exponents:

### Example Question #4 : How To Multiply Trinomials

Multiply:

Explanation:

To solve this problem, first FOIL the binomial.

FOIL stands for the multiplication between the first terms, outer terms, inner terms, and then the last terms.

Now, distribute the trinomials. Start with the first term on the left:

Now the middle term on the left:

Now, the third term on the left:

Combine all compatible terms:

### Example Question #5 : How To Multiply Trinomials

Multiply:

Explanation:

The easy way to perform this calculation (without using Pascal's Triangle) is to find , then square that trinomial.

So, our problem becomes

Start by distributing the first term on the left:

Now distribute the second term on the left:

Now distribute the third term on the left:

Now, combine the compatible terms:

### Example Question #6 : How To Multiply Trinomials

Expand and simplify the expression:

Explanation:

We are asked to expand and simplify the expression: .

This question is going to require knowledge of exponent rules and FOIL methods.

The first step is to create an inverse reciprocal of a negative exponent.

Now, we can expand the expression by removing the exponent in the denominator.

Use the FOIL method to first multiply and .

You'll find it creates . Replace it back into the expression because we have to multiply the result by one more time.

Be careful with exponents and coefficients!

Combine like terms to find the simplified answer.

### Example Question #7 : How To Multiply Trinomials

Evaluate the following:

Explanation:

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:

Multiply: