What Is the FOIL Method in Math? A Kid-Friendly Guide

Quick question: What’s (x + 2)(x + 3)?

If you’re thinking, “Wait, how do I even start?”—you’re in the right place! 

Multiplying binomials doesn’t have to be confusing or intimidating. In fact, with the FOIL method, it can actually be kind of fun (yes, fun!).

Whether you're just starting to learn about multiplying binomials, preparing for an important exam, or looking to get ahead in math, this guide is here to save the day.

Read on for clear definitions, step-by-step instructions, solved examples, and practice exercises to help you learn and master the FOIL method!

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What Does the FOIL Method Mean?

When multiplying two binomials, keeping track of each step can feel overwhelming. That’s where the FOIL method comes in! 

FOIL is a mnemonic (a memory trick) that helps us remember the correct order to multiply terms in two binomials—expressions with two terms, like (x + 2) or (y - 3). 

We’ve used helpful memory tricks in math before—just like PEMDAS for the order of operations! Remember?

Each letter in FOIL stands for a specific step in multiplying binomials:

• F – First (Multiply the first terms in each binomial)

• O – Outside (Multiply the outer terms)

• I – Inside (Multiply the inner terms)

• L – Last (Multiply the last terms)

Let’s break it down with a visual to make it even clearer!

How Do We Use the FOIL Method? (Solved Examples)

Now that we know how the FOIL method should be used, let’s see it in action with a few examples!

Example 1

We can start off with a simple example and demonstrate how FOIL works step by step.

We’ll multiply:

(x + 2)(x + 3)

Using the FOIL method, we multiply the terms in the correct order:

1. First: Multiply the first terms in each binomial.

x × x = x²

2. Outside: Multiply the outer terms.

x × 3 = 3x

3. Inside: Multiply the inner terms.

2 × x = 2x

4. Last: Multiply the last terms in each binomial.

2 × 3 = 6

Now, we combine all the terms:

x² + 3x + 2x + 6

Notice that 3x and 2x are like terms. We can combine them to simplify:

3x + 2x = 5x

So, now we have:

x² + 5x + 6

And that’s our final answer.

Using the FOIL method, we found:

(x+2)(x+3) = x² + 5x + 6

Example 2

Let’s try multiplying a binomial with a negative term.

(3x - 4)(x + 5)

Using the FOIL method, we multiply the terms in order:

1. First: Multiply the first terms in each binomial.

3x × x = 3x²

2. Outside: Multiply the outer terms.

3x × 5 = 15x

3. Inside: Multiply the inner terms.

-4 × x = -4x

4. Last: Multiply the last terms in each binomial.

-4 × 5 = -20

Now, we combine all the terms:

3x² + 15x - 4x - 20

Combine the like terms:

15x - 4x = 11x

So, our final expression is:

3x² + 11x - 20

Using the FOIL method, we found:

(3x - 4)(x + 5) = 3x² + 11x - 20

Example 3

Now, let’s try a slightly more challenging example where we have two different variables, x and y.

(2x + y)(3x + 4y)

We apply the FOIL method step by step:

1. First: Multiply the first terms in each binomial.

2x × 3x = 6x²

2. Outside: Multiply the outer terms.

2x × 4y = 8xy

3. Inside: Multiply the inner terms: 

y × 3x = 3xy

4. Last: Multiply the last terms in each binomial: 

y × 4y = 4y²

Now, we write the expression with all the terms:

6x² + 8xy + 3xy + 4y²

Next, we combine like terms:

8xy + 3xy = 11xy

Now, we have:

6x² + 11xy + 4y²

And that’s our final answer!

Using the FOIL method, we found:

(2x + y)(3x + 4y) = 6x² + 11xy + 4y²

Test Your Skills – FOIL Practice Exercises

Now that you've seen how the FOIL method works, it’s time to put your skills to the test!

When you’re finished, check your answers at the bottom of the guide.

Multiply the following binomials:

1. (x + 4)(x + 6)

2. (2x - 3)(x - 5)

3. (x + 3)(y - 5)

4. (x + 2y)(x - 3y)

Frequently Asked Questions About the FOIL Method

At Mathnasium of West Chester, we help students of all skill levels learn and master topics such as multiplying binomials. Here are the common questions we receive about the FOIL method:

1. Can I use FOIL for any multiplication problem?

No, FOIL only works for multiplying two binomials (expressions with two terms).

2. What happens if there are negative numbers in the binomials?

When multiplying with negatives, we pay close attention to the signs:

• A negative × positive gives a negative result.

• A negative × negative gives a positive result.

3. Does the order in FOIL matter?

Yes and no. As long as you multiply every term in the first binomial by every term in the second, you’ll get the correct answer. However, FOIL gives you a structured way to do it without missing any steps.

4. Can I use FOIL to multiply more than two binomials?

No, FOIL only works for two binomials. If you need to multiply three or more binomials, multiply the first two using FOIL, then multiply the result by the third binomial using distribution.

Master the FOIL Method at Mathnasium of West Chester

Mathnasium of West Chester is a math-only learning center for K-12 students in West Chester, OH.

Using a proprietary teaching approach called the Mathnasium Method™, our specially trained math tutors offer face-to-face instruction in an engaging and supportive environment to help students master any math class and topic, including the FOIL method. 

Students begin their Mathnasium enrollment with a diagnostic assessment that allows us to understand their specific strengths and knowledge gaps. Guided by assessment-based insights, we create personalized learning plans that will put them on the best path toward math mastery. 

Whether your student is looking to catch up, keep up, or get ahead in their math class, schedule an assessment, and enroll at Mathnasium of West Chester today! 

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Pssst! Check Your Answers Here

If you’ve given our exercises a try, check your answers below:

1. x² + 10x + 24

2. 2x² - 13x + 15

3. xy - 5x + 3y - 15

4. x² - xy - 6y²