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Multiplying Binomials
(the FOIL Method)

Accompanying Resources: Printable Study Guide, Speed Dating Group Activity, Boom Cards (digital task cards)
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The Distributive Property

We use the distributive property often in math. You may have used it before.  Here's what the property says:
The distributive property - katesmathlessons.com

Do you remember how to use the distributive property?  (If this is brand new to you, make sure to check out the Distributive Property Lesson.)  You simply take what's on the outside of the parentheses and "distribute" it to each term on the inside using multiplication.  If there are more than two terms inside the parentheses, you just have to make sure to distribute to each one.  Here are a few examples of the distributive property:
Distributive property examples


​Multiplying Binomials

In the examples above, there was only one term on the outside of the parentheses: an 8, a 2x and a -3.  When you multiply two binomials, the only difference is that there will be two terms out front instead of one (remember, binomial means 2​ terms).

To simplify this type of problem, you just need to distribute twice.  Distribute the first term, then distribute the second term. Let's look at an example:
Multiplying binomials using the distributive property and FOIL.

​First, pretend the 5 isn't there and distribute the x.
How to multiply polynomials using the distributive property.
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Teachers,make sure to check out the study guides and activities.
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Next, distribute the second term.
Using the distributive property to multiply binomials.

Last, combine like terms to get the simplified answer.
Using the distributive property to multiply binomials.


​The FOIL Method

When you multiply two binomials together, you're just using the distributive property twice.  This is often called the "FOIL" method.  FOIL stands for Firsts, Outsides, Insides, Lasts.  It's the same exact process that was described earlier, it's just a handy little acronym that some teachers use to help students remember the process.  Let's look at an example:
Multiply two binomials using FOIL.

Step 1: Multiply the "Firsts"
How to use FOIL to multiply binomials.

Step 2: Multiply the "Outsides"
How to use FOIL - katesmathlessons.com

Step 3: Multiply the "Insides"
What does FOIL mean? katesmathlessons.com

Step 4: Multiply the 'Lasts"
What is the FOIL method in math? katesmathlessons.com

Step 5: Combine like terms to get the simplified answer.
What does FOIL stand for in math? katesmathlessons.com

You can call the process distributing twice, or you can call it FOIL.  In the problem above if you distribute the x first you get the "F" and "O" terms. Then if you distribute the 1 next you get the "I" and "L" terms.  It doesn't matter what you call the process, you get the same exact answer. 

Additional Example

Multiplying two binomials practice.

Distribute the x first (Multiply the "Firsts" and the "Outsides")
How do you use FOIL? katesmathlessons.com

Then distribute the -3 (Multiply the "Insides" and the "Lasts")
Using the FOIL method in math - katesmathlessons.com

Last, combine like terms.
How to use the FOIL method in math - katesmathlessons.com


​Practice

Ready to try a few problems on your own? Click the START button to try a practice quiz.

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Want to try one of my digital math activities for free?  Click the link to grab the teacher version or student version.

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