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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:

Do you know how to use the distributive property?  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:

​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:

​First, pretend the 5 isn't there and distribute the x.

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Next, distribute the second term.

Last, combine like terms to get the simplified answer.

​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:

Step 1: Multiply the "Firsts"

Step 2: Multiply the "Outsides"

Step 3: Multiply the "Insides"

Step 4: Multiply the 'Lasts"

Step 5: Combine like terms to get the simplified answer.

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

Distribute the x first (Multiply the "Firsts" and the "Outsides")

Then distribute the -3 (Multiply the "Insides" and the "Lasts")

Last, combine like terms.

​Practice

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