**FOIL**.

Here's the thing, I know it helps you remember how to multiply two binomials together, like this:

But that's all it does, help you

*remember*. I'm starting to worry a little that we think FOIL is somehow its very own mathematical operation. It's not; it's just a handy way of keeping track of the four multiplications that you end up doing when you expand a two-binomial expression like the one above.When I was your age, Pluto hadn't been voted out of the solar system just yet, and so we learned a mnemonic device for remembering the planets from the sun outward: My Very Educated Mother Just Served Us Nine Pies (or Pizzas, depending on which teacher you had). Of course those aren't the actual planets of the solar system--no one is (we hope) searching for extraterrestrial life on Mother--they just make up a convenient memorization tool. FOIL is the same way. Really what we're using when we multiply two binomials is the

**Distributive Property**, and FOIL helps of make sure we're applying it correctly in this one particular case.First, we distribute the first x over the quantity (x-4), and then we distribute the 3 over that quantity, like this:

Then we have two separate distributive property problems that look a little more manageable, and we do those:

Finally, we can combine like terms (which, actually, we can only do in the first place because of the amazing power of the distributive property!):

And now we're done, having multiplied the

**f**irst,**o**uter,**i**nner, and**l**ast terms together. So that's it, I don't want to hear any more dirty words about applying the distributive property: no more F@#!, no more "smiley faces," no more "trick-or-treating." From now on, we use the distributive property, because it will never fail us. Besides, who wants to remember**FF/MOM/FMM/OIL/ML**when you have to expand something like this?Nobody.

Dedicated to Terry Wyberg and FAMTA.