Sunday, September 18, 2011

The F Word

I know it's early in the year, but we need to have a discussion about some of the language that's been thrown around the room so far--in particular, the F word.  You know which one I'm talking about...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 first, outer, inner, and last 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?


Dedicated to Terry Wyberg and FAMTA.