# How do you say FOIL in other languages?August 23, 2010 3:25 AM   Subscribe

How do people explain the FOIL rule of algebra in other languages?

The FOIL rule says if you multiply binomials (A + B)(C + D) you get the First (AC) plus the Outside (AD) plus the Inside (BC) plus the Last (BD) to get AC + AD + BC + BD

So the letters, F, O, I, L spell a word. What's that word in other languages?
posted by twoleftfeet to Writing & Language (31 answers total) 10 users marked this as a favorite

In Spanish, it's PEIÚ (Primero, Externo, Interno, Último)
posted by Ms. Next at 3:35 AM on August 23, 2010 [1 favorite]

I had to look op the FOIL rule to understand what you were exactly talking about. I never learnt to multiply binomials with a mnemonic, so speaking for Dutch, there is no equivalent word as far as I know.

Wikipedia, however, mentions the Spanish Método PEIÚ.
posted by lioness at 3:40 AM on August 23, 2010

lioness, I agree, I don't think there's a Dutch equivalent either.
posted by Ms. Next at 3:43 AM on August 23, 2010

I was told this in my all-English-speaking Midwestern U.S. college algebra class, so take it with a heaping pile of salt: some countries use a "box method" instead of FOIL. They set it up so A+B are the columns and C+D are the rows. Multiply each row by each column, then add across the diagonals. (Explanation works better with a visual, but I'm not sure I can do it justice with ascii art.)
posted by asciident at 3:58 AM on August 23, 2010

Does PEIÚ mean anything as a word in Spanish?
posted by twoleftfeet at 4:04 AM on August 23, 2010

Bablefish doesn't give me any English words when I translate it. Which I know doesn't necessarily mean anything worthwhile. I would imagine that it's like using Mimal to remember that line of states from Minnesota to Louisiana. Not a word, but close enough to work for it's purpose.

When you get down to it FOIL is just a way to remember that you need to multiply A by both C and D and B by both C and D. FOIL gives you a specific order to do that in so there's a smaller chance you forget one of them.
posted by theichibun at 4:10 AM on August 23, 2010 [1 favorite]

Does PEIÚ mean anything as a word in Spanish?

No, it's not an acronym, just an initialism.
posted by asciident at 4:11 AM on August 23, 2010

In Dutch there is the "papegaaienbek" (parrot's beak), which is a visual memetic.
posted by HFSH at 4:49 AM on August 23, 2010 [2 favorites]

I have always taught it as the monkey face. First and Last form the eyes on top, Inner and Outer form the bottom of the head and mouth on the bottom. Parenthesis, carefully drawn, are big ears. I never even heard of FOIL until another faculty member showed it to me.
posted by monkeymadness at 4:54 AM on August 23, 2010

Mnemonic, even.
posted by HFSH at 4:55 AM on August 23, 2010

You know, I never "got" foil, so in 9th grade I taught myself an equivalent: long multiplication.
(ax + b) * (cx + d) =
```       ax  +  b
×      cx  +  d
----------------
acx2   cbx
----------------
acx2  +  (ad + cd)x + db```
and then a few years later, I did an ad hoc proof that they are, in fact, exactly equivalent. FYI, the long multiplication approach, while slower than FOIL generalizes perfectly for polynomials of any degree, whereas FOIL only works for binomials.
posted by plinth at 5:28 AM on August 23, 2010 [3 favorites]

I didn't learn this FOIL acronym, but I don't think it matters that it is a 'real' word, anyway.

For example, I remember a primary school mathematics teacher who had my whole class chanting BOMDAS! BOMDAS! BOMDAS!, and this wasn't even Hogwart's. That's not a word in English, but I certainly won't forget it.

(Order of operations: brackets, other-brackets, multiplication, division, addition, subtraction.)
posted by rokusan at 5:46 AM on August 23, 2010 [2 favorites]

I don't remember learning any mnemonic like this in French schools, but it was a long time ago.
posted by mareli at 5:49 AM on August 23, 2010

I was thinking that there would be some play in the language, so people would have found other mnemonic words in other languages.

In English, this rule could have easily been called the FAIL rule (substituting Aparts for Outiside, say). Of course, calling it the FAIL rule might have negative pedagogical consequences, but the point is that you usually have some play like this in any language.
posted by twoleftfeet at 6:00 AM on August 23, 2010

I don't remeber learning any kind of nmemonic for expanding Binomials. And I was schooled in Australia in English obviously. never heard of FOIL.

I think we were taught initially to expand it into A (C+D) + B(C+D) then multiply those out.. then eventually you just skip that step.
posted by mary8nne at 6:03 AM on August 23, 2010

For several years, I've been tutoring math at a local community college in the US. The tutoring center there frowns on teaching students "FOIL", in part because it doesn't work for expressions larger than binomials. Instead, we just focus on "multiply every term of the first expression, by every term of the second expression". Which works out as being the same as the above examples of "long multiplication" and "box method".
posted by browse at 6:56 AM on August 23, 2010 [4 favorites]

To ask how people explain the FOIL rule in other languages presumes that this is a universal, or a widely used rule used in other parts of the world to explain or teach this concept. I don't know what part of the English-speaking world you're in, but are you sure that it's widespread even in the English-speaking world, or even in the specific English speaking country you are in? I went to school in the US, and never heard of it.

I just can't imagine that this FOIL technique that would be that common around the world, because frankly, it's pretty limited in scope and ineffective as far as learning algebra is concerned. It just creates a mnemonic that students memorize. Think about it -- students are taught FOIL, instead of understanding what and why they are doing. So if they are given (a + b)(c + d+ e), or any other variation thereof, they are totally lost because FOIL doesn't teach you this. Instead of FOIL, I was taught -- multiply each of the variables with each of the other variables. This is extremely simple and logical, and makes total sense. Because it makes total sense, you don't have to lean on a mnemonic to memorize it, AND, because you understand what's going on, you can then solve (A + B)(C + D +E) or any other variation thereof.

Mnemonic devises and other tricks work when you have to memorize a list of things, words, etc., that don't make sense ("My Very Elegant Mother Just Sat on Nine Pizzas" to memorize the order of planets, for example). But in this case, there's a very simple, elegant explanation that works much better.
posted by peachy at 7:02 AM on August 23, 2010 [4 favorites]

some countries use a "box method" instead of FOIL.

I went to school in the UK and this is how I did it.
posted by I_pity_the_fool at 7:06 AM on August 23, 2010

I don't understand the need for the mnemonic at all. It's just each term times each of the other terms, one time. Works for any number of terms. Or what browse said I guess.
posted by unSane at 7:07 AM on August 23, 2010

twoleftfeet: In English, this rule could have easily been called the FAIL rule (substituting Aparts for Outiside, say). Of course, calling it the FAIL rule might have negative pedagogical consequences, but the point is that you usually have some play like this in any language.

As an aside that doesn't directly answer your question: in English, you could also use LO-FI, FILO, LIFO, or any other combination of those letters - the actual order doesn't matter. As theichibun mentioned, the FOIL "rule" is not a rule at all, just a mnemonic to help you remember to hit all the combinations.
posted by dilettanti at 8:19 AM on August 23, 2010

Where'd they teach you this, twoleftfeet? (Or maybe, when?) Never heard of it before... browse and peachy point out what I'd consider the correct, scalable way to taech this calculation.
posted by Rash at 8:24 AM on August 23, 2010

Wow, I came in here to day pretty much what peachy and browse said. This FOIL mnemonic seems more complicated than the actual rationale which really just is multiply every term in the first bracket with every term in the second. This extends easily to more complicated cases with several terms in each bracket or several brackets in a row such as (a+b)*(c+d+e)*(f+g). Going to school in India we were taught this as the distributive law for multiplication.
posted by peacheater at 8:39 AM on August 23, 2010 [1 favorite]

I learned FOIL in 9th grade, 1990, in a private school north of Boston, MA. I'm pretty sure it fucked my math skills up for life.
posted by fairytale of los angeles at 8:40 AM on August 23, 2010 [1 favorite]

Never heard of it in Greece either, schools just teach the distributive property.

It's the wrong way to go about algebra anyway: You want to teach how to follow simple general rules to do complex stuff, not mnemonics that only apply in specific cases.
posted by Dr Dracator at 9:15 AM on August 23, 2010 [1 favorite]

I can't remember learning FOIL. The only mnemonic I remember is the PEMA rule for order of operations (Parentheses, Exponents, Multiplication, Addition).
posted by bgrebs at 9:52 AM on August 23, 2010

Thirding that it is bad pedagogy that only works for one special case and was probably made up by an education major that had a tenuous grasp of the mathematics in the first place.
posted by MonkeySaltedNuts at 10:25 AM on August 23, 2010

Huh. Nothing like this here in Argentina, as far as I know. We just deal with distributivity, nobody has died from it. ;-)
posted by Iosephus at 10:26 AM on August 23, 2010

I was specifically taught to avoid the FOIL rule in Junior High and to use the method peachy described. (Brooklyn, 1998.)
posted by griphus at 10:27 AM on August 23, 2010

peachy and others are explaining the box method, essentially; the visual box just helps to sort out each piece so that they don't get lost. It works with any polynomials, not just binomials. I use it to work through non-trivial polynomials because I'm a visual learner.
posted by asciident at 8:01 PM on August 23, 2010

I learned it (at least the first time) in fourth grade, 1994 or 1995. (In one of the better public school systems in Alabama, FWIW.) It never made much sense to me, so I generalized it myself to "everything in the first times everything in the second". I had a tougher time with factoring. I still can't remember the quadratic equation.

And I learned order of operations as "Please Excuse My Dear Aunt Sally" (paren, exp, mult, div, add, subt).
posted by supercres at 9:09 PM on August 23, 2010

FWIW, I was taught FOIL in Michigan, 1996 or so, but it doesn't seem to have had any great adverse effect on my math ability...
posted by FlyingMonkey at 4:39 PM on September 18, 2010

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