FOIL is Stupid and Silly

[@WrathofMath]

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[@silverknight784]

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[@xadielplasencia3674]

Why is foil even mentioned???? Isnt "each by each" way faster to understand and way more generaly aplicable????

[@NStripleseven]

Way harder to forget a term if there’s a different name for each

[@TheKastellan]

linear polynomials with the same variable. As in (mx + c)(nx +d), when you FOIL it becomes (mn)x^2 + (dm)x + (cn)x + cd. Which we then simplify to (mn)x^2 + (dm + cn)x + cd. At leazt for me this is the only time I was told to FOIL. Idk what education is elsewhere but otherwise you were told to do each-by-each. NEVER seen someone use foil in a scenario that wasnt the factorisation of that form. (By the way x could be something like y^2 so it isnt strictly linear polynomials but that scenario is EFFECTIVELY the same and has the same upsides)

[@TheKastellan]

I realise I didnt make it clear but FOIL orders the products in the way you want them to. While each by each usually adds a step of finding where the like terms are and reording stuff in order of powers of x/y/etc.

[@ENDI8089]

​@@TheKastellanno you just do each by each the order in which you do doesn't matter

[@Beheldtothesun]

​@@TheKastellan does that really matter? either way you end up with the same products. you really only have to remember the signs and stuff like exponents and roots etc

[@MathHunter]

FOIL(FS)(FT)(SF)(SS)(ST)(SL)(TF)(TS)(TT)(TL)(LS)(LT) very memorable (and easily pronounceable)

[@WrathofMath]

Yup! For anyone who didn't learn this in school, the S stands for 'second' and T for 'third. Happy FOIL(FS)(FT)(SF)(SS)(ST)(SL)(TF)(TS)(TT)(TL)(LS)(LT)ing!

[@eyesicecold]

@@WrathofMath And if you can remember that, you should move on to LOIRSTF(LS)(LT)(LF)(SL)(ST)(SF)(SR)(TL)(TS)(TF)(TR)(FL)(FS)(FT)(FR)(RS)(RT)(RF) for 5-nomials! (Left Outside Inside Right Second Third Fourth (LeftSecond)(LeftThird)(LeftFourth)(SecondLeft)(SecondThird)(SecondFourth)(SecondRight)(ThirdLeft)(ThirdSecond)(ThirdFourth)(ThirdRight)(FourthLeft)(FourthSecond)(FourthThird)(FourthRight)(RightSecond)(RightThird)(RightFourth)) I had to paste this into google docs, Use find and replace recursively, and then paste it back, and it still took 20 minutes 😂

[@roundhouse2616]

My younger sister was taught FOIL (in australia) and struggled with expanding polynomials bc it's so easy to literally just forget what FOIL means and what it wants you to do. She was never really taught what it actually means to expand polynomials, only how to follow a weird and confusing set of instructions. Teaching FOIL is the opposite of teaching math

[@WrathofMath]

Sorry to hear FOIL got her :(

[@jffrysith4365]

it always confused me why people use foil. just learn the distributive property and it instantly follows...

[@asagiai4965]

Isn't FOIL a distrubutative property with name

[@jffrysith4365]

@@asagiai4965 pretty much, except the distributive property is the general form. The distributive property states that a(b + c) = ab + ac. Therefore you take (a + b)(c + d) = (a + b)c + (a + b)d = ac + bc + ad + bd. But, if you want to be pendantic, you can also generalise it for: (a + b + c)(d + e + f) = (a + b + c)((d + e) + f) = (a + b + c)(d + e) + (a + b + c)f = (a + b + c)d + (a + b + c)e + ((a + b) + c)f = ((a + b) + c)d + ((a + b) + c)e + (a + b)f + cf = (a + b)d + cd + (a + b)e + ce + af + bf + cf = ad + bd + cd + ae + be + ce + af + bf + cf. Or you could use general distributive property like: (a + b + c)(d + e + f) = ad +ae + af + bd + be + bf + cd + ce + cf...

[@Beheldtothesun]

​@@asagiai4965 it literally is. its just the distributive property with extra (unnecessary) steps. it helps better to learn "multiply each term with each of the other" because thats literally it TwT

[@asagiai4965]

@Beheldtothesun yes do each by each is correct, but the reason foil exist (despite being similar) is probably because it helps you think Which part of each by each are you now. In other words it helps you remember which two terms you are multiplying. So I think knowing each by each is much better. But knowing foil is not bad also

[@Beheldtothesun]

@asagiai4965 not necessarily. say if im to do (a + b + c) (d + e + f) i can just write it out as d(a + b +c) + e(a + b + c) + f(a + b + c) if i need it to be more clear even so, its not necessary to do that if you just mark under each term (like just underline the term or circle it or something) you're done with multiplying and it does the exact same thing edit: spelling error

[@LividE101]

FOIL seems like a solution to a problem created not by mathematical/academic value but by curriculum structure. The problems being asked are "how do you solve this binomial multiplication problem", and we get FOIL to solve the exact problem being asked as quickly as possible while trading away the actual purpose (learn polynomial multiplication, I'd hope). Further, if you do enough binomial multiplication, you'll probably do it in that order anyway just because it's intuitive. I fear students may be learning a rote procedure *instead* of internalizing the method properly which is potentially worse than watching paint dry in the time it takes to teach the FOIL method.

[@Nikoline_The_Great]

Odd. I never learned anything like FOIL in my school. What we learned was that you can distribute a number across terms in a parenthesy and that you can treat an entire parenthesy as a unit. So when it came to multiplying two parentheses, we just distributed one of the parentheses across the terms of the other and then distributed the terms of the other over the terms of the first.

[@WrathofMath]

Yeah, that seems pretty reasonable to me! No silly single-case rules, just a general principle!

[@davidbailis8415]

It’s parenthesis

[@livedandletdie]

@@davidbailis8415 it's parentheses. British Spelling.

[@R.F.9847]

@@livedandletdie It's not American vs British. It's singular vs plural. One parenthesis, a pair of parentheses.

[@michaelpark]

@@livedandletdie I think @davidbailis8415's comment was referring to @Nikoline_The_Great's "parenthesy". Neither US nor British, just wrong :D

[@torfley]

I clicked on this video thinking it was a video about why foils like aluminium foil are stupid, like a video by technology connections

[@WrathofMath]

Well I'll bet you were disappointed

[@rjelstyx4909]

I never know FOIL until I begin teaching new high school students 😂 They asked me if I used foil method to expand, I was confused

[@WrathofMath]

😂 When I was in college and helping a math teacher out in her 8th grade class, she wanted me to help the kids as they worked on long division, at which point I realized I never learned long division the way most Americans do. Felt like a real dumbo!

[@ryanoftinellb]

A similar seemingly-useless mnemonic I’d never heard of before coming to the internet was LIATE, for integration by parts.

[@WrathofMath]

I've seen that too actually, it never stuck because I only ever saw it in passing and have no idea what it stands for

[@Asiago9]

I'm pretty sure I was told that, but forgot about it almost immediately, and just went off of vibes for what I should try to integrate first, and I know BlackpenRedPen did a video on why that mnemonic is harmful

[@fezziegd]

@@WrathofMath logarithms, inverse functions, algebraic functions, trigonometric functions, exponential functions it's a mnemonic for figuring out which function to use as u for integration by parts except it kinda sucks

[@minerscale]

​@@Asiago9 the DI method though. Delicious. So quick to integrate a monster. Worth understanding where IBP comes from first though.

[@Asiago9]

@@minerscale I like the DI method for some integrations, and prefer ultra violet vdu for other integrations, I'm not sure why

[@LTG_Lanny]

Yeah… “foil” is mainly for the kids who just memorize the topic and never try to understand the concept.

[@maartendegroot98]

Now I wonder if a FOILer computes a(b+c) by doing (a+0)(b+c) when can once again bask in the light of the FOIling method.

[@user-on6uf6om7s]

The truly enlightened foiler first realizes a = (a + 0)(1 + 0) b = (b + 0)(1 + 0) c = (c + 0)(1 + 0) so a(b + c) = [(a + 0)(1 + 0)][(b + 0)(1 + 0)+(c + 0)(1 + 0)] which we can simplify to [(a + 0)(1 + 0) + (0 + 0)(0 + 0)][(b + 0)(1 + 0) + (c + 0)(1 + 0)] And then from there it's pretty straightforward, though if the student is still struggling with conceptualizing the value of 1 in this equation, it can be helpful to think of 1 as (1 + 0)(1 + 0) just to clean things up a little bit

[@theVtuberCh]

To be honest I had a major math break through when I worked out that long multiplication is simply a type of polynomial multiplication. (21)(43) = (2*10 + 1)(4*10 + 3)

[@WrathofMath]

Bro these comments are killing me

[@duccline]

​@@theVtuberCh WOAH THANKS

[@CommDao]

1:53 - that whole "spell" analogy I think is applicable to any kind of academic learning. You see it a lot with language learning too.

[@TonOfAshYT]

2:42 Me solving right angle trig with sine or cosine rule instead of SOH CAH TOA every single time

[@Battlekaik5]

I was taught FOIL in 8th and 9th grade. I refused to use it and I just used the box/table method.

[@WrathofMath]

You're a man of principle!

[@minerscale]

Wow, can't believe I've never thought of organising my polynomial expansion using a table. So much easier!!

[@googelman]

@@WrathofMath ive noticed foil is related to area models, for example, if we try to expand the expression (x-4)(x+6) using an area model we get +---+-------+ | x - 4 | +---+-------+ | x | x² - 4x | | + | | | 6 | 6x - 24| +---+-------+ normally, youd fill it from the top-left corner to the bottom right-corner. when you first start filling out the table, you multiply x and x, which are the first terms in each binomial. F then you multiply x and -4, which are the outer 2 terms of the binomials. O then you multiply x and 6, which are the inner 2 terms. I last, you multiply -4 and 6 which are the last 2 terms L

[@nathanisbored]

10:09 the acronymist in me cant help but notice dOOef aObOOc and wonder what it stands for

[@tomq6491]

any d00ef-us knows the alphabet starts with a0b00c?

[@philosolog]

Me, CS-brained: That's a nice data structure!

[@DrawThatRedstone]

this is fantastic, but i'm honestly distracted by how consistently thick your sharpies are. do you ever get duds that are thin?? these are all fantastically bold

[@WrathofMath]

The duds go in the bad box, and the good ones go in my good box - which are used for the videos!

[@Vearru]

I vaguely remember this being mentioned in school, but I barely paid any attention in math class and just did my own thing since I learn best when I see the material and then figure out why that is for myself. So I proved all these things on my own and found my own methods to do things. Teachers didn’t like that I didn’t show my work but I always got the right answer and never cheated so they kinda just had to deal with it.

[@kyolin3875]

Teaching at a secondary level, FOIL is the bane of my existence. Students often never connect what they are doing with the "visual" or think back to the area models.

[@kruksog]

My favorite "mathism" are what i like to call "math poems." Im sure youve heard one before. For example "the derivative of the sum is the sum of the derivatives... the limit of the product is the product of the limits..." etc. I dunno, your intro made me think of that.

[@TheFansOfFiction]

This isn't an axiom, but it is a poem you might appreciate. [(12 + 144 + 20) + 3sqrt(4)]/7 + 5*11 = 9^2 + 0 a dozen a gross and a score plus three times the square root of four divided by seven plus five times eleven is nine squared and not a bit more

[@minerscale]

My favourite is the product rule: left d'right plus right d'left And in close second the quotient rule: down d'up minus up d'down on down down

[@hazevthewolf178]

As to mnemonics, my personal wrath of math is aimed at PEMDAS. I think that most middle schoolers would grasp the concept of a field (using Q as an example). Having that, one could replace a division sign b with a *(1 / b) and proceed with the usual rules for multiplying and adding in a field. Once, long ago, when I was in university, I asked a couple of my non math major friends if they'd ever heard of the distributive law. That led to some teaching moments. Based on your presentation, I think I could write an inductive proof where I claim to prove (in the spirit of Euclid) that the Foil Method May Be Extended Indefinitely. I can't see any reason why anyone would want to do that. Interestingly enough, Euclid never said that he attempted to prove that there were infinitely many primes. He said that primes could be produced "indefinitely" which amounts to the same thing, but infinity itself was never on Euclid's menu.

[@lillyflower7834]

something that my 7th grade math teachers taught was instead of PEMDAS was GEMA standing for: Groupings (parentheses, fractions, so on), Exponents, Multiplication (and division since you can multiply by a reciprocal), and Addition (and subtraction since you can add a negative)

[@hazevthewolf178]

@@lillyflower7834 I think that you've made my point. Thank you!

[@isaiah0xA455]

What’s so interesting about Euclid’s word choice? The statements “there are infinitely many primes” and “primes can be produced indefinitely” are logically equivalent.

[@hazevthewolf178]

@@isaiah0xA455 That's what I said or, at least implied.

[@minerscale]

I bet there's some infinite sum you can calculate by recursively FOILing.

[@douglasmagowan2709]

I am generally against acronyms, memory tools, and memorization in general. Memorization becomes an impediment to understanding.

[@WrathofMath]

I am sympathetic to that perspective. I respect the utility of them though. Even so much as, in a classroom setting, completely committing to overusing a mnemonic can help the students remember just by having all these key moments in class that the phrase keys their brain into.

[@SomeInternetUser45]

Bro has never taken biology and chemistry

[@DemonessMari]

Learning should be about knowing when and how to use a tool correctly instead of trying to make students recall what the tools even are. Give them the tools and teach them to use them if you truly care about students learning and not just pointlessly memorizing.

[@DanksterPaws]

As much as I agree with you, it is a necessary evil. - Med Student

[@Nicoder6884]

@@SomeInternetUser45 Or history for that matter.

[@ZaySFH]

Im definitely using the table method from now on

[@filedotnix]

The "table method" was always called the "box method" in my education, and I'm its most arduent defender anytime someone brings up FOIL. It has the added benefit of making the 3blue1brown video on convolutions feel more satisfying.

[@MathsOwl2950]

I do not use FOIL, when i tutored maths, my students often struggle with understanding 2-bracket expansion, but they knew how to distribute a single value across brackets e.g. a * (b + c) = ab + bc. So when we did (a + b)(c + d) i would ask them to think of the first bracket (a + b) as a single value and expand brackets their usual way

[@pyp2205]

FOIL was one method that I remember being taught in school. But I never use it because it's pretty confusing in my opinion. One of my math teachers also taught the table method. Which is what I prefer to use, because it's easy to setup and use compared to FOIL. Even the math teacher who taught it prefers this method.

[@mstmar]

for multiplying big polys, i'll usually do something similar to the table method, but without drawing the table. you start with the 2 highest exponent terms, then see how you can combine a left and right term to get that exponent. drop an exponent and see what multiples to that exponent, adding all the terms that do. repeat for all exponents. this saves having to write all terms using the multiply each by each method as you get it in a simplified version right away

[@SarahTheAmbiguous]

My problem with FOIL as I encountered it in middle school was I was taught it was a universal way to multiply any polynomial which is untrue. Trying to extend FOIL to trinomials and such is a waste of time, box method is superior anyway. It's quick, easy, and you don't have to memorize a mnemonic. The diagonals being like terms is also really convenient

[@mrosskne]

When you learn foil, you're learning about binomial expressions. So you use a method for binomials. When you learn about expressions including more terms, then you can learn another method. The best method is the one that works for whatever specific application you're dealing with. Generality is not inherently desirable. No one who learns foil is ever going to use it to solve your example with the literals.

[@WrathofMath]

That's fair but it leaves many students confused when they encounter things beyond binomials because all they know is the FOIL magic trick; when if they had just learned that to multiply binomials they use the distributive property (which they already know), they wouldn't even need to be taught how to deal with bigger examples, they would just know how to apply properties of mathematics they've mastered before even to new situations.

[@mrosskne]

@WrathofMath Of course not. When they are introduced to a new concept, they're also introduced to a new method for handling the concept. Just like when you learn any new concept in math.

[@scottabroughton]

I’ve encountered many students who are confused by concepts more basic than expanding polynomials. When they get FOIL, it gives them a boost of confidence that they need to keep going. There’s plenty of time to teach them each by each or the grid method as they progress.

[@xanderlastname3281]

I dont think ive seen a single person expand (2+3)(4+5) using FOIL before

[@tdubmorris]

I really like to just think about it like a(c+d) + b(c+d) or for trinomial a(d+e+f) + b(d+e+f) + c(d+e+f)

[@spencerkatty]

While I typically just distribute accordingly, I actually really like the idea of the table method to understand and follow through with that distribution. You can even do it when it's not polynomials like you did, you just have to write the ENTIRE term in the column/row (ex. write ax^5 instead of just a). With that you also don't have to know which diagonal corresponds to which power of x.

[@DeJay7]

Grateful to have never been taught "first, outside, inside, last" 🙏

[@travcollier]

The "spells" thing is so true. Trying to avoid that mindset is why young kids these days are taught a lot of different methods (some rather cumbersome but illustrating a particular property) instead of just the single 'easiest' methods their parents were taught. And their parents too often freak out because they aren't just using the simple "spell" ETA: Honestly the table thing isn't bad. Of course it would be insane to use it routinely, but it is a decent illustration to teach why the distributive property is "each by each". What I've actually seen taught in grade school doesn't bother to separate the coefficients from the x's though... So it is a lot more compact.

[@CookieMage27]

Funnily enough I had never even used the term “foil” used before a week ago, I just always followed the multiplication to its logical conclusion, as I was homeschooled for most of my education and it seems to have, for the most part, been beneficial for my learning, I would never just learn a method to do it without thinking using rule such as “foil” ever like it was a spell, I would much rather truly learn the logic behind it creating a far better intuition for things like math as it serves much better for everything in life. There my essay is done(sry for rambling)

[@soupy5890]

I was thinking, it might just be easier, assuming distributing a product over a sum is introduced first, to just say "Hey, this left sum is also... just a term itself we can distribute. So we get a sum of these products, then we do normal distribution over each sum term, and just add them all together. It doesn't introduce any new ideas or require any new mnemonics, it just re-uses old ideas. Then, once students are able to compute expressions like that, maybe introduce some shortcuts to make it easier.

[@Jack-vm1kp]

I came up with the table method i think in freshman year of high school, right after learning of Punnet Squares in biology. I keep the xs in mine, tho i do recognize that the negative diagonals have the same powers of x. Neat to see im not the only one!

[@jackkalver4644]

Matrix products are particular and limited to 2 dimensions, but expression products exist for all finite grids of 1+dimensions.

[@TheFansOfFiction]

I guess my math textbooks were remiss because I missed this mnemonic in my education. Why do you even need a mnemonic to distribute the terms? Sure, it's easy to miss one, or several, but that's not because you didn't remember what to do, you just did it sloppily. There is no need for a pneumonic here. Now if there was one for _factoring_ a polynomial, I'd love that (there probably is. I clearly missed the chapter on mnemonics lol)

[@OldSoulClimber]

The only time a use a semi foil method is when multiplying arbitrary polynomials of arbitrary degree in a polynomial ring. It helps group terms with same degree. (Also for formal power series where an infinite table might be cumbersome)

[@ussgordoncaptain]

table method underrated, you'd be surprised how good it is at avoiding errors.

[@brianlane723]

4:33 I will say I do like how this applies iterative thinking, even if it's clunky as you illustrate.

[@alecjohnson9626]

I must have missed the day “foil” was explained because I was literally 27 years old when I learned it was an acronym haha. I just thought it was a weird bit of school math jargon and always felt that “unfoil” would have made more sense.

[@TimwiTerby]

In your list at the start I’m surprised you didn’t mention SOH-CAH-TOA. Is that not taught in the US? Also, I couldn’t make out the third one you listed; it sounded like TONCAS but I can’t find that by googling. If that’s a US equivalent of SOH-CAH-TOA, what does it stand for?

[@WrathofMath]

kzbin.info/www/bejne/fZvPg4F-atCJma8

[@TimwiTerby]

@@WrathofMath Thanks, although you may notice that TONCAS is not in the video title; in fact, the video title is completely useless and says nothing about the video.

[@WrathofMath]

The video is about a math acronym people haven't heard of, so I have no idea what you're on about with the title.

[@IznbranahlGoose]

I always like that table method. It works with any kind of multiplication even if you're doing something like converting 245×63 into (200+40+5)(60+3)

[@Asiago9]

I was taught that as the lattice method of multiplication in elementary school

[@angeldude101]

I think I tend to treat FOIL as a sort of "canonical ordering" when expending products of two binomials, and then extend that canonical ordering to more complex products, giving one less thing to think about. Said canonical ordering by the way does not match the given "mnemonics" for trinomial and qutranomial products. Rather, it's the first term on the left times everything in the right, plus the second term on the left times everything in the right, etc. Only after expanding each pair of terms do I collect like terms. Which stage I normalise the ordering of different variable factors depends on whether the product is commutative or not.

[@richardhole8429]

Look, if you don't like FOIL, do it whatever way that works for you. As long as you get the same result, go for it. To rail against it is nuts.

[@KingGisInDaHouse]

use the box method. works for every scenario.

[@txikitofandango]

"each by each" is also a reasonable definition of multiplication, since 3 x 4 = (111)(1111) = 1111 1111 1111 = 111 111 111 111

[@txikitofandango]

FOIL is fine, it's a concrete example of a general concept to be studied later. "Let's reexamine FOIL in a more general way..." can't be uttered until you've learned it

[@1234larry1]

Obviously, FOIL wouldn’t be used for anything but binomials. The broader term would be distribution.

[@OhhCrapGuy]

I think the better way to deal with polynomial multiplication is thus: Let N be the number of terms in the first, let M be the number of terms in the second. Draw a grid of size NxM Write the terms of the first polynomial along the top, above, of the grid, write the terms of second along the right, beside, the grid. For every cell in the grid, multiply the terms to the top and to the right outside the grid. Add up all the terms in the grid Done. a....b ac.bc.c ad.bd.d ac+bc+ad+bd

[@kyay10]

Foil technically does give you how to multiply any polynomial by any polynomial. Simply bracket the sum inside the polynomial so that there's only one main addition, then foil, remove the brackets, and repeat. It thus technically is all you need for any n-degree polynomial multiplication for example: (a+b+c)*(d+e) = (a+(b+c))*(d+e) = ad + ae + (b+c)*d + (b+c)*e = ad + ae + bd + cd + be + ce Edit: lol I commented before watching the full video! Glad this was addressed.

[@CarolynOsborne]

The "Pharoah of Phoil" Great video.

[@WrathofMath]

Thank you!

[@entityredstoneonyt]

The moment i learnt about variables, coefficients, terms, and polynomials, i immeadiately knew to multiply two binomials i just use the distributive property. I don't think you should just teach people foil and abstract it that way, you should let them know how the distributive property applies to polynomials and it might help with even multiplying trinomials or bigger polynomials.

[@bradx3827]

FOILM(FM)(MF)(ML)(LM) GOT ITS OWN FULL VIDEO!!

[@tomq6491]

This is symptomatic of a more general problem of reducing mathematics to a sequence of algorithms. I like asking kids "why did you do that?" and getting an answer like "because that is how you do it" or "it gives you the right answer" In fact I would go further than this and say that education in general is quite algorithmic. Even in English they will teach people numonic algorithms like PEE, write down your point, give a piece of supporting evidence, and then explain. This is great if you are writing a business report, not great for creative, entertaining, emotive, captivating writing.

[@etrisplayer6169]

honestly i would use an area model. SOOOO much less complicated sounding

[@krwada]

A generalization of multiplying any nxnomial by any mxnomial is to do a dot product of the two equations. You will always get the correct answer by doing this.

[@isaiah0xA455]

What exactly is a dot product of equations? For that matter, what are the two equations in question? A polynomial is an expression, not an equation.

[@fullfungo]

Don’t you mean a convolution? Dot product doesn’t seem to make sense here

[@krwada]

@@isaiah0xA455 A simple linear equation, the coefficients can be expressed as a vector or matrix. Taking the dot product of the coefficients is the same as what is shown in this video

[@isaiah0xA455]

@@krwada The dot product only multiplies like terms by like terms. It would leave out the “outside, inside” part of the FOIL algorithm. It doesn’t resemble the table multiplication at all.

[@dadmitri4259]

It reminds me of other "tricks" like this, which when taught instead of actual fundamental mechanics causes people to have a hard time with math. The neat tricks and shortcuts should come as a RESULT of the fundamental mechanics, not instead of them.

[@WrathofMath]

Very good point

[@Juttutin]

Is WLOG always just a summoning and invocation of the -demon- axiom of choice?

[@NinjaCat-lb3vv]

I love how sincerely you hate FOIL, not even for a meme. And those sarcastic jokes... Brilliant

[@WrathofMath]

one must let the hate flow through him

[@DriftinVr]

Foil is silly yes, but it is a good first method of learning expanding these things out, I was taught distribution to each, then the area method as a easier way to write out long ones, and foil for those smaller expands. Foil is helpful for teaching beginners just a quick method

[@ExzaktVid]

FOILM(FM)(MF)(ML)(LM)! So simple!

[@pikminman13]

Me, who has used the box method for over 12 years: (I call it box over table)

[@averagelightningenjoyer285]

Weird Al would beg to differ

[@SomeInternetUser45]

I agreed with the thing that foil is stupid in the sense that it hinders learning the actual concept of polynomial distribution. It is taught as a method for less mathematically inclined students to just be able to solve the problem without actually understand the concept. And that is ok to an extent because at least they are learning something. At my school we were taught both the formal method and foil as an emergency pneumonic in case we blank on a test. You have to think of your self in the shoes of a 8th or 9th harder just first learning algebra. It may seem so simple now but back then these things were very helpful. Eventually all students continuing through math will learn the concept of distribution and they go up into algebra 2, precalc, and calc. Would it be nice if schools always taught the proper wat? Yes, however they have to cater to the masses who may still struggle with fractions in 9th grade. Concepts like binomial expansion working upon this was dropped in us curriculums because they were “too hard” for them. Back to the video, your table method is even stupider than foil. At least foil is foolproof and quick for binomial x binomial which is the most common setup. The table method is slow and teaches even less about the concept of distribution. Also you spent a good chunk of your video distributing constants over other constants. Foil and distribution in general was never taught for this stupid application. Everyone would just add and multiply. What people have to realize is (a +b + c+…)(d+e+f+…) is the same as a((d+e+f+…)+b((d+e+f+…)+c((d+e+f+…)+…((d+e+f+…) In conclusion stupid video 2/10 two points for having a correct opinion on foil.

[@WrathofMath]

1. I respect the utility of FOIL and mnemonics in general. 2. I don't like the table method either. If you watched the video you might have heard me say 'that was nice and easy, we just had to make this giant fucking table', which was my way of saying 'I don't like this method either'. 3. Constants? Most of the video was done with letters which were never specified to be constants or variables. 4. *mnemonic In conclusion, stupid comment.

[@schoktra]

I like that table method, that would have been handy to know years ago xD

[@SomeInternetUser45]

No it wouldn’t have, it is very slow. Just distribute each term of the first polynomial to each term of the second polynomial. This guy is complaining about foil and proposes an even worse method.

[@WrathofMath]

I don't like the table method either, and I denigrate it in the video. But my role here is to hate on FOIL, so if someone prefers a different method I fully support that

[@kyolin3875]

@@WrathofMath Pedagogically, I think it's pretty good. Not necessarily as an efficient method, but to help students make connections before going into 'foiling'.

[@deleted-something]

I never learned foiled LFMAO, I knew what it was, but never that it was a pneumonic, I guess my brain thought something with literally “foiling?” A square or the expression or smth

[@noknownalias1353]

I’ve always been partial to the “ box method” which seems very similar to your tabular method, except instead of multiplying, just the coefficient you multiply with the coefficient and the given power of X (it actually works for any set of variables as well, such as trying to multiply (ax by) and (cx^2 fy^3) for example). This means you don’t have to include all the tedious zeros in your tubular method, but still allows the handling much larger polynomials. kzbin.infoYOUzwI6wX_s?si=HTofRxiFtpCF4HfM this is a good video demonstration of it.

[@TheRealSoftR]

Underrated video wtf

[@solipse.]

10:10 I use a method inspired by base 10 number column multiplication and omit the x to the power just like omitting 10 to the power in the column multiplication. So treating x as a “base” kinda

[@mjay_arts4]

WE'RE FOILS, WE DIDN'T SEE THIS THROUGH!

[@benjamingoldstein1111]

I never, ever heard of FOIL before.

[@WrathofMath]

I envy you!

[@jackkalver4644]

Mathematicians use FOIL for large numbers, broken into two parts. For instance, (z+a)(z+b)=zz+za+zb+ab=z(z+a+b)+ab

[@Playtonz]

I literally just figured out a formula on my own

[@pittdancer85]

Im sad you didn’t spend much time the fundamental algebra. Like why does FOIL work, and compare it to simple distribution.

[@LyleLylefr]

The box method is so much better

[@comp.lex4]

when all you have is a hammer, everything looks like a nail-- but that's not the hammer's fault! leave foil alone!!

[@WrathofMath]

i respect your sympathy for foil

[@Jaixex2]

the Box method wayyy better than foil

[@samueldeandrade8535]

HAHAHAHAHA. That's one of the reasons I am sibscribed to this channel. This guy is reasonable. Of course FOIL is useless.

[@foiledits]

rude but justified

[@Playtonz]

*Laughs in distributive property*

[@icedo1013]

Acting like people actually use FOIL for arithmetic equations is a little disingenuous if you ask me. You don't even learn the technique until algebra. It's fun to do in your head every so often just to remind yourself that it works every single time, but nobody is doing (2+3)(4+5) the FOIL way instead of 5*9 in any real formal setting.

[@Neko_Necromancer]

Hey, foil cards are cool, don't- oh, you mean the multiplication thing. Carry on

[@Blackmuhahah]

@7:38 yes

[@lalapreseraah6845]

1 hours gang?

[@therealmacaron]

it infuriates me how we’re not just taught to D I S T R I B U T E .

[@alisonhansel9202]

Hallelujah!

[@isobarkley]

once again HOW ARE YOUR SHARPIES SO VIVID

[@WrathofMath]

Really just a combo of good lighting and color correction

[@kingstonchow]

Wtf is foil? Is this why the westerner hates maths?

[@asagiai4965]

I think it is not a problem with FOIL but how we teach math. US is not the only place FOIL is commonly use.

[@jjpower6769]

Over & over & under & under.

[@dmace14]

Unless you chose to study maths further than you are required to, people who learn FOIL in school are only ever going to need to multiply binomials, not trininomials, and you only need common sense to know not to use it on (2+3)(4+5) because when you are taught FOIL you are taught it for when you CANT combine the terms in the brackets, such as (2x + 3) If you do study maths as your chosen subject, then you’re probably smart enough to know to disregard FOIL as you move into any polynomial multiplication more complicated than binomials

[@roshansimkhada9472]

Ok don't foil your self

[@writerightmathnation9481]

I think that if you accept any Mnemonics, FOIL isn’t a bad one compared to many others. If it’s presented carefully, the “FOIL Method” can actually help students remember how to use distributivity of multiplication over addition. Your concern about using this method to compute products of numbers that are written as sums also is, in my opinion, a bit overblown, especially with that clickbait thumbnail that suggests an incrimination towards those who teach using that particular Mnemonic. Consider the problem of multiplying two matrix binomials: (A+B)(C+D)=AC+AD+BC+BD. Did I use the “FOIL” mnemonic to do that? Yes, but I didn’t write it out. Writing the following would have been wrong, however: (A+B)(C+D)=CA+AD+CB+BD. Of course, if you know, you know, that matrix multiplication isn’t commutative. A problem with teaching binomial expansions using the “FOIL” mnemonic, teachers shouldn’t apply commutativity in a first step, only because not all students are going to never take linear algebra or matrix algebra, or some other form of Noncommutative algebra. The kind of example that you exhibited involves numerals that are small in value, so that certain useful mental arithmetic tools aren’t well illustrated, but that’s exactly one I’d the reasons the “FOIL” mnemonic is taught. To review that scenario (with small numbers again but not the same), we see that a more detailed illustration would be the following “proof” that a product of 7 with 8 is 56: (5+2)(5+3)=(5+2)(5)+(5+2)(3)=(5)(5)+(2)(5)+(5)(3)+(2)(3)=25+10+15+6=35+15+6=56. Now, if you teach a second grader to do arithmetic this way on certain problems, they learn how the properties of arithmetic work for the step by step justifications. Then during a parent teacher conference you’ll be accosted by parents who already can multiply pairs of one digit numbers whose product odd a two digit result, but their second grader isn’t there yet. Why would you be accosted (verbally)? Well, when the child did their homework, they asked for help from a parent who isn’t equipped to explain the steps or how the distributive law applies in this case. If someone knows how to justify each step above, then they can also justify some useful things about products of larger numbers. For instance, consider the problem of multiplying 435 by 263: (435)(263)=(400+35)(203+60) =(400)(203+60)+(35)(203+60) =(400)(203)+(400)(60)+(35)(203)+(35)(60) =(4)(10^2)(200+3)+24(10^3)+(35)(200+3)+(30+5)(60) =(4)(10^2)(200)+(4)(10^2)(3)+24(10^3)+(35)(200)+(35)(3)+(30)(60)+(5)(60) =(8)(10^2)(10^2)+(12)(10^2)+24(10^3)+(70)(10^2)+(30+5)(3)+(18)(100)+(30)(10) =24(10^3)+(8)(10^4)+(12)(10^2)+(7)(10^3)+90+15+(18)(10^2)+(3)(10^2) =8(10^4)+(24+7)(10^3)+(12+18+3)(10^2)+90+15 =11(10^4)+(1+3)(10^3)+3(10^2)+100+5 =114405. This is by far a not most efficient solution, and one would not use it to solve problems quickly, but to illustrate how the laws of arithmetic work so you can teach yourself some speed for mental arithmetic. Doing no problems in this much detail would make the mental math tricks look more like magic, and so a healthy mixture of methods is better. Here’s a way to use the “FOIL” method on the above problem instead: (435)(263)=(500-65)(200+63) =(500)(200)+(500)(63)-(65)(200)-(65)(63) =(5)(2)(10^4)+(5)(63)(10^2)-(130)(10^2)-(60+5)(70-7) =(10^5)+(315)(10^2)-(13)(10^3)-((60)(70)+(5)(70)-(60)(7)-35) =(10^5)+3(10^4)+(5)(10^2)-(13-1)(10^3)-((42)(10^2)+(35)(10)-(42)(10)-35) =(10^5)+3(10^4)-(13-1)(10^3)-(42-5)(10^2)+(42-35)(10)+35 =(10^5)+3(10^4)-12(10^3)-37(10^2)+(7+3)(10)+5 =(10^5)+(30-12)(10^3)-(37-1)(10^2)+5 =(10^5)+18(10^3)-36(10^2)+5 =(10^5)+(10^4)+(80-36)(10^2)+5 =(10^5)+(10^4)+(50-6)(10^2)+5 =114405. Needless to say there are much faster ways to compute this, but the “FOIL” Mnemonic can help one do all the above steps in one’s head, rather than writing it all on paper. Shortcuts are needed for students who participate in arithmetic competitions. Not knowing the “FOIL” method can in some cases cost a student precious time in such an enjoyable competition. Those who object to showing the above steps may in many cases be those who’d rather you just do a calculator problem instead. Of course, some computations are competitions, but some are not. Check the steps: (435)(263)-(400+35)(203+60)=0 (400+35)(203+60)-((400)(203+60)+(35)(203+60))=0 (400)(203)+(400)(60)+(35)(203)+(35)(60)-((4)(10^2)(200+3)+24(10^3)+(35)(200+3)+(30+5)(60))=0 =(4)(10^2)(200+3)+24(10^3)+(35)(200+3)+(30+5)(60)-((4)(10^2)(200)+(4)(10^2)(3)+24(10^3)+(35)(200)+(35)(3)+(30)(60)+(5)(60))=0 (4)(10^2)(200)+(4)(10^2)(3)+24(10^3)+(35)(200)+(35)(3)+(30)(60)+(5)(60)-((8)(10^2)(10^2)+(12)(10^2)+24(10^3)+(70)(10^2)+(30+5)(3)+(18)(100)+(30)(10))=0 (8)(10^2)(10^2)+(12)(10^2)+24(10^3)+(70)(10^2)+(30+5)(3)+(18)(100)+(30)(10)-(24(10^3)+(8)(10^4)+(12)(10^2)+(7)(10^3)+90+15+(18)(10^2)+(3)(10^2))=0 24(10^3)+(8)(10^4)+(12)(10^2)+(7)(10^3)+90+15+(18)(10^2)+(3)(10^2)-(8(10^4)+(24+7)(10^3)+(12+18+3)(10^2)+90+15)=0 8(10^4)+(24+7)(10^3)+(12+18+3)(10^2)+90+15-(8(10^4)+(30+1)(10^3)+(30+3)(10^2)+100+5)=0 8(10^4)+(24+7)(10^3)+(12+18+3)(10^2)+90+15-(11(10^4)+(1+3)(10^3)+3(10^2)+100+5)=0 11(10^4)+(1+3)(10^3)+3(10^2)+100+5-114405=0 +++++++* (500)(200)+(500)(63)-(65)(200)-(65)(63)-((5)(2)(10^4)+(5)(63)(10^2)-(130)(10^2)-(60+5)(70-7))=0 (5)(2)(10^4)+(5)(63)(10^2)-(130)(10^2)-(60+5)(70-7)-((10^5)+(315)(10^2)-(13)(10^3)-((60)(70)+(5)(70)-(60)(7)-35))=0 (10^5)+(315)(10^2)-(13)(10^3)-((60)(70)+(5)(70)-(60)(7)-35)-((10^5)+3(10^4)+(5)(10^2)-(13-1)(10^3)-((42)(10^2)+(35)(10)-(42)(10)-35))=0 (10^5)+3(10^4)+(5)(10^2)-(13-1)(10^3)-((42)(10^2)+(35)(10)-(42)(10)-35)-((10^5)+3(10^4)-(13-1)(10^3)-(42-5)(10^2)+(42-35)(10)+35)=0 (10^5)+3(10^4)-(13-1)(10^3)-(42-5)(10^2)+(42-35)(10)+35-((10^5)+3(10^4)-12(10^3)-37(10^2)+(7+3)(10)+5)=0 (10^5)+3(10^4)-12(10^3)-37(10^2)+(7+3)(10)+5-((10^5)+(30-12)(10^3)-(37-1)(10^2)+5)=0 (10^5)+(30-12)(10^3)-(37-1)(10^2)+5-((10^5)+18(10^3)-36(10^2)+5)=0 (10^5)+18(10^3)-36(10^2)+5-((10^5)+(10^4)+(80-36)(10^2)+5)=0 (10^5)+(10^4)+(80-36)(10^2)+5-((10^5)+(10^4)+(50-6)(10^2)+5)=0 …

[@R.F.9847]

These kids must not have very good teachers if they think (2+3) or (4+5) are binomials when they are in fact like terms.

[@AnshumanShrestha-re3bi]

i love ur channel, can i please get a shoutout someday mr. wrath of math?

[@biometrix_]

No

[@picardcook7569]

touch grass, it's a good mnemonic

[@mandolinic]

Have you considered the possibility that you might need to GET A LIFE?

[@andrebeck27]

average FOILer