Why do we need a mnemonic or a meme for this? Is understanding distribution really that much harder than memorizing FOIL?
At the same time, understanding distribution is so much more powerful because it generalizes to many other uses and later concepts.
I think FOIL sticks around primarily because it is what people are taught. Even when people actually do understand distribution, they may not realize that FOIL is just a special case of distributing.
Is it harder to understand distribution than memorize FOIL? Probably. It's memorizing a process vs. understanding a concept. FOILing won't help you master algebra but if you're in a science class and your teacher needs to get you up to speed on multiplying pairs of binomials then they'll likely just show you FOIL.
I agree with you that FOILing is stupid and might make the student worse off in the long run, but I think depriving them of getting practive with heuristics might be worse. Ideally a student would notice that FOIL isn't a good trick and stop using it, but there are other "tricks" that are extremely useful.
If you're using FOIL to replace the distributive property then you're doing it wrong. It's simply a bookkeeping device, like the little ditties that people have to "memorize" the names of the planets or the Great Lakes.
At the same time, understanding distribution is so much more powerful because it generalizes to many other uses and later concepts.
I think FOIL sticks around primarily because it is what people are taught. Even when people actually do understand distribution, they may not realize that FOIL is just a special case of distributing.