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I use to wonder why there was an outside and inside part when doing FOIL. It was after that I saw the visual proof, and doing other types of multiplication wit
by iamwil 17y ago
I use to wonder why there was an outside and inside part when doing FOIL. It was after that I saw the visual proof, and doing other types of multiplication with multiple 'parts/terms', that it slowly dawned on me that there's cross-components. It's the same sort of thing when you multiple matricies or covariances. You need the contribution from every combination of terms.
- philwelch 17y agoYeah...I was in a program called Kumon and learned most of my math there, more than I learned in school. There was a lot of multiplying together polynomials, so I got used to the idea of handling each combination of terms. There was also a fair amount of factoring. Let me rephrase that: an unreasonable amount of factoring. Factoring down 4th and 5th and I think 6th degree polynomials by hand, for instance, in the equivalent of 10th grade algebra. By the way, there are analogous patterns between even degreed polynomials, 4th degree polynomials look kind of like quadratics and 6ths do as well, with a kind of rippling pattern in the intermediate terms. By the time anyone told me about FOIL, I just squinted and shrugged it off. I was so used to taking these polynomials apart that enumerating through all possible combinations was trivial to me. Incidentally, I always considered it more artful to factor quadratic equations to solve them rather than applying the quadratic formula.