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i never found foil stupid, but i also only have a bachelors in math. maybe this was because i had already been exposed to multiplying polynomial expressions, beyond just a 2 term * 2 term by the time i had learned it in school, but i never found it particularly complicated to grasp. foil was never taught to me as the only way to multiply polynomials, rather, an easy algorithm to apply in a certain case. the goal is for you to make the connection that oh, in a 3x2 case, u have to multiply each term in the 3 with each term in the 2, etc.

i think your problems with foil can be extended to the general way math is taught. at least for me, it was always full of tricks, little rules that can be broken sometimes, and i was constantly learning new things that made me realize my old teachers had taught us tricks to shortcut solutions.



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