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It’s so strange that it was always taught me as a²+b²+2ab. Of course I know it doesn’t matter, but still strange to see it this way.
FOIL reading left to right.
It makes more sense to me because, when binomials are taught, it’s usually in the form of a variable and a constant.
E.G. a = x, b = 3: (x + 3)^2. When expanded, that’s usually x^2 + 6x + 9, and not x^2 + 9 + 6x.
Exactly, you are going to lower and lower powers. (Is power the word in English here?)
ax², bx¹, cx⁰