I remember “discovering” shift and add as a high school student for doing multiply by 40 (a useful operation for screen mapping) as an improvement over the more

I remember “discovering” shift and add as a high school student for doing multiply by 40 (a useful operation for screen mapping) as an improvement over the more naïve x×y = x+x+…(y times)…+x. But seeing the table of squares thing, I see the genius of being able to take (x+y)²-(x-y)²=(x²+2xy+y²)-(x²-2xy+y²)= 4xy and what a brilliant piece of math that is.