Who even needs the binomial theorem?
and so on.

@jsiehler I tried:
(2125+4231)²=40398736. Does this only work for cherry picked numbers?

@AskChip Yes... actually, finding pairs of numbers that do this makes a nice little puzzle. They are not common.

@ZacharyHerold You can find these systematically using modular arithmetic and, particularly, the Chinese Remainder Theorem. It's not particularly nasty, though you'd want to have a computer or calculator handy if you're going to try to find bigger examples like (1975308+2469136)².

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