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View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science
Your "formula" is, in fact, a formula.
More so than testing a couple of examples, you can quickly verify it with a bit of algebraic manipulation.
(a - 1)(a + 2)
a^2 + 2a - a - 2
a^2 + a - 2
a(a + 1) - 2
A formula is just a generally useful mathematical shortcut, and can cut out as many or as few steps as you like. If there's an application for it, you're free to use it, but something like this comes up infrequently.
Generally you'd just get from one side of the "formula" to the other via algebraic manipulation as above, since it's easier to jot down a few extra lines than to memorize and apply a gigantic set of generic algebraic formulas.
There's nothing here!