Theory is nasty. Case in point, it just became useful to rewrite (ab + cd) as [(a+d)*(b+c) - ad - bc]. That's some counterintuitive bullshit, right there.
Oddly enough, though, it does have a point--it changes a particular algorithm's execution time from O(n^2) to O(n^1.58). As an example of what that means, if you have an initial input of 100 elements, if the original way took 10 seconds, then the new way would take only 1.5 seconds. Fuckin' weird. If for some ungodly reason anyone wants to know the details, I can furnish them. But I don't guarantee you won't think less of me afterward.