Here 49^3=(48*49*50)+(1^2*49). We can solve 48*49 by the factoring method, but for this sort of problem, I prefer to use the close-together method. Using that method, we get 48*49=(50*47)+(1*2)=2352. Multiplying this by 50, we get 117,600, and therefore: 49^3=117,600+49=117,649.
—from Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks, a book by Arthur Benjamin and Michael Shermer
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