Arthur Benjamin's book Secrets of Mental Math has similar tricks to this one. One I like is multiplying 10x+y by 10x+z where y+z = 10, then the answer is 100x(

Arthur Benjamin's book Secrets of Mental Math has similar tricks to this one. One I like is multiplying 10x+y by 10x+z where y+z = 10, then the answer is 100x(x+1) + yz (such that the two multiplications can be concatenated). So 53*57 = [5*(5+1)][3*7] = 3021. The article mentions its trick > saves the student from having to learn the scary outer reaches of the multiplication table — they only have to know how to multiply digits up to 5. Similarly, another cool trick I like allows quick calculation of all squares up to 125^2 (you could go higher too if you extend it, but through 125^2 is simpler), and you only need to memorize the squares up to 25^2. The trick is to expand (x)*(x) into (x+y)(x-y) + y^2, picking y such that one of the sum/difference factors becomes 50 or 100. Then, you can easily halve the other factor (which will also be even) and shift it two places (if 50), or simply shift it two places (if 100), and then add the square of the small y which has been memorized. For example, 78^2 = (78-22)(78+22) + 22^2 = 56*100 + 484 = 5600 + 484 = 6084. Or 74^2 = (74+24)(74-24) + 24^2 = 98*50 + 576 = 4900 + 576 = 5476. Or 123^2 = (123+23)(123-23) + 23^2 = 146*100 + 529 = 14600 + 529 = 15129. Since the distance to the nearest multiple of 50 is at most 25, you only need to remember your squares through 25^2 = 625, and the rest of the work is division by two, place shifting, and addition.