secrets-of-mental-math-malestrom

The Tough Stuff Made Easy: Advanced Multiplication 187
For example, in the problem above, 900 829 1729 just as
876 853 1729. This is because:
z [(z a) b] (z a) (z b)
Thus, to obtain the number to be multiplied by 900 (which
you know will be 800 plus something), you need only look at
the last two digits of 76 53 129 to determine 829.
In the next problem, adding 827 761 1588 tells us that
we should simply multiply 800 788, then subtract 27 39 as
follows:
827 (27)
761 (39)
800 788 630,400
39 27 1,053 (39 9 3)
629,347
This method is so effective that if the 3-by-3 problem you are
presented with has numbers that are not close together, you can
sometimes modify the problem by dividing one and multiplying
the other, both by the same number, to bring them closer together.
For instance, 672 157 can be solved by:
672
157
2
2
336 (36)
314 (14)
300 350 105,000
36 14 504
105,504
(36 7 2)
When the numbers being multiplied are the same (you can’t
get any closer than that!), notice that the close-together method