secrets-of-mental-math-malestrom

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Secrets of Mental Math
Chapter 8), we obtain 9 (8,600 48) 77,400 432
77,832, and therefore 90 92 94 778,320. Since 4 92
368, we get
92 3 778,320 368 778,688
We note that when the close-together method is used for the
multiplication problems that arise when cubing two-digit numbers,
the small product being added will either be (depending on
whether d 1, 2, 3, 4, or 5) 1 2 2, 2 4 8, 3 6 18,
4 8 32, or 5 10 50. Let’s finish with the cube of 96.
96 3 (92 96 100) (4 2 96)
The product 92 96 8,832 can be done many different
ways. To celebrate the end of this chapter, let’s do some of them.
I’ll start with what I consider to be the hardest way, and end
with what I consider the easiest way. By the addition method,
(90 2) 96 8,640 192 8,832; by the subtraction
method, 92 (100 4) 9,200 368 8,832; by the factoring
method, 92 6 4 4 552 4 4 2,208 4 8,832; by
squaring, 94 2 2 2 8,836 4 8,832; by the close-together
method with a base of 90, (90 98) (2 6) 8,820 12
8,832; and by the close-together method with a base of 100,
(100 88) (8 4) 8,800 32 8,832.
The product 4 2 96 1,536 can also be done a few different
ways, such as 96 4 4 384 4 1,536, or as 16
(100 4) 1,600 64 1,536. Finally, since 8,832 100
883,200, we have
96 3 883,200 1,536 884,736