Re: Cool math shortcuts
 

I do this kinda crap when I'm bored. The one Homer came up with is something I figured out when I was 13 or so. There's a bunch that I read in some book, like squaring numbers where the first two digits are the same and the second two digits add up to ten.

39 * 31
(3*(3+1))(9*1)
(12)(09)
1209

Re: Cool math shortcuts
 

[ QUOTE ]
Unless I'm missing something>

I'd make a = 3 to square 37, so 34*40 + 9 = 1369.

Thanks Homer!

edit: Homer responded the same time I did, but I think that 34*40 + 9 (basically 34*4 + 9) is easier to do quickly in your head than 37*37.

[/ QUOTE ]

I think that overcounting then subtracting then re-adding might be simpler, but I could be wrong. Or, undercounting then adding then re-adding.

Examples:

37*37 = 40*40 - 2*(3*40) + 3*3 (uses 3 as the "difference" number)

42*42 = 40*40 + 2*(2*40) + 2*2 (uses 2 as the "difference" number)

In Edit: I understand that this is basically the same FOIL method as Homer's, but I think that breaking it down like this, while it requires 3 steps, is simpler due to the simpler numbers.

-RMJ