(50-3)^2

I was at the AT&T store yesterday thinking I was going to get an iPhone (turns out I could order one and get it in a few weeks - no thanks - if the gratification isn't instant I don't want any part of it). There were a few kids in the store playing with the iPhones on display. I think they were about 10, but I think all kids are about 10 (if you ever listen to my childhood stories you'll realize that I think half my life occurred during that one year). One of them decided that the most interesting thing to do with the iPhone was to type math problems into its calculator and then see if the other kids could get the right answer. While I wanted to play with the iPhone (although I'm a bit ashamed that I would have been using it to watch TV) I liked that the kid was doing math and doing the problems in my head provided entertainment while I waited to be disappointed by the lack of iPhones.

At one point the kid asked his mom - what is 47 times 47 and she responded 10,000 clearly just brushing off the question. To her credit - she was at a cell phone store with her kids - I think if you make it through that without going on a murderous rampage you've done good (I think that counts even without the kids). But I was so tempted to tell the kid how to do the problem. (instead of doing 47*47 do (50-3)^2 which is then just three easy problems: 50*50, 2*50*3, and 3*3 then subtract and add) but I figured that would not have been appreciated. But don't you think that in the interest of teaching a kid math most normal social rules should be suspended?

I convinced myself that I wrote this as just an amusing story since I haven't posted in a bit and as a question about societal rules. But I'm afraid it is really just a way to release a pent up need to tell someone how to easily square 47, which really isn't that satisfying considering that many of you know as much or more math than I do.