Can you identify this equation?

Hi,

While I was back in school, during a maths class I had finished some coursework early and had to sit out the remaining time. For some reason related to the work, there was a list of square numbers in front of me. After staring at them for a while I picked up on pattern when doing some mental arithmetic and formed a rule which I've used ever since to help with long multiplication. I'm pretty sure it is either a famous rule/sequence or just an obvious statement to a mathematician. Anyway, after mentioning it to someone recently, I decided to transcribe it to a formula which goes as follows:

$\displaystyle xy = ((x+y)/2)^2 - ((x-y)/2)^2)$

I'm pretty sure I've written that right. Does anyone know what this is or if it is obvious. Like I said, I find it useful for doing multiplication in my head for numbers in the tens, aslong as you know a midpoint (between x and y) square number.

Thanks