I've been asked to simplify this expression:

$\displaystyle (i - n)(i - m)(i - y)(i - s)$

All I can come up with is:

$\displaystyle i^4(1 - ni^{-1})(1 - mi^{-1})(1 - yi^{-1})(1 - si^{-1})$

I'm having a hard time convincing myself that this is simpler. Does anyone have any input on simplification? I'm looking for how I can confidently know that an expression is in its simplest form. Any input?

Thanks a lot for your help... I feel like this right now...