# Math Help - simplification question

1. ## simplification question

I've been asked to simplify this expression:

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

All I can come up with is:

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

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...

2. Tell me, is $i$ in this context the square root of minus one?

If so, then remember that $i^2 = -1$ and $i^4 = 1$ and of course $i^{-1} = -i$.

Then you could multiply it out, but I can't see this making it simpler ...

3. No. i is just a regular variable. Very confusing, I know...