Can you multiply this polynomial?

GammaGrozza
Mon, 06 Jul 2009 20:37:03 +0000

Yeah, I forgot to add something, because it’s kind of hard to read expressions an a computer (I’m used to crossing off stuff when I simplify). I fixed that, though.

So, to save time, I didn’t write out everything. But, you have (x-1)^4(x+1)^4 after you do the first substitution. That is equivalent to (x-1)(x-1)(x-1)(x-1)(x+1)(x+1)(x+1)(x+1) which, by reordering, equals (x-1)(x+1)(x-1)(x+1)(x-1)(x+1)(x-1)(x+1). You know that (x-1)(x+1)=xx+1x-1x+(-1)1=x^2-1. So, you substitute x^2-1 for (x-1)(x+1) in the previous expression to get (x^2-1)(x^2-1)(x^2-1)(x^2-1)=(x^2-1)^4.

edit: i started writing this before seeing the post above.