Factoring a large Diff of Squares

**y = x^1000 - 1**

I would like to **factor out an x-1** from this but I don't remember which rules apply.

1) Do I apply something similar to a difference of squares and just keep going until I get (x-1)(....)?

(x^500)^2 - (1)^2 = (x^500+1)(x^500-1) = (x^500+1)(x^250+1)(x^250-1) = (x^500+1)(x^250+1)(x^125+1)(x^125-1) = now I'm stuck and I couldn't even get it to x-1 because I ran into an odd exponent ... well I'll try difference of cubes in that last factor...: = (x^500+1)(x^250+1)(x^125+1)(x^5-1)(x^10+x^5+1)... Okay, now I'm stuck, unless I remember how to factor (x^10+x^5+1)...

2) Or do I use some kind of Binomial Theorem.

Is it true that

x^1000 - 1 = (x-1)(x^999+x^998+x^997......+1) ?

3) Do I have to remember Pascal's Triangle at all?

For example, if number 2 above is true, then do I have to put in pascal's coefficients? ie.

(x-1)(**1**x^999 + **999**x^998 + ...... + **1**)?