These are what are called “difference of perfect squares”…

For x^2 – 1…. you would have x^2 – 1 = (x+1)(x-1) … right???

So this is no different… it’s the same idea…!!!

x^4 – 1 = (x^2 + 1)(x^2 – 1)

DONE!!!

When the problem is the difference of two squares… you know you will have two sets of ( )’s…. the first terms in both ()’s is the squareroot of the first square… so what is the sqrt of x^4? x^2 … right? And what is the sqrt of 1? 1, right? so the 1 is the 2nd term in both sets of ()’s…. and because it is the difference of two squares, you put + in one of the ()’s… and – in the other…. see? x^4 – 1 = (x^2 +1)(x^2 – 1)….

Let’s see if you know what I’m talking about…

What would you do if you had… hmm… say… x^8 – 16 ???

Well, this is the difference of two squares…. Ask yourself… what is the sqrt of x^8? You should have gotten x^4 … now what is the sqrt of 16? You should have said 4…. Okay….

so…. x^8 – 16 = (x^4 + 4)(x^4 – 4) …. Got it now???