Question

I tried, but can't get any further

Answer 1

The next step would be to recognize your expression as a difference of squares:

$64z^2-1=(8z)^2-1^2$

We have a neat rule for factorization of a difference of squares:

$a^2-b^2=(a-b)(a+b)$

So you would have

$64z^2-1=(8z-1)(8z+1)$