The next step would be to recognize your expression as a difference of squares:
[tex]64z^2-1=(8z)^2-1^2[/tex]
We have a neat rule for factorization of a difference of squares:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
So you would have
[tex]64z^2-1=(8z-1)(8z+1)[/tex]
