Answer
$$(a+8)(a-8)$$
Work Step by Step
$a^{2}-64$
This is the difference between two squares.
There is a simple formula for this case:
$x^{2}-y^{2}=(x+y)(x-y)$
So, applying this formula,
We need to take the square of both terms.
$\sqrt a^{2}=a$
$\sqrt 64=8$
So the answer would look like:
$$(a+8)(a-8)$$
(One with a positive sign and one with a negative sign.)