Question

How do you factor `64z − z^3`?

Answer 1

`z(8+z)(8-z)`

Explanation:

First of all, you can factor a `z`, to obtain

`z(64-z^2)`

Inside the parenthesis now we have the difference of two squares: we know that `a^2-b^2=(a+b)(a-b)`, and thus

`(64-z^2) = (8^2-z^2)=(8+z)(8-z)`

Since now all three factors `z`, `8+z` and `8-z` are linear (i.e. polynomials of first degree), we can no longer simplify the answer.