How do you factor $64z − z^3$ ?

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Answer 1 · 2016-06-15T13:23:37

$z(8+z)(8-z)$

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.

How do you factor 64z − z^3 64z − z^3 ?