Answer
$125z^3+8=(5z+2)(25z^2-10z+4)$
Work Step by Step
The given expression can be written as:
$=(5z)^3+2^3$
RECALL:
A sum or difference of two cubes can be factored using the following:
(i) $a^3-b^3=(a-b)(a^2+ab+b^2)$
(ii) $a^3+b^3 = (a+b)(a^2-ab+b^2)$
Use formula (2) above with $a=5z$ and $b=2$ to have:
$=(5z+2)[(5z)^2-5z(2)+2^2]
\\=(5z+2)(25z^2-10z+4)$
