Answer
$ 8(y-5z^2)(y^2+5yz^2+25z^4)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $ 8y^3-1000z^6 ,$ factor first the $GCF.$ Then use the factoring of the sum or difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=8,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 8(y^3-125z^6) .\end{array}
Both $y^3$ and $125z^6$ are perfect cubes (the cube root is exact.) Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent\begin{array}{l}\require{cancel}
\\\\=8[y^3-(5z^2)^3]
\\\\=8(y-5z^2)(y^2+5yz^2+25z^4) .\end{array}
