Answer
$5(4z-w)^2$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
80z^2-40zq+5w^2
,$ factor first the $GCF.$ Then, the resulting trinomial is a perfect square trinomial. Use the factoring of perfect square trinomials.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=
5
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
5(16z^2-8zq+w^2)
.\end{array}
The trinomial above is a perfect square trinomial. Using $a^2\pm2ab+b^2=(a\pm b)^2,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
5(4z-w)^2
.\end{array}
