Answer
$(8w-3z )(2w+7z)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
16w^2+50wz -21z^2
,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $
16(-21)=-336
$ and the value of $b$ is $
50
.$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{
-6,56
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
16w^2-6wz +56wz -21z^2
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(16w^2-6wz )+(56wz -21z^2)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
2w(8w-3z )+7z(8w -3z)
.\end{array}
Factoring the $GCF=
(8w-3z )
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(8w-3z )(2w+7z)
.\end{array}