Answer
$-2a^2(5a-2)(7a-4)$
Work Step by Step
Factoring the negative $GCF=
-2a^2
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
-70a^4+68a^3-16a^2
\\\\=
-2a^2(35a^2-34a+8)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
-2a^2(35a^2-34a+8)
\end{array} has $ac=
35(8)=280
$ and $b=
-34
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-14,-20
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
-2a^2(35a^2-14a-20a+8)
.\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}
-2a^2[(35a^2-14a)-(20a-8)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
-2a^2[7a(5a-2)-4(5a-2)]
.\end{array}
Factoring the $GCF=
(5a-2)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
-2a^2[(5a-2)(7a-4)]
\\\\=
-2a^2(5a-2)(7a-4)
.\end{array}
