Answer
$5(3a-4b)(a+b)$
Work Step by Step
Factoring the $GCF=
5
,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
15a^2-5ab-20b^2
\\\\=
5(3a^2-ab-4b^2)
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
5(3a^2-ab-4b^2)
\end{array} has $ac=
3(-4)=-12
$ and $b=
-1
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-4,3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
5(3a^2-4ab+3ab-4b^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}
5[(3a^2-4ab)+(3ab-4b^2)]
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5[a(3a-4b)+b(3a-4b)]
.\end{array}
Factoring the $GCF=
(3a-4b)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
5[(3a-4b)(a+b)]
\\\\=
5(3a-4b)(a+b)
.\end{array}
