Answer
$(7a-4b)(3a+b)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
21a^2-5ab-4b^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
21
,b=
-5
,\text{ and } c=
-4
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
21(-4)=-84
$ and whose sum is $b$ are $\left\{
-12,7
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
21a^2-12ab+7ab-4b^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(21a^2-12ab)+(7ab-4b^2)
\\\\=
3a(7a-4b)+b(7a-4b)
\\\\=
(7a-4b)(3a+b)
.\end{array}
