Answer
$(2r+5s)(5r-s)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
10r^2+23rs-5s^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
10
,b=
23
,\text{ and } c=
-5
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
10(-5)=-50
$ and whose sum is $b$ are $\left\{
25,-2
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
10r^2+25rs-2rs-5s^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(10r^2+25rs)-(2rs+5s^2)
\\\\=
5r(2r+5s)-s(2r+5s)
\\\\=
(2r+5s)(5r-s)
.\end{array}
