Answer
$(7x+5q)(2x-5q)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
14x^2-25xq-25q^2
,$ use the factoring of trinomials in the form $ax^2+bx+c.$
$\bf{\text{Solution Details:}}$
In the trinomial expression above, $a=
14
,b=
-25
,\text{ and } c=
-25
.$ Using the factoring of trinomials in the form $ax^2+bx+c,$ the two numbers whose product is $ac=
14(-25)=-350
$ and whose sum is $b$ are $\left\{
10,-35
\right\}.$ Using these two numbers to decompose the middle term results to
\begin{array}{l}\require{cancel}
14x^2+10xq-35xq-25q^2
.\end{array}
Using factoring by grouping, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(14x^2+10xq)-(35xq+25q^2)
\\\\=
2x(7x+5q)-5q(7x+5q)
\\\\=
(7x+5q)(2x-5q)
.\end{array}
