Answer
$(2y+3x)(8y-9x)$
Work Step by Step
The two numbers whose product is $ac=
3(-27)=-432
$ and whose sum is $b=
6
$ are $\{
24,-18
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
16y^2+6yx-27x^2
$, is
\begin{array}{l}\require{cancel}
16y^2+24yx-18yx-27x^2
\\\\=
(16y^2+24yx)-(18yx+27x^2)
\\\\=
8y(2y+3x)-9x(2y+3x)
\\\\=
(2y+3x)(8y-9x)
.\end{array}
