Answer
$2y(3y-4)(9y^2+12y+16)$
Work Step by Step
Factoring the $GCF=
2y
,$ the given expression, $
54y^4-128y
,$ is equivalent to
\begin{array}{l}
2y(27y^3-64)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $
8(8x^6-t^6)
,$ is
\begin{array}{l}
2y(3y-4)[ (3y)^2-(3y)(-4)+(-4)^2]
\\\\=
2y(3y-4)(9y^2+12y+16)
.\end{array}