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