Answer
$3(2n+3p)(4n^2-6np+9p^2)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
24n^3+81p^3
,$ factor first the $GCF$. Then use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Factoring the $GCF=
3
,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3(8n^3+27p^3)
.\end{array}
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or $a^3-b^3=(a-b)(a^2+ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
3(2n+3p)[(2n)^2-2n(3p)+(3p)^2]
\\\\=
3(2n+3p)(4n^2-6np+9p^2)
.\end{array}
