Answer
$(a^3-b^4c^5)(a^6+a^3b^4c^5+b^8c^{10})$
Work Step by Step
Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the given expression, $
a^{9}+b^{12}c^{15}
,$ is
\begin{array}{l}
(a^3-b^4c^5)[ (a^3)^2-(a^3)(-b^4c^5)+(-b^4c^5)^2]
\\\\=
(a^3-b^4c^5)(a^6+a^3b^4c^5+b^8c^{10})
.\end{array}