Answer
$(3r-4s)(9r^2+12rs+16s^2)$
Work Step by Step
RECALL:
$a^3-b^3 = (a-b)(a^2+ab+b^2)$
Write $27r^3$ and $64s^3$ as cubes to have:
$(3r)^3-(4s)^3$
Factor the difference of two cubes using the formula above with $a=3r$ and $b=4s$ to have:
$=(3r-4s)[(3r)^2+(3r)(4s) + (4s)^2]
\\=(3r-4s)(9r^2+12rs+16s^2)$
