Answer
$(r+3)(r^2-3r+9)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
r^3+27
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
The expressions $
r^3
$ and $
27
$ are both perfect cubes (the cube root is exact). Hence, $
r^3+27
$ is a $\text{
sum
}$ of $2$ cubes. Using the factoring of the sum or difference of $2$ cubes which is given by $a^3+b^3=(a+b)(a^2-ab+b^2)$ or by $a^3-b^3=(a-b)(a^2+ab+b^2)$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(r)^3+(3)^3
\\\\=
(r+3)[(r)^2-r(3)+(3)^2]
\\\\=
(r+3)(r^2-3r+9)
.\end{array}