Answer
$(r+7)(r^2-7r+49)$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To factor the given expression, $
r^3+343
,$ use the factoring of the sum/difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using $(a\pm b)(a^2\mp ab+b^2)$ or the factoring of the sum/difference of $2$ cubes, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(r+7)[(r)^2-r(7)+(7)^2]
\\\\=
(r+7)(r^2-7r+49)
.\end{array}
