Answer
$(9r+1)(9r-1)$
Work Step by Step
$81r^{2}-1=$
...write each term as a square.
$=(9r)^{2}-1^{2}$
...factor using the rule for a difference of two squares.
($a^{2}-b^{2}=(a+b)(a-b),\ a=9r,\ b=1$)
$=(9r+1)(9r-1)$
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