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\left(9n-m\right)\left(9n+m\right)
Rewrite 81n^{2}-m^{2} as \left(9n\right)^{2}-m^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-m+9n\right)\left(m+9n\right)
Reorder the terms.