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\left(3r-2m\right)\left(3r+2m\right)
Rewrite 9r^{2}-4m^{2} as \left(3r\right)^{2}-\left(2m\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(-2m+3r\right)\left(2m+3r\right)
Reorder the terms.