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\frac{9n^{2}-24nm+16m^{2}}{36}
Factor out \frac{1}{36}.
\left(-4m+3n\right)^{2}
Consider 9n^{2}-24nm+16m^{2}. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=-4m and b=3n.
\frac{\left(-4m+3n\right)^{2}}{36}
Rewrite the complete factored expression.