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3\left(m^{2}-8mn+16n^{2}\right)
Factor out 3.
\left(m-4n\right)^{2}
Consider m^{2}-8mn+16n^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=m and b=4n.
3\left(m-4n\right)^{2}
Rewrite the complete factored expression.