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2\left(m^{2}-4n^{2}\right)
Factor out 2.
\left(m-2n\right)\left(m+2n\right)
Consider m^{2}-4n^{2}. Rewrite m^{2}-4n^{2} as m^{2}-\left(2n\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
2\left(m-2n\right)\left(m+2n\right)
Rewrite the complete factored expression.