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2m\left(2m+n\right)-\left(2m+n\right)
Do the grouping 4m^{2}+2mn-2m-n=\left(4m^{2}+2mn\right)+\left(-2m-n\right), and factor out 2m in the first and -1 in the second group.
\left(2m+n\right)\left(2m-1\right)
Factor out common term 2m+n by using distributive property.