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m\left(p+2\right)+n\left(p+2\right)
Do the grouping 2m+mp+np+2n=\left(2m+mp\right)+\left(np+2n\right), and factor out m in the first and n in the second group.
\left(p+2\right)\left(m+n\right)
Factor out common term p+2 by using distributive property.