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m^{2}\left(a+b\right)+n^{2}\left(a+b\right)
Do the grouping am^{2}+bm^{2}+bn^{2}+an^{2}=\left(am^{2}+bm^{2}\right)+\left(bn^{2}+an^{2}\right), and factor out m^{2} in the first and n^{2} in the second group.
\left(a+b\right)\left(m^{2}+n^{2}\right)
Factor out common term a+b by using distributive property.