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a^{2}\left(3a+2b\right)+5b^{2}\left(3a+2b\right)
Do the grouping 3a^{3}+2a^{2}b+15ab^{2}+10b^{3}=\left(3a^{3}+2a^{2}b\right)+\left(15ab^{2}+10b^{3}\right), and factor out a^{2} in the first and 5b^{2} in the second group.
\left(3a+2b\right)\left(a^{2}+5b^{2}\right)
Factor out common term 3a+2b by using distributive property.