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4\left(2a^{3}b^{2}+3ab^{2}\right)
Factor out 4.
ab^{2}\left(2a^{2}+3\right)
Consider 2a^{3}b^{2}+3ab^{2}. Factor out ab^{2}.
4ab^{2}\left(2a^{2}+3\right)
Rewrite the complete factored expression. Polynomial 2a^{2}+3 is not factored since it does not have any rational roots.