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