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\frac{6a^{3}b^{2}-9a^{2}b^{3}+18a^{2}b^{3}+2a^{2}b^{3}}{3}
Factor out \frac{1}{3}.
a^{2}b^{2}\left(6a-9b+18b+2b\right)
Consider 6a^{3}b^{2}-9a^{2}b^{3}+18a^{2}b^{3}+2a^{2}b^{3}. Factor out a^{2}b^{2}.
6a+11b
Consider 6a-9b+18b+2b. Multiply and combine like terms.
\frac{a^{2}b^{2}\left(6a+11b\right)}{3}
Rewrite the complete factored expression.