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6\left(2a^{2}b^{2}c-ab^{2}c^{2}+3a^{2}bc\right)
Factor out 6.
abc\left(2ab-bc+3a\right)
Consider 2a^{2}b^{2}c-ab^{2}c^{2}+3a^{2}bc. Factor out abc.
6abc\left(2ab-bc+3a\right)
Rewrite the complete factored expression.