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ab\left(6a^{4}b^{2}-12a^{3}b^{3}+10b-5a\right)
Factor out ab.
6b^{2}a^{3}\left(a-2b\right)-5\left(a-2b\right)
Consider 6a^{4}b^{2}-12a^{3}b^{3}+10b-5a. Do the grouping 6a^{4}b^{2}-12a^{3}b^{3}+10b-5a=\left(6a^{4}b^{2}-12a^{3}b^{3}\right)+\left(10b-5a\right), and factor out 6b^{2}a^{3} in the first and -5 in the second group.
\left(a-2b\right)\left(6b^{2}a^{3}-5\right)
Factor out common term a-2b by using distributive property.
ab\left(a-2b\right)\left(6b^{2}a^{3}-5\right)
Rewrite the complete factored expression.