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-3a^{2}-ba+2b^{2}
Consider -ab+2b^{2}-3a^{2} as a polynomial over variable a.
\left(3a-2b\right)\left(-a-b\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power -3a^{2} and n divides the constant factor 2b^{2}. One such factor is 3a-2b. Factor the polynomial by dividing it by this factor.