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2a^{2}-ba-6b^{2}
Consider 2a^{2}-ab-6b^{2} as a polynomial over variable a.
\left(2a+3b\right)\left(a-2b\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 2a^{2} and n divides the constant factor -6b^{2}. One such factor is 2a+3b. Factor the polynomial by dividing it by this factor.