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6a^{2}+ba-15b^{2}
Consider 6a^{2}+ab-15b^{2} as a polynomial over variable a.
\left(2a-3b\right)\left(3a+5b\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 6a^{2} and n divides the constant factor -15b^{2}. One such factor is 2a-3b. Factor the polynomial by dividing it by this factor.