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8a^{2}+\left(-12+2b\right)a-b^{2}+4
Consider 8a^{2}-12a+2ab-b^{2}+4 as a polynomial over variable a.
\left(2a+b-2\right)\left(4a-b-2\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 8a^{2} and n divides the constant factor -b^{2}+4. One such factor is 2a+b-2. Factor the polynomial by dividing it by this factor.