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4a^{2}-4a-b^{2}-4b-3
Consider 4a^{2}-4a-b^{2}-4b-3 as a polynomial over variable a.
\left(2a+b+1\right)\left(2a-b-3\right)
Find one factor of the form ka^{m}+n, where ka^{m} divides the monomial with the highest power 4a^{2} and n divides the constant factor -b^{2}-4b-3. One such factor is 2a+b+1. Factor the polynomial by dividing it by this factor.