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b^{2}a^{2}+12ba+32
Consider a^{2}b^{2}+12ab+32 as a polynomial over variable a.
\left(ab+8\right)\left(ab+4\right)
Find one factor of the form b^{k}a^{m}+n, where b^{k}a^{m} divides the monomial with the highest power b^{2}a^{2} and n divides the constant factor 32. One such factor is ab+8. Factor the polynomial by dividing it by this factor.