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27b^{2}a^{2}+42ba+8
Consider 42ab+27a^{2}b^{2}+8 as a polynomial over variable a.
\left(3ab+4\right)\left(9ab+2\right)
Find one factor of the form kb^{m}a^{n}+p, where kb^{m}a^{n} divides the monomial with the highest power 27b^{2}a^{2} and p divides the constant factor 8. One such factor is 3ab+4. Factor the polynomial by dividing it by this factor.