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3b^{2}+7wb+2w^{2}
Consider 3b^{2}+7bw+2w^{2} as a polynomial over variable b.
\left(w+3b\right)\left(2w+b\right)
Find one factor of the form kb^{m}+n, where kb^{m} divides the monomial with the highest power 3b^{2} and n divides the constant factor 2w^{2}. One such factor is w+3b. Factor the polynomial by dividing it by this factor.