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b^{2}+6db+5d^{2}
Consider b^{2}+6bd+5d^{2} as a polynomial over variable b.
\left(b+5d\right)\left(b+d\right)
Find one factor of the form b^{k}+m, where b^{k} divides the monomial with the highest power b^{2} and m divides the constant factor 5d^{2}. One such factor is b+5d. Factor the polynomial by dividing it by this factor.