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b\left(-8ab+a^{2}+15b^{2}\right)
Factor out b.
a^{2}-8ba+15b^{2}
Consider -8ab+a^{2}+15b^{2}. Consider -8ab+a^{2}+15b^{2} as a polynomial over variable a.
\left(a-5b\right)\left(a-3b\right)
Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{2} and m divides the constant factor 15b^{2}. One such factor is a-5b. Factor the polynomial by dividing it by this factor.
b\left(a-5b\right)\left(a-3b\right)
Rewrite the complete factored expression.