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a^{2}-4ba+3b^{2}
Consider a^{2}-4ab+3b^{2} as a polynomial over variable a.
\left(a-3b\right)\left(a-b\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 3b^{2}. One such factor is a-3b. Factor the polynomial by dividing it by this factor.