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