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a^{2}+ca-b^{2}+bc
Consider a^{2}-b^{2}+ac+bc as a polynomial over variable a.
\left(a+b\right)\left(a-b+c\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 -b^{2}+bc. One such factor is a+b. Factor the polynomial by dividing it by this factor.