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a^{3}-a-d^{3}+d
Consider a^{3}-d^{3}-a+d as a polynomial over variable a.
\left(a-d\right)\left(a^{2}+ad+d^{2}-1\right)
Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{3} and m divides the constant factor -d^{3}+d. One such factor is a-d. Factor the polynomial by dividing it by this factor.