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-d^{3}c^{3}+216
Consider 216-c^{3}d^{3} as a polynomial over variable c.
\left(cd-6\right)\left(-c^{2}d^{2}-6cd-36\right)
Find one factor of the form kd^{m}c^{n}+p, where kd^{m}c^{n} divides the monomial with the highest power -d^{3}c^{3} and p divides the constant factor 216. One such factor is cd-6. Factor the polynomial by dividing it by this factor.