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3\left(8c^{4}d+125cd^{4}\right)
Factor out 3.
cd\left(8c^{3}+125d^{3}\right)
Consider 8c^{4}d+125cd^{4}. Factor out cd.
\left(2c+5d\right)\left(4c^{2}-10cd+25d^{2}\right)
Consider 8c^{3}+125d^{3}. Rewrite 8c^{3}+125d^{3} as \left(2c\right)^{3}+\left(5d\right)^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).
3cd\left(2c+5d\right)\left(4c^{2}-10cd+25d^{2}\right)
Rewrite the complete factored expression.