Factor
4\left(5c+1\right)\left(25c^{2}-5c+1\right)
Evaluate
500c^{3}+4
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4\left(125c^{3}+1\right)
Factor out 4.
\left(5c+1\right)\left(25c^{2}-5c+1\right)
Consider 125c^{3}+1. Rewrite 125c^{3}+1 as \left(5c\right)^{3}+1^{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).
4\left(5c+1\right)\left(25c^{2}-5c+1\right)
Rewrite the complete factored expression. Polynomial 25c^{2}-5c+1 is not factored since it does not have any rational roots.
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