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c^{2}\left(c-49\right)-9\left(c-49\right)
Do the grouping c^{3}-49c^{2}-9c+441=\left(c^{3}-49c^{2}\right)+\left(-9c+441\right), and factor out c^{2} in the first and -9 in the second group.
\left(c-49\right)\left(c^{2}-9\right)
Factor out common term c-49 by using distributive property.
\left(c-3\right)\left(c+3\right)
Consider c^{2}-9. Rewrite c^{2}-9 as c^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(c-49\right)\left(c-3\right)\left(c+3\right)
Rewrite the complete factored expression.