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c^{3}\left(c^{2}-14c+49\right)
Factor out c^{3}.
\left(c-7\right)^{2}
Consider c^{2}-14c+49. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=c and b=7.
c^{3}\left(c-7\right)^{2}
Rewrite the complete factored expression.