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3\left(c^{4}+8c^{3}+16c^{2}\right)
Factor out 3.
c^{2}\left(c^{2}+8c+16\right)
Consider c^{4}+8c^{3}+16c^{2}. Factor out c^{2}.
\left(c+4\right)^{2}
Consider c^{2}+8c+16. Use the perfect square formula, a^{2}+2ab+b^{2}=\left(a+b\right)^{2}, where a=c and b=4.
3c^{2}\left(c+4\right)^{2}
Rewrite the complete factored expression.