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v^{3}\left(v^{2}-6v+9\right)
Factor out v^{3}.
\left(v-3\right)^{2}
Consider v^{2}-6v+9. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=v and b=3.
v^{3}\left(v-3\right)^{2}
Rewrite the complete factored expression.