Factor completely.
\[
v^{3}+k^{3}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $v^{3}+k^{3}=$
B. $v^{3}+k^{3}$ is prime.

Answer

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Answer

Final Answer: $v^{3}+k^{3} = \boxed{(v + k)(v^2 - vk + k^2)}$

Steps

Step 1 ：The given expression is a sum of cubes. The sum of cubes can be factored using the formula: $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$.

Step 2 ：Here, $a = v$ and $b = k$. So, we can use this formula to factor the given expression.

Step 3 ：The factored form of the expression $v^{3}+k^{3}$ is $(v + k)(v^2 - vk + k^2)$.

Step 4 ：Final Answer: $v^{3}+k^{3} = \boxed{(v + k)(v^2 - vk + k^2)}$