Factor.
\[
w^{3}-64
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $w^{3}-64=\square$
B. $w^{3}-64$ is prime.

Answer

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Answer

$\boxed{w^{3}-64=(w-4)(w^{2}+4w+16)}$ is the final answer.

Steps

Step 1 ：The given expression is $w^{3}-64$.

Step 2 ：This is a difference of cubes problem. The formula for factoring the difference of cubes is $a^{3} - b^{3} = (a - b)(a^{2} + ab + b^{2})$.

Step 3 ：In this case, $a = w$ and $b = 4$ because $4^{3} = 64$.

Step 4 ：We can use this formula to factor the expression.

Step 5 ：Applying the formula, we get $w^{3}-64=(w-4)(w^{2}+4w+16)$.

Step 6 ：$\boxed{w^{3}-64=(w-4)(w^{2}+4w+16)}$ is the final answer.