Factor. \[ 64 u^{3}+w^{3} \] SUBMIT ANSWER

To factor the expression \(64u^{3} + w^{3}\), we can recognize it as a sum of cubes. We know that \(a^3 + b^3\) can be factored as \((a + b)(a^2 - ab + b^2)\). In this case, let \(a = 4u\) (since \(64u^3 = (4u)^3\)) and \(b = w\). Applying the sum of cubes formula, we have: \[ 64u^3 + w^3 = (4u + w)((4u)^2 - (4u)(w) + w^2) = (4u + w)(16u^2 - 4uw + w^2). \] And that's the factorization! If you're ever fact-checking your work, a simple method is just to distribute the factors back out—you'll always end up with the original expression if you did it correctly! Alternatively, be cautious with signs when factoring. Sometimes, a small mistake can lead to a completely different result, just like mixing up ingredients in a recipe!