10. [-/1 Points] DETAILS MY NOTES TGEIALG6 5.8.093. Perform the division. (Simplify your answer completely.) \( \frac{a^{3}-64}{a-4} \) SUBMIT ANSWER

To perform the division \( \frac{a^3 - 64}{a - 4} \), you can start by recognizing that \( a^3 - 64 \) is a difference of cubes, which can be factored as follows: \( a^3 - 64 = (a - 4)(a^2 + 4a + 16) \). Now, simplifying \( \frac{(a - 4)(a^2 + 4a + 16)}{(a - 4)} \) cancels out \( (a - 4) \) from both the numerator and the denominator, leading to: \( a^2 + 4a + 16 \). Thus, the simplified answer is \( a^2 + 4a + 16 \).