c) \( \frac{8 a^{3}-27}{6 a^{2}-27 a+27} \)

To simplify the expression \( \frac{8 a^{3}-27}{6 a^{2}-27 a+27} \), we can start by factoring both the numerator and the denominator. The numerator \( 8a^3 - 27 \) can be recognized as a difference of cubes, which factors as: \[ 8a^3 - 27 = (2a - 3)(4a^2 + 6a + 9) \] The denominator \( 6a^2 - 27a + 27 \) can be factored using the quadratic formula or checking for common factors. It turns out it can be factored directly as: \[ 6a^2 - 27a + 27 = 3(2a^2 - 9a + 9) = 3(2a - 3)(a - 3) \] Now, substituting in our factored forms: \[ \frac{(2a - 3)(4a^2 + 6a + 9)}{3(2a - 3)(a - 3)} \] Here, we can cancel the common factor of \( (2a - 3) \): \[ \frac{4a^2 + 6a + 9}{3(a - 3)} \] Thus, the expression simplifies to: \[ \frac{4a^2 + 6a + 9}{3(a - 3)} \] In conclusion, the simplified form of the expression is: \[ \frac{4a^2 + 6a + 9}{3(a - 3)} \]