Perform the subtraction: \( (8a^{3} - 4a + 12) - (3a^{3} + 2a - 5) \)

To perform the subtraction \( (8a^{3} - 4a + 12) - (3a^{3} + 2a - 5) \), distribute the negative sign across the second polynomial: \[ (8a^{3} - 4a + 12) - 3a^{3} - 2a + 5 \] Now, combine like terms: 1. For \(a^3\): \(8a^3 - 3a^3 = 5a^3\) 2. For \(a\): \(-4a - 2a = -6a\) 3. For the constant terms: \(12 + 5 = 17\) Putting it all together gives: \[ 5a^3 - 6a + 17 \] So, the final result is \( 5a^3 - 6a + 17 \).