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

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To perform the subtraction $$ (8a^{3} - 4a + 12) - (3a^{3} + 2a - 5) $$, follow these steps:

1. **Distribute the negative sign** to each term in the second polynomial:
   $$
   8a^{3} - 4a + 12 - 3a^{3} - 2a + 5
   $$

2. **Combine like terms**:
   - **Cubic terms**:
     $$
     8a^{3} - 3a^{3} = 5a^{3}
     $$
   - **Linear terms**:
     $$
     -4a - 2a = -6a
     $$
   - **Constant terms**:
     $$
     12 + 5 = 17
     $$

3. **Write the simplified expression**:
   $$
   5a^{3} - 6a + 17
   $$

**Final Answer:**
$$
5a^{3} - 6a + 17
$$
The result of the subtraction is $$ 5a^{3} - 6a + 17 $$.

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

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