A mathematics club designs a number machine that accepts three integers \(a\), \(b\), \(c\). The machine follows the same rule for every input. Students observe the outputs below and try to identify the hidden expression. The teacher then challenges them to find missing inputs and predicts outputs without performing unnecessary calculations.
| \(a\) | \(b\) | \(c\) | Output |
| 6 | −5 | 3 | −27 |
| −7 | 8 | −3 | −59 |
| 8 | −3 | −6 | −30 |
| −9 | −5 | 6 | ? |
Based on the above information, answer the following questions.
1. Which expression represents the machine's rule?
2. What is the missing output in the fourth row?
3. If \(a = -12\), \(b = 7\), and the output is −89, what is the value of \(c\)?
4. If the values of both \(a\) and \(b\) are replaced by their additive inverses while \(c\) remains unchanged, what happens to the output?