Add:
`-7mn + 5, 12mn + 2, 9mn -8, -2mn - 3`

Answer

To solve the problem of adding the algebraic expressions \(-7mn + 5\), \(12mn + 2\), \(9mn - 8\), and \(-2mn - 3\), we will follow these steps:

### Step 1: Rewrite the expressions
We will replace the commas with plus signs and enclose the entire expression in brackets:
\[ (-7mn + 5) + (12mn + 2) + (9mn - 8) + (-2mn - 3) \]

### Step 2: Remove the brackets
Now, we can remove the brackets since addition is associative:
\[ -7mn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3 \]

### Step 3: Combine like terms
Next, we will group the like terms together. The like terms here are those that contain \(mn\) and the constant terms:
- For the \(mn\) terms: \(-7mn + 12mn + 9mn - 2mn\)
- For the constant terms: \(5 + 2 - 8 - 3\)

### Step 4: Calculate the \(mn\) terms
Now, let's calculate the coefficients of \(mn\):
\[ -7 + 12 + 9 - 2 = 12mn \]

### Step 5: Calculate the constant terms
Next, we calculate the constant terms:
\[ 5 + 2 - 8 - 3 = -4 \]

### Step 6: Combine the results
Now, we can combine the results from the \(mn\) terms and the constant terms:
\[ 12mn - 4 \]

### Final Answer
Thus, the final answer is:
\[ 12mn - 4 \]

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