Add :
`14x +10y - 12xy - 13, 18 - 7x - 10y + 8xy, 4xy`

Answer

To solve the problem of adding the algebraic expressions \( 14x + 10y - 12xy - 13 \), \( 18 - 7x - 10y + 8xy \), and \( 4xy \), we will follow these steps:

### Step 1: Write down all the terms
We start by writing all the terms from the expressions we need to add:

\[ 14x + 10y - 12xy - 13 + 18 - 7x - 10y + 8xy + 4xy \]

### Step 2: Group similar terms
Next, we group the similar terms together. We will group the terms involving \( x \), \( y \), \( xy \), and the constant terms separately:

- Terms with \( x \): \( 14x - 7x \)
- Terms with \( y \): \( 10y - 10y \)
- Terms with \( xy \): \( -12xy + 8xy + 4xy \)
- Constant terms: \( -13 + 18 \)

### Step 3: Simplify each group
Now we simplify each group of similar terms:

1. For \( x \):
\[ 14x - 7x = 7x \]

2. For \( y \):
\[ 10y - 10y = 0 \]

3. For \( xy \):
\[ -12xy + 8xy + 4xy = (-12 + 8 + 4)xy = 0xy = 0 \]

4. For the constants:
\[ -13 + 18 = 5 \]

### Step 4: Combine the simplified terms
Now we combine the results from each group:

\[ 7x + 0 + 0 + 5 = 7x + 5 \]

### Final Answer
Thus, the final answer is:

\[ \boxed{7x + 5} \]