Add :
`13ab - 9cd - xy, 5xy, 15cd - 7ab, 6xy - 3cd`

Answer

To solve the problem of adding the algebraic expressions \( 13ab - 9cd - xy, 5xy, 15cd - 7ab, 6xy - 3cd \), we will follow these steps:

### Step 1: Write down all the expressions
We have the following expressions to add:
1. \( 13ab - 9cd - xy \)
2. \( 5xy \)
3. \( 15cd - 7ab \)
4. \( 6xy - 3cd \)

### Step 2: Combine all expressions
We can combine all the expressions into one:
\[ (13ab - 9cd - xy) + (5xy) + (15cd - 7ab) + (6xy - 3cd) \]

### Step 3: Rearrange the terms
Now, we will rearrange the terms to group similar variables together:
\[ (13ab - 7ab) + (-9cd + 15cd - 3cd) + (-xy + 5xy + 6xy) \]

### Step 4: Combine similar terms
Now we will combine the coefficients of similar terms:
1. For \( ab \):
\[ 13ab - 7ab = 6ab \]
2. For \( cd \):
\[ -9cd + 15cd - 3cd = -9cd + 15cd - 3cd = 3cd \]
3. For \( xy \):
\[ -xy + 5xy + 6xy = -1xy + 5xy + 6xy = 10xy \]

### Step 5: Write the final expression
Now we can write the final expression by combining all the results:
\[ 6ab + 3cd + 10xy \]

### Final Answer:
Thus, the result of adding the given expressions is:
\[ 6ab + 3cd + 10xy \]

---