Simplify : `7xy - 3xy - 6xy + xy - 5xy`

Answer

To simplify the expression \( 7xy - 3xy - 6xy + xy - 5xy \), we will follow these steps:

### Step 1: Write down the expression
We start with the expression:
\[ 7xy - 3xy - 6xy + xy - 5xy \]

### Step 2: Group like terms
We can group all the terms that have \( xy \) in them:
\[ (7 - 3 - 6 + 1 - 5)xy \]

### Step 3: Simplify the coefficients
Now, we will simplify the coefficients (the numbers in front of \( xy \)):
1. Start with \( 7 \).
2. Subtract \( 3 \): \( 7 - 3 = 4 \)
3. Subtract \( 6 \): \( 4 - 6 = -2 \)
4. Add \( 1 \): \( -2 + 1 = -1 \)
5. Subtract \( 5 \): \( -1 - 5 = -6 \)

So, the simplified coefficient is \( -6 \).

### Step 4: Write the final expression
Now we can write the final simplified expression:
\[ -6xy \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{-6xy} \]

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