Simplify combining like terms:
`p - (p -q) - q - (q - p)`

Answer

To simplify the expression \( p - (p - q) - q - (q - p) \), we will follow these steps:

### Step 1: Remove the parentheses
We start by distributing the negative signs across the terms inside the parentheses.

\[ p - (p - q) - q - (q - p) = p - p + q - q + p \]

### Step 2: Combine like terms
Now, we combine the like terms. The like terms here are \( p \) and \( -p \), and \( q \) and \( -q \).

\[ p - p + p + q - q = (p - p + p) + (q - q) \]

### Step 3: Simplify
Now, we can simplify the expression further:

1. \( p - p = 0 \)
2. \( q - q = 0 \)

So we have:

\[ 0 + 0 = 0 \]

### Final Result
Thus, the simplified expression is:

\[ p - (p - q) - q - (q - p) = 0 \]

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