Add :` 6p^(2)q - 5pq^(2) -3pq, 8pq^(2)+2p^(2)q -2pq`

Answer

To solve the problem of adding the two algebraic expressions \(6p^2q - 5pq^2 - 3pq\) and \(8pq^2 + 2p^2q - 2pq\), we will follow these steps:

### Step 1: Write down the expressions to be added
We have:
\[ x = 6p^2q - 5pq^2 - 3pq \]
\[ y = 8pq^2 + 2p^2q - 2pq \]

### Step 2: Combine the expressions
Now we will add \(x\) and \(y\):
\[ x + y = (6p^2q - 5pq^2 - 3pq) + (8pq^2 + 2p^2q - 2pq) \]

### Step 3: Group like terms
Next, we will group the like terms together:
- For \(p^2q\): \(6p^2q + 2p^2q\)
- For \(pq^2\): \(-5pq^2 + 8pq^2\)
- For \(pq\): \(-3pq - 2pq\)

### Step 4: Simplify each group
Now we will simplify each group:
1. \(6p^2q + 2p^2q = 8p^2q\)
2. \(-5pq^2 + 8pq^2 = 3pq^2\)
3. \(-3pq - 2pq = -5pq\)

### Step 5: Write the final expression
Combining all the simplified terms, we get:
\[ x + y = 8p^2q + 3pq^2 - 5pq \]

### Final Answer:
Thus, the result of adding the two expressions is:
\[ \boxed{8p^2q + 3pq^2 - 5pq} \]