Add :
`3p^(2)q^(2) - 4pq + 5, - 10p^(2) q^(2), 15 + 9pq + 7p^(2)q^(2)`

Answer

To solve the problem of adding the algebraic expressions \(3p^2q^2 - 4pq + 5\), \(-10p^2q^2\), and \(15 + 9pq + 7p^2q^2\), we will follow these steps:

### Step 1: Write down all the expressions
We have the following expressions to add:
1. \(3p^2q^2 - 4pq + 5\)
2. \(-10p^2q^2\)
3. \(15 + 9pq + 7p^2q^2\)

### Step 2: Combine like terms
We will group the like terms together:
- The \(p^2q^2\) terms: \(3p^2q^2\), \(-10p^2q^2\), and \(7p^2q^2\)
- The \(pq\) terms: \(-4pq\) and \(9pq\)
- The constant terms: \(5\) and \(15\)

### Step 3: Add the \(p^2q^2\) terms
\[ 3p^2q^2 - 10p^2q^2 + 7p^2q^2 = (3 - 10 + 7)p^2q^2 = 0p^2q^2 \]
So, the \(p^2q^2\) terms cancel out.

### Step 4: Add the \(pq\) terms
\[ -4pq + 9pq = (-4 + 9)pq = 5pq \]

### Step 5: Add the constant terms
\[ 5 + 15 = 20 \]

### Step 6: Combine all results
Now, we combine the results from the previous steps:
\[ 0p^2q^2 + 5pq + 20 = 5pq + 20 \]

### Step 7: Factor out the common term
We can factor out the common term \(5\):
\[ 5(pq + 4) \]

### Final Answer
Thus, the final answer is:
\[ 5(pq + 4) \]

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