Subtract `3pq(p-q)` from `2pq(p+q)`

Options

A. `-3p^2q+5pq^2`
B. `-p^2q+5pq^2`
C. `-p^2q+5p^2q^2`
D. `p^2q-5pq^2`

Explanation

To solve the problem of subtracting \(3pq(p-q)\) from \(2pq(p+q)\), we will follow these steps:

### Step 1: Write the expression for subtraction
We need to subtract \(3pq(p-q)\) from \(2pq(p+q)\). This can be expressed as:
\[ 2pq(p+q) - 3pq(p-q) \]

### Step 2: Expand both expressions
Now we will expand both expressions using the distributive property.

1. **Expanding \(2pq(p+q)\)**:
\[ 2pq(p+q) = 2pq \cdot p + 2pq \cdot q = 2p^2q + 2pq^2 \]

2. **Expanding \(3pq(p-q)\)**:
\[ 3pq(p-q) = 3pq \cdot p - 3pq \cdot q = 3p^2q - 3pq^2 \]

### Step 3: Substitute the expanded forms back into the expression
Now we substitute the expanded forms back into the expression:
\[ (2p^2q + 2pq^2) - (3p^2q - 3pq^2) \]

### Step 4: Distribute the negative sign
Distributing the negative sign across the second expression:
\[ 2p^2q + 2pq^2 - 3p^2q + 3pq^2 \]

### Step 5: Combine like terms
Now we combine the like terms:
1. For \(p^2q\):
\[ 2p^2q - 3p^2q = -p^2q \]

2. For \(pq^2\):
\[ 2pq^2 + 3pq^2 = 5pq^2 \]

### Step 6: Write the final result
Combining the results from the previous step, we have:
\[ -p^2q + 5pq^2 \]

Thus, the final answer is:
\[ -p^2q + 5pq^2 \]