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
We start with the expression:
\[ 2pq(p + q) - 3pq(p - q) \]

### Step 2: Distribute the terms
Next, we will distribute \(2pq\) and \(3pq\) into their respective brackets:
\[ 2pq(p + q) = 2pq \cdot p + 2pq \cdot q = 2p^2q + 2pq^2 \]
\[ 3pq(p - q) = 3pq \cdot p - 3pq \cdot q = 3p^2q - 3pq^2 \]

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

### Step 4: Simplify the expression
Now we simplify the expression by distributing the negative sign:
\[ 2p^2q + 2pq^2 - 3p^2q + 3pq^2 \]

### Step 5: Combine like terms
Next, we combine the like terms:
- For \(p^2q\): \(2p^2q - 3p^2q = -1p^2q\)
- For \(pq^2\): \(2pq^2 + 3pq^2 = 5pq^2\)

So, we have:
\[ -p^2q + 5pq^2 \]

### Final Result
The final result of the expression after subtracting \(3pq(p-q)\) from \(2pq(p+q)\) is:
\[ -p^2q + 5pq^2 \]

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