Show that : `(4pq+3q)-(4pq-3q)= 6q`

Answer

To solve the expression \((4pq + 3q) - (4pq - 3q)\) and show that it equals \(6q\), we will follow these steps:

### Step 1: Write down the expression
We start with the left-hand side (LHS) of the equation:
\[ LHS = (4pq + 3q) - (4pq - 3q) \]

### Step 2: Distribute the negative sign
Next, we need to distribute the negative sign across the second part of the expression:
\[ LHS = 4pq + 3q - 4pq + 3q \]

### Step 3: Combine like terms
Now, we will combine the like terms. The \(4pq\) terms will cancel each other out:
\[ LHS = (4pq - 4pq) + (3q + 3q) \]
This simplifies to:
\[ LHS = 0 + 6q \]
Thus, we have:
\[ LHS = 6q \]

### Step 4: Conclusion
Now we can see that:
\[ LHS = 6q \]
This matches the right-hand side (RHS) of the equation, which is also \(6q\). Therefore, we have shown that:
\[ (4pq + 3q) - (4pq - 3q) = 6q \]