Evaluate: `(4a + 3b)^(2)- (4a-3b)^(2) + 48ab`

Answer

To evaluate the expression \((4a + 3b)^{2} - (4a - 3b)^{2} + 48ab\), we can follow these steps:

### Step 1: Expand the squares
We will use the formula for the square of a binomial, which states that \((x + y)^{2} = x^{2} + 2xy + y^{2}\) and \((x - y)^{2} = x^{2} - 2xy + y^{2}\).

1. Expand \((4a + 3b)^{2}\):
\[ (4a + 3b)^{2} = (4a)^{2} + 2(4a)(3b) + (3b)^{2} = 16a^{2} + 24ab + 9b^{2} \]

2. Expand \((4a - 3b)^{2}\):
\[ (4a - 3b)^{2} = (4a)^{2} - 2(4a)(3b) + (3b)^{2} = 16a^{2} - 24ab + 9b^{2} \]

### Step 2: Substitute the expanded forms into the expression
Now, substitute the expanded forms back into the original expression:
\[ (16a^{2} + 24ab + 9b^{2}) - (16a^{2} - 24ab + 9b^{2}) + 48ab \]

### Step 3: Simplify the expression
Now, simplify the expression by distributing the negative sign:
\[ 16a^{2} + 24ab + 9b^{2} - 16a^{2} + 24ab - 9b^{2} + 48ab \]

### Step 4: Combine like terms
Now, combine the like terms:
- The \(16a^{2}\) terms cancel out:
\[ 16a^{2} - 16a^{2} = 0 \]
- The \(9b^{2}\) terms also cancel out:
\[ 9b^{2} - 9b^{2} = 0 \]
- Combine the \(ab\) terms:
\[ 24ab + 24ab + 48ab = 96ab \]

### Final Result
Thus, the final result is:
\[ \boxed{96ab} \]