The sum of two numbers is 104 and their difference is 30. The difference of their squares is-

Options

A. 74
B. 2160
C. 2320
D. 3120

Answer

To solve the problem, we need to find the difference of the squares of two numbers given their sum and difference.

Let's denote the two numbers as \( A \) and \( B \).

### Step 1: Set up the equations
We are given:
1. The sum of the two numbers:
\[ A + B = 104 \quad \text{(1)} \]
2. The difference of the two numbers:
\[ A - B = 30 \quad \text{(2)} \]

### Step 2: Use the difference of squares formula
The difference of their squares can be expressed as:
\[ A^2 - B^2 = (A + B)(A - B) \]

### Step 3: Substitute the known values
From equations (1) and (2), we can substitute the values:
- \( A + B = 104 \)
- \( A - B = 30 \)

Now substituting these values into the difference of squares formula:
\[ A^2 - B^2 = (104)(30) \]

### Step 4: Calculate the product
Now we calculate:
\[ 104 \times 30 = 3120 \]

### Conclusion
Thus, the difference of their squares is:
\[ A^2 - B^2 = 3120 \]