What is the value of `(37+23)^(2)-(37-23)^(2)` ?

Options

A. 1905
B. 1602
C. 1702
D. 3404

Answer

To solve the expression \((37 + 23)^2 - (37 - 23)^2\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\).

### Step-by-step Solution:

1. **Identify \(A\) and \(B\)**:
Let \(A = 37 + 23\) and \(B = 37 - 23\).

2. **Calculate \(A\) and \(B\)**:
\[ A = 37 + 23 = 60 \]
\[ B = 37 - 23 = 14 \]

3. **Apply the difference of squares formula**:
Using the formula \(A^2 - B^2 = (A + B)(A - B)\):
\[ (37 + 23)^2 - (37 - 23)^2 = A^2 - B^2 = (A + B)(A - B) \]

4. **Calculate \(A + B\) and \(A - B\)**:
\[ A + B = 60 + 14 = 74 \]
\[ A - B = 60 - 14 = 46 \]

5. **Multiply the results**:
\[ (A + B)(A - B) = 74 \times 46 \]

6. **Calculate \(74 \times 46\)**:
\[ 74 \times 46 = 3404 \]

### Final Answer:
The value of \((37 + 23)^2 - (37 - 23)^2\) is \(3404\).