If `x^(2) - y^(2) = 28` and x + y = 7 then `(x - y)^(2) = "_________"` .

Options

A. 8
B. 4
C. 16
D. 12

Explanation

To solve the problem step by step, we start with the given equations:

1. **Given Equations**:
- \( x^2 - y^2 = 28 \) (1)
- \( x + y = 7 \) (2)

2. **Using the Difference of Squares**:
The expression \( x^2 - y^2 \) can be factored using the difference of squares formula:
\[ x^2 - y^2 = (x + y)(x - y) \]
Substituting equation (2) into this gives:
\[ (x + y)(x - y) = 28 \]
\[ 7(x - y) = 28 \]

3. **Solving for \( x - y \)**:
To find \( x - y \), we divide both sides by 7:
\[ x - y = \frac{28}{7} = 4 \]

4. **Finding \( (x - y)^2 \)**:
Now, we need to find \( (x - y)^2 \):
\[ (x - y)^2 = 4^2 = 16 \]

Thus, the final answer is:
\[ (x - y)^2 = 16 \]