If `x -y = -6 and x + y= 16,` then `x ^(2) - y ^(2)` is

Options

A. 96
B. `-96`
C. 22
D. `-22`

Answer

To solve the problem, we need to find the value of \( x^2 - y^2 \) given the equations \( x - y = -6 \) and \( x + y = 16 \).

### Step-by-Step Solution:

1. **Use the algebraic identity**:
We know that \( x^2 - y^2 \) can be expressed using the identity:
\[ x^2 - y^2 = (x - y)(x + y) \]

2. **Substitute the given values**:
From the problem, we have:
\[ x - y = -6 \quad \text{and} \quad x + y = 16 \]
Now, substitute these values into the identity:
\[ x^2 - y^2 = (-6)(16) \]

3. **Calculate the product**:
Now, we perform the multiplication:
\[ x^2 - y^2 = -6 \times 16 = -96 \]

4. **Final answer**:
Therefore, the value of \( x^2 - y^2 \) is:
\[ x^2 - y^2 = -96 \]