Factorise `x^(2)-(y-z)^(2)`.

Options

A. `(x+y-z)(x+y+z)`
B. `(x+y-z)(x-y-z)`
C. `(x-y-z)(x-y+z)`
D. `(x+y-z)(x-y+z)`

Explanation

To factorise the expression \( x^2 - (y - z)^2 \), we can follow these steps:

### Step 1: Identify the formula
We will use the difference of squares formula, which states:
\[ a^2 - b^2 = (a + b)(a - b) \]
In our case, we can identify:
- \( a = x \)
- \( b = (y - z) \)

### Step 2: Apply the formula
Using the difference of squares formula, we can rewrite the expression:
\[ x^2 - (y - z)^2 = (x + (y - z))(x - (y - z)) \]

### Step 3: Simplify the factors
Now, we simplify the factors:
1. For the first factor:
\[ x + (y - z) = x + y - z \]
2. For the second factor:
\[ x - (y - z) = x - y + z \]

### Step 4: Write the final factorised form
Putting it all together, we have:
\[ x^2 - (y - z)^2 = (x + y - z)(x - y + z) \]

Thus, the factorised form of \( x^2 - (y - z)^2 \) is:
\[ (x + y - z)(x - y + z) \]