Expand: `(x+y- z)^(2)`

Answer

To expand the expression \((x + y - z)^2\), we can use the formula for the square of a binomial, which states that \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\). In this case, we treat \(-z\) as a negative term.

### Step-by-Step Solution:

1. **Identify the terms**:
We have three terms in the expression: \(x\), \(y\), and \(-z\).

2. **Apply the expansion formula**:
Using the formula \((a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca\), we can substitute \(a = x\), \(b = y\), and \(c = -z\).

3. **Calculate \(a^2\), \(b^2\), and \(c^2\)**:
- \(x^2\) (which is \(a^2\))
- \(y^2\) (which is \(b^2\))
- \((-z)^2 = z^2\) (which is \(c^2\))

4. **Calculate the cross terms**:
- \(2ab = 2xy\)
- \(2bc = 2y(-z) = -2yz\)
- \(2ca = 2(-z)x = -2zx\)

5. **Combine all parts**:
Putting it all together, we have:
\[ (x + y - z)^2 = x^2 + y^2 + z^2 + 2xy - 2yz - 2zx \]

### Final Expanded Form:
\[ (x + y - z)^2 = x^2 + y^2 + z^2 + 2xy - 2yz - 2zx \]