If sides of a square is (x+2y-z) units then the area of the square is.......

Answer

To find the area of a square when the side length is given as \( (x + 2y - z) \) units, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the formula for the area of a square**:
The area \( A \) of a square is given by the formula:
\[ A = \text{side} \times \text{side} \]
In this case, the side is \( (x + 2y - z) \).

2. **Substitute the side length into the area formula**:
Substitute the given side length into the area formula:
\[ A = (x + 2y - z) \times (x + 2y - z) \]
This can be simplified to:
\[ A = (x + 2y - z)^2 \]

3. **Expand the expression using the algebraic identity**:
We will use the algebraic identity for the square of a trinomial:
\[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \]
Here, let:
- \( a = x \)
- \( b = 2y \)
- \( c = -z \)

4. **Apply the identity**:
Now, substitute \( a \), \( b \), and \( c \) into the identity:
\[ A = x^2 + (2y)^2 + (-z)^2 + 2(x)(2y) + 2(2y)(-z) + 2(-z)(x) \]

5. **Calculate each term**:
- \( x^2 \) remains \( x^2 \)
- \( (2y)^2 = 4y^2 \)
- \( (-z)^2 = z^2 \)
- \( 2(x)(2y) = 4xy \)
- \( 2(2y)(-z) = -4yz \)
- \( 2(-z)(x) = -2zx \)

6. **Combine all terms**:
Now, combine all the terms to get the final expression for the area:
\[ A = x^2 + 4y^2 + z^2 + 4xy - 4yz - 2zx \]

### Final Answer:
The area of the square is:
\[ A = x^2 + 4y^2 + z^2 + 4xy - 4yz - 2zx \text{ square units} \]