Expand using suitable identity `(2x-3y+z)^(2)`.

Answer

To expand the expression \((2x - 3y + z)^2\) using the suitable identity, we will follow these steps:

### Step 1: Identify the identity
We will use the algebraic identity for the square of a trinomial:
\[ (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca \]
In our case, we can identify:
- \(a = 2x\)
- \(b = -3y\)
- \(c = z\)

### Step 2: Substitute into the identity
Now, we substitute \(a\), \(b\), and \(c\) into the identity:
\[ (2x - 3y + z)^2 = (2x)^2 + (-3y)^2 + z^2 + 2(2x)(-3y) + 2(-3y)(z) + 2(z)(2x) \]

### Step 3: Calculate each term
Now, we will calculate each term:
1. \( (2x)^2 = 4x^2 \)
2. \( (-3y)^2 = 9y^2 \)
3. \( z^2 = z^2 \)
4. \( 2(2x)(-3y) = -12xy \)
5. \( 2(-3y)(z) = -6yz \)
6. \( 2(z)(2x) = 4zx \)

### Step 4: Combine all the terms
Now, we combine all the calculated terms:
\[ (2x - 3y + z)^2 = 4x^2 + 9y^2 + z^2 - 12xy - 6yz + 4zx \]

### Final Answer
Thus, the expanded form of \((2x - 3y + z)^2\) is:
\[ 4x^2 + 9y^2 + z^2 - 12xy - 6yz + 4zx \]

---