Expand `(4x-3y-2z)^(2)` .

Answer

To expand the expression \((4x - 3y - 2z)^2\), we can use the formula for the square of a trinomial, which is given by:

\[ (a - b - c)^2 = a^2 + b^2 + c^2 - 2ab - 2ac + 2bc \]

Here, we will identify:
- \(a = 4x\)
- \(b = 3y\)
- \(c = 2z\)

Now, we will apply the formula step by step.

### Step 1: Calculate \(a^2\)
\[ a^2 = (4x)^2 = 16x^2 \]

### Step 2: Calculate \(b^2\)
\[ b^2 = (3y)^2 = 9y^2 \]

### Step 3: Calculate \(c^2\)
\[ c^2 = (2z)^2 = 4z^2 \]

### Step 4: Calculate \(-2ab\)
\[ -2ab = -2(4x)(3y) = -24xy \]

### Step 5: Calculate \(-2ac\)
\[ -2ac = -2(4x)(2z) = -16xz \]

### Step 6: Calculate \(2bc\)
\[ 2bc = 2(3y)(2z) = 12yz \]

### Step 7: Combine all the results
Now, we can combine all the calculated components:
\[ (4x - 3y - 2z)^2 = a^2 + b^2 + c^2 - 2ab - 2ac + 2bc \]
Substituting the values we calculated:
\[ = 16x^2 + 9y^2 + 4z^2 - 24xy - 16xz + 12yz \]

### Final Answer
Thus, the expanded form of \((4x - 3y - 2z)^2\) is:
\[ 16x^2 + 9y^2 + 4z^2 - 24xy - 16xz + 12yz \]