Simplify: `(1- 3omega + omega^(2)) (1 + omega- 3omega^(2))`

Answer

To simplify the expression \((1 - 3\omega + \omega^2)(1 + \omega - 3\omega^2)\), we will follow these steps:

### Step 1: Identify the property of \(\omega\)
We know that for the cube roots of unity, the following property holds:
\[ 1 + \omega + \omega^2 = 0 \]
From this, we can express \(\omega^2\) in terms of \(\omega\):
\[ \omega^2 = -1 - \omega \]

### Step 2: Substitute \(\omega^2\) in the expression
Now, let's substitute \(\omega^2\) in the original expression:
\[ (1 - 3\omega + (-1 - \omega))(1 + \omega - 3(-1 - \omega)) \]
This simplifies to:
\[ (1 - 3\omega - 1 - \omega)(1 + \omega + 3 + 3\omega) \]
Which further simplifies to:
\[ (-4\omega)(4 + 4\omega) \]

### Step 3: Multiply the two factors
Now we will multiply the two factors:
\[ -4\omega \cdot (4 + 4\omega) = -4\omega \cdot 4 - 4\omega \cdot 4\omega \]
This gives:
\[ -16\omega - 16\omega^2 \]

### Step 4: Substitute \(\omega^2\) again
Now we substitute \(\omega^2\) back into the expression:
\[ -16\omega - 16(-1 - \omega) = -16\omega + 16 + 16\omega \]
This simplifies to:
\[ 16 \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{16} \]