Simplify :
`-3(1-x^(2)) - 2{x^(2) - (3-2x^(2))}`

Answer

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

### Step 1: Distribute the terms in the first bracket
We start with the first part of the expression:
\[ -3(1 - x^2) = -3 \cdot 1 + 3 \cdot x^2 = -3 + 3x^2 \]
So, the expression now looks like:
\[ -3 + 3x^2 - 2(x^2 - (3 - 2x^2)) \]

### Step 2: Simplify the second bracket
Next, we simplify the second part:
\[ x^2 - (3 - 2x^2) = x^2 - 3 + 2x^2 = 3x^2 - 3 \]
Thus, we replace the second bracket in the expression:
\[ -3 + 3x^2 - 2(3x^2 - 3) \]

### Step 3: Distribute the \(-2\) across the second bracket
Now, we distribute \(-2\):
\[ -2(3x^2) + 2(3) = -6x^2 + 6 \]
So, the expression now becomes:
\[ -3 + 3x^2 - 6x^2 + 6 \]

### Step 4: Combine like terms
Now, we combine the like terms:
1. Combine the \(x^2\) terms: \(3x^2 - 6x^2 = -3x^2\)
2. Combine the constant terms: \(-3 + 6 = 3\)

Putting it all together, we have:
\[ -3x^2 + 3 \]

### Final Expression
Thus, the simplified expression is:
\[ 3 - 3x^2 \]