12-(4-x)²+ x×(3-x)

To simplify the expression \( 12 - (4 - x)^2 + x \times (3 - x) \), we can follow these steps:

1. Expand \( (4 - x)^2 \): \[ (4 - x)^2 = 16 - 8x + x^2 \]

2. Substitute back into the expression: \[ 12 - (16 - 8x + x^2) + x(3 - x) \] Distributing the negative sign: \[ 12 - 16 + 8x - x^2 + 3x - x^2 \]

3. Combine like terms: \[ 12 - 16 + 8x + 3x - x^2 - x^2 = -4 + 11x - 2x^2 \]

4. Rearranging the expression: \[ -2x^2 + 11x - 4 \]

Thus, the simplified form of the expression \( 12 - (4 - x)^2 + x(3 - x) \) is: \[ -2x^2 + 11x - 4 \]