1. The problem is to find the expression for $N^2 \times 2$ given $N(x) = 2 - 2x$. 2. First, understand that $N^2$ means $N(x)$ squared, or $(2 - 2x)^2$. 3. The formula for squaring a binomial $(a - b)^2$ is $a^2 - 2ab + b^2$. 4. Applying this, we get: $$ (2 - 2x)^2 = 2^2 - 2 \times 2 \times 2x + (2x)^2 = 4 - 8x + 4x^2 $$ 5. Now multiply this result by 2: $$ 2 \times (4 - 8x + 4x^2) = 8 - 16x + 8x^2 $$ 6. So, the final expression for $N^2 \times 2$ is: $$ 8 - 16x + 8x^2 $$ This completes the problem.