The expression provided is:

$\sqrt{x^2 - 2x + 1} - \sqrt{x^2 + 4x + 4}, \quad \text{for } -2 \leq x \leq 1$

Step-by-Step Simplification:

1. Simplify each square root:

   • The first term is $\sqrt{x^2 - 2x + 1}$. We can factorize the quadratic expression inside the square root: $x^2 - 2x + 1 = (x - 1)^2$ So, we have: $\sqrt{(x - 1)^2} = |x - 1|$

   • The second term is