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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

Simplify the expression: sqrt(x^2 - 2x + 1) - sqrt(x^2 + 4x + 4), for -2 ≤ x ≤ 1.

This problem simplifies the expression sqrt(x^2 - 2x + 1) - sqrt(x^2 + 4x + 4), focusing on key algebraic concepts like factoring and square root properties. Ideal for students in Grades 9-11, learn step-by-step methods for simplifying such expressions.

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