1. **State the problem:** Given $x = -1234567$, find the value of the expression $$\sqrt{100 - 20x + x^2} - \sqrt{x^2}$$ 2. **Recall the formula and rules:** - The square root of a square is the absolute value: $\sqrt{x^2} = |x|$. - The expression inside the first square root can be simplified by recognizing it as a perfect square: $$100 - 20x + x^2 = (x - 10)^2$$ 3. **Simplify the expression:** $$\sqrt{100 - 20x + x^2} - \sqrt{x^2} = \sqrt{(x - 10)^2} - |x| = |x - 10| - |x|$$ 4. **Evaluate the absolute values:** Since $x = -1234567$: - $|x| = |-1234567| = 1234567$ - $x - 10 = -1234567 - 10 = -1234577$ - $|x - 10| = |-1234577| = 1234577$ 5. **Calculate the final value:** $$|x - 10| - |x| = 1234577 - 1234567 = 10$$ **Final answer:** 10 This corresponds to option (B).