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Let's solve the given mathematical expression step by step:

\[
\sqrt{8} - 2 \sin 30^\circ - |1 - \sqrt{2}| + \left(\frac{1}{2}\right)^{-2} - (\pi - 2020)^0
\]

1. **Simplify each term:**

   - \(\sqrt{8}\):
     \[
     \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
     \]
   - \(\sin 30^\circ\):
     \[
     \sin 30^\circ = \frac{1}{2}
     \]
   - \(2 \sin 30^\circ\):
     \[
     2 \sin 30^\circ = 2 \times \frac{1}{2} = 1
     \]
   - \(|1 - \sqrt{2}|\):
     \[
     \sqrt{2} \approx 1.414 \Rightarrow 1 - \sqrt{2} \approx 1 - 1.414 = -0.414 \Rightarrow |1 - \sqrt{2}| = 0.414
     \]
   - \(\left(\frac{1}{2}\right)^{-2}\):
     \[
     \left(\frac{1}{2}\right)^{-2} = \left(\frac{2}{1}\right)^2 = 2^2 = 4
     \]
   - \((\pi - 2020)^0\):
     \[
     (\pi - 2020)^0 = 1
     \]

2. **Substitute back into the expression:**

   \[
   2\sqrt{2} - 1 - 0.414 + 4 - 1
   \]

3. **Combine and simplify:**

   - Combine the constants:
     \[
     -1 - 0.414 - 1 = -2.414
     \]
   - Combine the entire expression:
     \[
     2\sqrt{2} - 2.414 + 4
     \]
   - Simplify further:
     \[
     2\sqrt{2} + 1.586
     \]

So, the simplified value of the given expression is:
\[
2\sqrt{2} + 1.586 \approx 4.414
\]

Would you like details or have any questions?

Here are 5 more questions you can ask:

1. How do I solve a quadratic equation using the quadratic formula?
2. What are the properties of logarithmic functions?
3. Can you explain how to find the derivative of a function?
4. How do I calculate the area under a curve using integration?
5. What are the common trigonometric identities and how are they used?

**Tip:** When solving complex expressions, break them down into simpler parts and solve each part step by step to avoid errors.

Learn how to simplify a mathematical expression involving square roots, trigonometric functions, and exponents step by step. This problem covers key mathematical concepts such as arithmetic, trigonometry, algebra, and exponents. Suitable for high school students.

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