Let's fully simplify the given expression step by step without calculating each part individually until the end:

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

1. **Simplify each component within the expression:**

   - \(\sqrt{8} = 2\sqrt{2}\)
   - \(\sin 30^\circ = \frac{1}{2}\)
   - \(2 \sin 30^\circ = 2 \times \frac{1}{2} = 1\)
   - \(|1 - \sqrt{2}|\)
     \[
     1 - \sqrt{2} \text{ is negative, so } |1 - \sqrt{2}| = \sqrt{2} - 1
     \]
   - \(\left(\frac{1}{2}\right)^{-2} = 2^2 = 4\)
   - \((\pi - 2020)^0 = 1\)

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

\[
2\sqrt{2} - 1 - (\sqrt{2} - 1) + 4 - 1
\]

3. **Combine like terms:**

Combine constants and \(\sqrt{2}\) terms separately:

   - Constants:
     \[
     -1 + 4 - 1 = 2
     \]
   - \(\sqrt{2}\) terms:
     \[
     2\sqrt{2} - \sqrt{2} = \sqrt{2}
     \]

4. **Combine everything:**

\[
\sqrt{2} + 2
\]

So, the fully simplified expression is:

\[
\sqrt{2} + 2
\]

Would you like details or have any questions?

Here are 5 more questions you can ask:

1. How do you solve systems of linear equations using matrices?
2. What are the properties of exponential functions?
3. Can you explain how to integrate by parts?
4. How do you determine the convergence of a series?
5. What is the binomial theorem and how is it used?

**Tip:** Simplify mathematical expressions by handling each part step by step and combining like terms before performing any calculations.

Learn how to simplify a complex mathematical expression step-by-step without performing individual calculations until fully simplified. This problem involves key concepts such as square roots, trigonometric functions, absolute value, and exponentiation, suitable for high school students.

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