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The image contains three mathematical problems where the task is to simplify or modify expressions by adding or subtracting specific terms.

Here’s a breakdown of each:

1. **First expression:**
   The given expression is:
   \[
   2x^2 + 4x - 5
   \]
   And you need to modify it using:
   \[
   2(x+1)^2 - 7
   \]
   This likely means you need to complete the square and express \( 2x^2 + 4x - 5 \) in a similar form, or simplify after performing some additions/subtractions.

2. **Second expression:**
   The given expression is:
   \[
   x^2 + 2x
   \]
   And you need to modify it using:
   \[
   (x+1)^2 - 1
   \]
   This involves recognizing that \( (x+1)^2 = x^2 + 2x + 1 \), and subtracting 1 will give you \( x^2 + 2x \), so this should simplify directly.

3. **Third expression:**
   The given expression is:
   \[
   2x^2 + 8x - 2
   \]
   And you need to modify it using:
   \[
   2(x+2)^2 - 10
   \]
   Again, this likely involves completing the square and comparing with the given structure.

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Would you like to see step-by-step solutions for any or all of these expressions? Here are five related questions to expand on this:

1. How can completing the square help in simplifying quadratic expressions?
2. What are the general steps to rewrite quadratic expressions in the form of a perfect square?
3. What role do constants play when manipulating expressions involving squares?
4. How do you recognize common patterns between different quadratic expressions?
5. Why is subtracting or adding constants important in these types of problems?

**Tip:** Completing the square is a useful technique when simplifying or solving quadratic equations, especially for expressing them in vertex form.

Při úpravě výrazu 2x^2 + 4x - 5 na výraz 2(x+1)^2 - 7 začneme přičtením a následným odečtením výrazu.

Learn how to simplify quadratic expressions such as 2x^2 + 4x - 5 using the method of completing the square, and modify them to forms like 2(x+1)^2 - 7. Explore detailed steps suitable for high school students in Grades 9-12.

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