why dont the negative signs between - 4y + 5 change, but the signs between 4y - 2 change

Great question! The difference in how the signs change depends on whether there's a negative sign directly in front of the expression inside the parentheses. Let's break it down:

### Expression 1: \((2y^2 - 4y + 5)\)
- This expression is not preceded by a negative sign outside the parentheses, so **no signs change** when the parentheses are removed. It's as if you’re just writing it out again:
  \[
  2y^2 - 4y + 5
  \]

### Expression 2: \(-(-3y^2 + 1)\)
- Here, there is a negative sign in front of the parentheses. This negative sign affects everything inside the parentheses. When you remove the parentheses, you **change the sign** of each term inside:
  \[
  -(-3y^2 + 1) = 3y^2 - 1
  \]

### Expression 3: \(-(4y - 2)\)
- Again, there's a negative sign outside the parentheses, so it changes the sign of each term inside the parentheses when removed:
  \[
  -(4y - 2) = -4y + 2
  \]

### Summary
- **If there's no negative sign** outside the parentheses (like in \(2y^2 - 4y + 5\)), then the signs of the terms inside **remain the same** when the parentheses are removed.
- **If there is a negative sign** directly in front of the parentheses (like in \(-(-3y^2 + 1)\) and \(-(4y - 2)\)), then the signs of all terms inside **are reversed** when the parentheses are removed.

Would you like further clarification or have any other questions?

Here are some related questions you might find helpful:
1. What is the distributive property, and how does it work with negative signs?
2. How do you simplify expressions with multiple sets of parentheses?
3. How do positive and negative signs affect multiplication and division?
4. What are the rules for combining like terms in algebraic expressions?
5. How can you check your work when simplifying algebraic expressions?

**Tip:** Always be cautious with negative signs, especially when they are outside parentheses. Misinterpreting them is a common source of errors in algebra.

Explore why negative signs in algebraic expressions behave differently based on their placement inside or outside parentheses. This detailed explanation covers the rules for changing signs when simplifying expressions and includes examples for clarity. Suitable for Grades 7-9.

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