(2𝑦
2 − 4𝑦 + 5) − (−3𝑦
2 + 1) − (4𝑦 − 2)

To simplify the expression \((2y^2 - 4y + 5) - (-3y^2 + 1) - (4y - 2)\), we can follow these steps:

1. **Distribute the negative signs** to remove the parentheses:
   \[
   2y^2 - 4y + 5 + 3y^2 - 1 - 4y + 2
   \]

2. **Combine like terms** (group the \(y^2\), \(y\), and constant terms):
   - \(y^2\) terms: \(2y^2 + 3y^2 = 5y^2\)
   - \(y\) terms: \(-4y - 4y = -8y\)
   - Constant terms: \(5 - 1 + 2 = 6\)

3. **Write the final simplified expression**:
   \[
   5y^2 - 8y + 6
   \]

This is the simplified form of the given expression.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How do you factor a quadratic expression like \(5y^2 - 8y + 6\)?
2. What are the roots of the quadratic equation \(5y^2 - 8y + 6 = 0\)?
3. How do you complete the square for a quadratic expression?
4. Can you solve a quadratic equation using the quadratic formula?
5. What are the applications of quadratic equations in real-world problems?

**Tip:** Always distribute any negative signs before combining like terms to avoid mistakes in simplification.

Learn how to simplify the expression 2y^2 - 4y + 5 - (-3y^2 + 1) - (4y - 2) step-by-step. This problem covers algebraic simplification and combining like terms. Suitable for students in Grades 7-9.

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