To simplify the given expression:

$(-2y^2 + 5y + 4) + (9y^2 + 7y - 7) - (5y^2 - 4y - 3)$

we will follow these steps:

Step 1: Distribute the negative sign to the third group

The negative sign before the third group affects all terms inside the parentheses:

$(-2y^2 + 5y + 4) + (9y^2 + 7y - 7) - 5y^2 + 4y + 3$

Step 2: Combine like terms

Combine $y^2$ terms:

$-2y^2 + 9y^2 - 5y^2 = 2y^2$

Combine $y$ terms:

$5y + 7y + 4y = 16y$

Combine constant terms:

$4 - 7 + 3 = 0$

Final Simplified Expression:

$2y^2 + 16y$

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. How would the process differ if there were more variables?
2. Can you explain the importance of distributing negative signs in expressions?
3. How do you simplify polynomials with higher degrees (e.g., $y^3$)?
4. What is the general approach for combining like terms in an expression?
5. How would you factor the simplified expression $2y^2 + 16y$?

Tip: Always remember to apply the distributive property carefully when dealing with parentheses in algebraic expressions.