We are asked to simplify the expression:

$-\left(5m^2 - 2m - 5\right) - \left(4 - 3m - 4m^2\right)$

Let's go step by step.

Step 1: Distribute the negative signs

First, distribute the negative sign in both parentheses.

$-\left(5m^2 - 2m - 5\right) = -5m^2 + 2m + 5$ $-\left(4 - 3m - 4m^2\right) = -4 + 3m + 4m^2$

Step 2: Combine the terms

Now we rewrite the entire expression after distribution:

$-5m^2 + 2m + 5 - 4 + 3m + 4m^2$

Now, let's combine like terms:

• Combine $-5m^2$ and $4m^2$: $-5m^2 + 4m^2 = -m^2$
• Combine $2m$ and $3m$: $2m + 3m = 5m$
• Combine constants $5$ and $-4$: $5 - 4 = 1$

Final simplified expression:

$-m^2 + 5m + 1$

This matches the expression given in the problem.

Would you like further details on any of these steps?

Here are 5 related questions to deepen your understanding:

1. How do you distribute a negative sign across a polynomial?
2. Can you simplify $-(a - b) - (c + d)$?
3. How do you identify and combine like terms in an expression?
4. What happens if both parentheses contain terms with different variables?
5. How would the process change if you were asked to factor instead of simplify?

Tip: Always combine like terms only after distributing negative signs to avoid errors in sign changes.