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We are tasked with subtracting \( 9x^2 + 4x \) from \( -4x^2 - 7 \). Let's go step by step:

### Given expression:
We need to perform:

\[
\left( -4x^2 - 7 \right) - \left( 9x^2 + 4x \right)
\]

### Step 1: Distribute the negative sign across \( 9x^2 + 4x \):

\[
-4x^2 - 7 - 9x^2 - 4x
\]

### Step 2: Combine like terms:
- Combine the \( x^2 \) terms: \( -4x^2 - 9x^2 = -13x^2 \)
- Combine the \( x \) terms: There is only \( -4x \).
- The constant term is \( -7 \).

Thus, the simplified expression is:

\[
-13x^2 - 4x - 7
\]

So the answer is:

\[
-13x^2 - 4x - 7
\]

Would you like further details or have any questions? 

Here are some related questions:
1. How do you combine like terms in polynomial expressions?
2. What happens if you subtract two expressions with the same variable powers?
3. Can you explain how negative signs are distributed in polynomial subtraction?
4. What are the rules for subtracting a polynomial from another polynomial?
5. How can you verify your solution by expanding the result?

**Tip**: Always be careful when distributing negative signs across multiple terms in parentheses!

Learn how to subtract the polynomial 9x^2 + 4x from -4x^2 - 7 step-by-step. This problem explains polynomial subtraction, combining like terms, and distribution. Suitable for students in Grades 8-10.

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