https://file.aiquickdraw.com/mathbot/file/172675268048748mktzu4.jpg

Let's go through the two problems shown in the image one by one.

### Problem 1:
You are given two polynomials:
\[
A = 4x^2 + 9x - 5 \quad \text{and} \quad B = 6x^2 - 3x - 9
\]
The question asks for \(A - B\).

We subtract \(B\) from \(A\):
\[
A - B = (4x^2 + 9x - 5) - (6x^2 - 3x - 9)
\]

Now, distribute the negative sign to each term in \(B\):
\[
A - B = 4x^2 + 9x - 5 - 6x^2 + 3x + 9
\]

Combine like terms:
\[
(4x^2 - 6x^2) + (9x + 3x) + (-5 + 9) = -2x^2 + 12x + 4
\]

Thus, the correct answer is:
\[
\boxed{-2x^2 + 12x + 4}
\]
So the correct option is **(C)**.

---

### Problem 2:
The expression to simplify is:
\[
(5x - 4)^2
\]

Use the formula for expanding a binomial square:
\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = 5x\) and \(b = 4\). Apply the formula:
\[
(5x - 4)^2 = (5x)^2 - 2(5x)(4) + (4)^2
\]

Simplify each term:
\[
(5x)^2 = 25x^2, \quad -2(5x)(4) = -40x, \quad 4^2 = 16
\]

So:
\[
(5x - 4)^2 = 25x^2 - 40x + 16
\]

Thus, the correct answer is:
\[
\boxed{25x^2 - 40x + 16}
\]
So the correct option is **(C)**.

---

Would you like more details on these steps or additional explanations?

### Here are 5 related questions:
1. How do you combine like terms when subtracting polynomials?
2. What are the rules for expanding binomials like \((a - b)^2\)?
3. Can you explain how to distribute negative signs in polynomial subtraction?
4. How do you factor a trinomial back into a binomial squared form?
5. How does the degree of a polynomial affect its graph?

### Tip:
When expanding binomials, always check your middle term carefully—it's easy to miss the negative signs or coefficient multiplications.

If A = 4x^2 + 9x - 5 and B = 6x^2 - 3x - 9, find A - B. Simplify (5x - 4)^2.

This solution explains how to subtract two polynomials and expand a binomial square. Learn step-by-step methods for A - B and (5x - 4)^2, including polynomial subtraction and the binomial expansion formula. Suitable for high school students in Grades 9-11.

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