Fill in the blanks to complete the polynomial equation that shows the subtraction of the second expression from the first and the resulting difference. (2 points)

To complete the polynomial equation, we will subtract the second expression from the first and determine the resulting difference.

Given the first expression:
\( 9x^2 + x + 13 \)

And the second expression:
\( 2x^2 + 12x + (x^2 + 5x + 2) \)

First, we need to combine the terms of the second expression:

- Combine the \( x^2 \) terms:
- \( 2x^2 + x^2 = 3x^2 \)

- Combine the \( x \) terms:
- \( 12x + 5x = 17x \)

- The constant term remains \( 2 \).

Thus, the second expression simplifies to:
\( 3x^2 + 17x + 2 \)

Now, we can perform the subtraction:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

Distributing the negative sign across the terms of the second expression:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

Now, combine like terms.
1. For \( x^2 \) terms:
- \( 9x^2 - 3x^2 = 6x^2 \)

2. For \( x \) terms:
- \( x - 17x = -16x \)

3. For constant terms:
- \( 13 - 2 = 11 \)

Therefore, the resulting expression after subtracting is:
\[
6x^2 - 16x + 11
\]

Now we can fill in the blanks:

- The term representing the missing expression after subtraction is \( 3x^2 + 17x + 2 \).
- The resulting difference is \( 6x^2 - 16x + 11 \).

So the completed polynomial equation is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

bot are you sure?

Let’s go through the problem step by step again to ensure accuracy.

1. **First Expression**:
\[
9x^2 + x + 13
\]

2. **Second Expression**:
\[
2x^2 + 12x + (x^2 + 5x + 2)
\]

We need to simplify the second expression first:

- Combine \( x^2 \) terms:
\[
2x^2 + x^2 = 3x^2
\]
- Combine \( x \) terms:
\[
12x + 5x = 17x
\]
- The constant term remains \( 2 \).

Therefore, the second expression simplifies to:
\[
3x^2 + 17x + 2
\]

3. **Now we perform the subtraction**:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

When we distribute the negative sign:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

4. **Combining like terms**:
- For \( x^2 \) terms:
\[
9x^2 - 3x^2 = 6x^2
\]
- For \( x \) terms:
\[
x - 17x = -16x
\]
- For constants:
\[
13 - 2 = 11
\]

Therefore, the final result after performing the subtraction is:
\[
6x^2 - 16x + 11
\]

So the filled in polynomial equation is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

This result appears to be accurate based on the calculations provided. If there's anything specific you'd like to clarify or if I misunderstood your question, please let me know!

bot each equation needs to be separate from each other

I understand now that you want the equations separated clearly to show the subtraction process step by step. Let’s format it properly.

1. **First Expression**:
\[
9x^2 + x + 13
\]

2. **Second Expression**:
\[
2x^2 + 12x + (x^2 + 5x + 2)
\]

Simplifying the second expression:
- Combine \( x^2 \) terms:
\[
2x^2 + x^2 = 3x^2
\]
- Combine \( x \) terms:
\[
12x + 5x = 17x
\]
- The constant term remains:
\[
+ 2
\]

So the second expression becomes:
\[
3x^2 + 17x + 2
\]

3. **Subtraction Setup**:
We want to subtract the second expression from the first:
\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

4. **Distributing the Negative Sign**:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

5. **Combine Like Terms**:
- For \( x^2 \) terms:
\[
9x^2 - 3x^2 = 6x^2
\]
- For \( x \) terms:
\[
x - 17x = -16x
\]
- For the constant terms:
\[
13 - 2 = 11
\]

6. **Final Result**:
Thus, the result of the subtraction is:
\[
6x^2 - 16x + 11
\]

Finally, putting it all together, the filled-in polynomial equation, clearly separated, looks like this:

\[
9x^2 + x + 13
\]
\[
- (3x^2 + 17x + 2)
\]
\[
= 6x^2 - 16x + 11
\]

If this format is what you were looking for, let me know! Thank you for your patience.