Add the polynomial expressions 2r2−3r+4 and −2r2+3r+6 .(1 point)

To add the polynomial expressions \( 2r^2 - 3r + 4 \) and \( -2r^2 + 3r + 6 \), you can combine like terms.

Here’s the step-by-step addition:

1. Write the expressions:
\[
(2r^2 - 3r + 4) + (-2r^2 + 3r + 6)
\]

2. Combine like terms:
- For \( r^2 \) terms: \( 2r^2 + (-2r^2) = 0 \)
- For \( r \) terms: \( -3r + 3r = 0 \)
- For constant terms: \( 4 + 6 = 10 \)

Putting it all together, we have:
\[
0 + 0 + 10 = 10
\]

So, the sum of the two polynomial expressions is:
\[
\boxed{10}
\]

Question Add the expressions. Expression 1: −3k+4k3−2 Expression 2: 9k2−3k3+4k−3 (2 points) k3+ k2+ k+ Remaining Attempts : 3

To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), let's first write them clearly and then combine like terms.

**Expression 1:**
\[ -3k + 4k^3 - 2 \]

**Expression 2:**
\[ 9k^2 - 3k^3 + 4k - 3 \]

Now, let's combine these expressions:

\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

Next, we'll organize them by their degree:

- \( k^3 \) terms: \( 4k^3 - 3k^3 = 1k^3 \)
- \( k^2 \) terms: \( 9k^2 \) (since there is no \( k^2 \) term in Expression 1)
- \( k \) terms: \( -3k + 4k = 1k \)
- Constant terms: \( -2 - 3 = -5 \)

Now, putting it all together, we have:

\[
k^3 + 9k^2 + k - 5
\]

So, the result of adding the two expressions is:

\[
\boxed{k^3 + 9k^2 + k - 5}
\]

Simplify (9x2−6x+2)−(x2+4x−39) .(1 point) The difference of the polynomials is . Remaining Attempts : 3

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), we start by distributing the negative sign through the second polynomial.

Here's the step-by-step process:

1. Write the expression:
\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39)
\]

2. Distribute the negative sign:
\[
9x^2 - 6x + 2 - x^2 - 4x + 39
\]

3. Combine like terms:
- \(x^2\) terms: \(9x^2 - x^2 = 8x^2\)
- \(x\) terms: \(-6x - 4x = -10x\)
- Constant terms: \(2 + 39 = 41\)

Putting it all together, the simplified expression is:
\[
8x^2 - 10x + 41
\]

Thus, the difference of the polynomials is:
\[
\boxed{8x^2 - 10x + 41}
\]

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) 9x2 + x + 13 – 2x2 + 12x + x2 + 5x + 2 Remaining Attempts : 3

Let's first write out the polynomial equation clearly and then perform the subtraction.

We want to subtract the second polynomial from the first one:

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

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

Now, we need to combine the terms in the second expression before performing the subtraction:

1. Combine like terms in the second expression:
- \( 2x^2 + x^2 = 3x^2 \)
- \( 12x + 5x = 17x \)
- The constant term is \( 2 \).

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

Now we can set up our polynomial equation to show the subtraction:

\[
(9x^2 + x + 13) - (3x^2 + 17x + 2)
\]

Now we will perform the subtraction:

1. Distributing the negative sign gives:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

2. Combine the like terms:
- \(9x^2 - 3x^2 = 6x^2\)
- \(x - 17x = -16x\)
- \(13 - 2 = 11\)

Putting it all together, the resulting difference is:
\[
6x^2 - 16x + 11
\]

Thus, the complete polynomial equation that shows the subtraction and the resulting difference is:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

Filling in the blanks:

**First Expression Blank:** \(9x^2 + x + 13\)

**Second Expression Blank:** \(3x^2 + 17x + 2\)

**Resulting Difference Blank:** \(6x^2 - 16x + 11\)

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

incorrect

I apologize for any confusion in my previous response. Let's carefully go through your request again to correctly set up the polynomial equation you've given.

You provided:

1. The first expression: **\(9x^2 + x + 13\)**
2. The second expression: **\(2x^2 + 12x + x^2 + 5x + 2\)**

Let's simplify the second expression:

- Combine like terms in the second expression:
\[
2x^2 + x^2 + 12x + 5x + 2 = (2x^2 + x^2) + (12x + 5x) + 2 = 3x^2 + 17x + 2
\]

Now if we want to subtract the second expression from the first, the setup would be:

### Subtraction Expression
\[
9x^2 + x + 13 - (3x^2 + 17x + 2)
\]

### Performing the Subtraction
1. Distributing the negative sign:
\[
9x^2 + x + 13 - 3x^2 - 17x - 2
\]

2. Combine the like terms:
- For \(x^2\) terms: \(9x^2 - 3x^2 = 6x^2\)
- For \(x\) terms: \(x - 17x = -16x\)
- For constants: \(13 - 2 = 11\)

### Resulting Difference
Therefore, the resulting polynomial after subtraction is:
\[
6x^2 - 16x + 11
\]

### Completing the Blanks
- **First Expression:** \(9x^2 + x + 13\)
- **Second Expression:** \(3x^2 + 17x + 2\) (this is the simplified version of your second expression)
- **Resulting Difference:** \(6x^2 - 16x + 11\)

Putting it all together:
\[
9x^2 + x + 13 - (3x^2 + 17x + 2) = 6x^2 - 16x + 11
\]

Thank you for your patience, and I hope this clears up any confusion! If you have any further questions or need more assistance, feel free to ask.

Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) The sum of the polynomials is . Remaining Attempt

To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we will combine like terms.

### Step 1: Write the expression
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]

### Step 2: Combine like terms

**Combine \(x^2\) terms:**
\[
14x^2 + 0.75x^2 = 14.75x^2
\]

**Combine \(x\) terms:**
\[
-3x + 2x = -1x \quad \text{(or simply } -x\text{)}
\]

**Combine constant terms:**
\[
2.25 - 14 = -11.75
\]

### Step 3: Write the simplified polynomial
Putting it all together, we have:
\[
14.75x^2 - x - 11.75
\]

### Final Answer
The sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]