Add the polynomial expressions 2r2−3r+4

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

1. Combine the \( r^2 \) terms:
\[
2r^2 + (-2r^2) = 0r^2
\]

2. Combine the \( r \) terms:
\[
-3r + 3r = 0r
\]

3. Combine the constant terms:
\[
4 + 6 = 10
\]

Putting it all together, we have:
\[
0r^2 + 0r + 10 = 10
\]

Thus, the sum of the two polynomials is \( \boxed{10} \).

Add the expressions.

Expression 1: −3k+4k3−2


Expression 2: 9k2−3k3+4k−3


(2 points)

To add the expressions \( -3k + 4k^3 - 2 \) and \( 9k^2 - 3k^3 + 4k - 3 \), we'll combine like terms.

**Expression 1:**
\(-3k + 4k^3 - 2\)

**Expression 2:**
\(9k^2 - 3k^3 + 4k - 3\)

Now, let's arrange and group the like terms:

1. **Cubic Terms (\(k^3\))**:
\(4k^3 - 3k^3 = 1k^3\)

2. **Quadratic Terms (\(k^2\))**:
\(0k^2 + 9k^2 = 9k^2\)

3. **Linear Terms (\(k\))**:
\(-3k + 4k = 1k\)

4. **Constant Terms**:
\(-2 - 3 = -5\)

Putting all these together, we get the final result:

\[
1k^3 + 9k^2 + 1k - 5
\]

Thus, the added expression can be written as:

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

The final answer is \( \boxed{k^3 + 9k^2 + k - 5} \).

try again please

Let’s carefully add the two expressions step-by-step:

### Given Expressions

**Expression 1:**
\(-3k + 4k^3 - 2\)

**Expression 2:**
\(9k^2 - 3k^3 + 4k - 3\)

### Step 1: Write the expressions together

Combine both expressions:

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

### Step 2: Rearrange and group like terms

Now we can group all the \(k^3\), \(k^2\), \(k\), and constant terms:

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

### Step 3: Combine like terms

1. **Cubic Terms (\(k^3\))**:
\[
4k^3 - 3k^3 = 1k^3
\]

2. **Quadratic Terms (\(k^2\))**:
\[
0k^2 + 9k^2 = 9k^2
\]

3. **Linear Terms (\(k\))**:
\[
-3k + 4k = 1k
\]

4. **Constant Terms**:
\[
-2 - 3 = -5
\]

### Final Result

Putting it all together gives us:

\[
1k^3 + 9k^2 + 1k - 5
\]

This can be written more simply as:

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

Therefore, the final answer is \( \boxed{k^3 + 9k^2 + k - 5} \).

Simplify (9x2−6x+2)−(x2+4x−39)

.(1 point)
The difference of the polynomials is
.

To simplify the expression \( (9x^2 - 6x + 2) - (x^2 + 4x - 39) \), we will first distribute the negative sign across the second polynomial and then combine like terms.

### Step 1: Distributing the negative sign

\[
(9x^2 - 6x + 2) - (x^2 + 4x - 39) = 9x^2 - 6x + 2 - x^2 - 4x + 39
\]

### Step 2: Combine like terms

Now, we group the terms:

1. **Quadratic terms (\(x^2\))**:
\[
9x^2 - x^2 = 8x^2
\]

2. **Linear terms (\(x\))**:
\[
-6x - 4x = -10x
\]

3. **Constant terms**:
\[
2 + 39 = 41
\]

### Step 3: Write the simplified expression

Combining all of these, we get:

\[
8x^2 - 10x + 41
\]

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

To fill in the blanks, we need to set up the subtraction of the second polynomial from the first polynomial and also show the resulting difference.

### Starting Polynomial Expressions
1. **First Polynomial (Expression 1)**:
\( 9x^2 + x + 13 \)

2. **Second Polynomial (Expression 2)**:
\( 2x^2 - 12x - (x^2 + 5x + 2) \)

Let's correctly set this up step-by-step:

### Step 1: Formatting the Equation
To subtract the second polynomial, we rewrite it such that we switch the signs of the terms in the second polynomial:

\[
(9x^2 + x + 13) - (2x^2 + 12x + (x^2 + 5x + 2))
\]

This can also be rephrased as:

\[
(9x^2 + x + 13) - (2x^2 + 12x + 2x^2 + 5x + 2)
\]

### Step 2: Combine the Terms

Let's simplify this equation:
1. Combine the second polynomial:

\[
2x^2 + 12x + 2
\]

### Step 3: Writing the Final Polynomial
We can now set it up in blanks as requested:
1. The first polynomial is \( 9x^2 \).
2. The second polynomial is \( 2x^2 + 12x + 2 \).

Thus the entire setup will be:

\[
9x^2 + x + 13 - (2x^2 + 12x + 2) = (9x^2 - 2x^2) + (x - 12x) + (13 - 2)
\]

### Step 4: Calculation of the Resulting Difference
Now calculating the resulting differences:
- Quadratic terms: \( 9x^2 - 2x^2 = 7x^2 \)
- Linear terms: \( x - 12x = -11x \)
- Constant terms: \( 13 - 2 = 11 \)

Thus the final expression becomes:

### Final Result
The resulting polynomial expression is:

\[
7x^2 - 11x + 11
\]

### Filling in the Blanks
Given these details, here is how you might fill in the blanks:

- First blank (first polynomial, \(9x^2\)): **\(9x^2\)**
- Second blank (linear term, \(x\)): **\(x\)**
- Third blank (constant term, \(13\)): **\(13\)**
- Fourth blank (for \(12x\)): **\(12x\)**
- Fifth blank (constant term, \(2\)): **\(2\)**

So the completed equation with blanks would be:

\[
9x^2 + x + 13 - (2x^2 + 12x + 2)
\]

Resulting in the difference:

\[
= 7x^2 - 11x + 11
\]

If there are any adjustments needed based on the blanks provided in the original prompt, please let me know!