Add the polynomial expressions 2r^2−3r+4

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

Here are the steps:

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

2. **Group the like terms:**
- Combine the \(r^2\) terms: \(2r^2 - 2r^2\)
- Combine the \(r\) terms: \(-3r + 3r\)
- Combine the constant terms: \(4 + 6\)

3. **Perform the addition:**
\[
2r^2 - 2r^2 = 0
\]
\[
-3r + 3r = 0
\]
\[
4 + 6 = 10
\]

4. **Combine the results:**
\[
0 + 0 + 10 = 10
\]

So, the sum of the polynomials \(2r^2 - 3r + 4\) and \(-2r^2 + 3r + 6\) is \(\boxed{10}\).

Expression 1: −3k+4k^3−2

Expression 2: 9k^2−3k^3+4k−3


(2 points)
( )k3+ ( )
k^2+ ( )
k+ ( )

To add the two polynomial expressions and organize the like terms, let's start by rewriting the expressions:

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

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

Now, let's combine the polynomials:

1. **Combine the \(k^3\) terms:**

\[
4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 \quad \text{(or simply } k^3\text{)}
\]

2. **Combine the \(k^2\) terms:**

\[
0 + 9k^2 = 9k^2 \quad \text{(there is no } k^2 \text{ term in Expression 1)}
\]

3. **Combine the \(k\) terms:**

\[
-3k + 4k = (4 - 3)k = 1k \quad \text{(or simply } k\text{)}
\]

4. **Combine the constant terms:**

\[
-2 - 3 = -5
\]

Now, putting everything together, the result of adding the two expressions is:

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

Thus, we can fill in the blanks as follows:

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

So, to explicitly answer your question:

- Coefficient of \(k^3\): **1**
- Coefficient of \(k^2\): **9**
- Coefficient of \(k\): **1**
- Constant term: **-5**

The final answer is:

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

Simplify (9x^2−6x+2)−(x^2+4x−39)

To simplify the expression \((9x^2 - 6x + 2) - (x^2 + 4x - 39)\), follow these steps:

1. Distribute the negative sign across the second polynomial:

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

2. Combine like terms:

- Combine the \(x^2\) terms:
\[
9x^2 - x^2 = 8x^2
\]

- Combine the \(x\) terms:
\[
-6x - 4x = -10x
\]

- Combine the constant terms:
\[
2 + 39 = 41
\]

3. Put it all together:

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

Thus, the simplified expression is:

\[
\boxed{8x^2 - 10x + 41}
\]