Find the sum. (4p−2p2+8)+(5p2+2p)+(7−3p) (1 point)

Responses

3p2+6p+15
3 p squared plus 6 p plus 15

5p2+p+15
5 p squared plus p plus 15

−2p2+8p+15

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

To find the sum of the expression \((4p−2p^2+8)+(5p^2+2p)+(7−3p)\), we can first combine like terms.

1. Rewrite the expression without parentheses:
\[
4p - 2p^2 + 8 + 5p^2 + 2p + 7 - 3p
\]

2. Group like terms together:
- For \(p^2\) terms: \(-2p^2 + 5p^2 = 3p^2\)
- For \(p\) terms: \(4p + 2p - 3p = 3p\)
- For constant terms: \(8 + 7 = 15\)

3. Combine everything together:
\[
3p^2 + 3p + 15
\]

Upon simplifying, we will see that the sum of the expression is:

\[
3p^2 + 3p + 15
\]

However, this does not match any options directly. It appears an error occurred; let’s ensure we have everything correctly accounted for:

- Collect terms for \(p^2\): \(-2p^2 + 5p^2 = 3p^2\),
- Collect terms for \(p\): \(4p + 2p - 3p = 3p\),
- Collect constant terms: \(8 + 7 = 15\).

So, we now look again at choices given:

- **3p² + 6p + 15**
- **5p² + p + 15**
- **−2p² + 8p + 15**

The option that matches our calculations most closely is not indicated.

Let's closely recount:
Adding \(4p +2p - 3p\) correctly gives \(3p\) not \(6p\). The constants tally up correctly:

Thus our final correct sum is:

**3p² + 3p + 15**.
None of the provided options are correct based on our calculations. If forced to select the closest, more review would be necessary. Given an option like **3p² + 6p + 15** might flow logically, but again mathematically from prior lead, it doesn't hold when we add through properly.

If there's an aim to clarify further total selections or choice revisions, surely do provide further insight into desired angles for better summary access.