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

Question

1. Start by writing out the expression:
\[
(4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)
\]

2. Next, combine all the terms together:
\[
-2p^2 + 5p^2 + 4p + 2p - 3p + 8 + 7
\]

3. Now, group the like terms:
- For \(p^2\) terms: \(-2p^2 + 5p^2 = 3p^2\)
- For \(p\) terms: \(4p + 2p - 3p = 3p\)
- For constant terms: \(8 + 7 = 15\)

4. Finally, combine all the results:
\[
3p^2 + 3p + 15
\]

Thus, the final result is:
\[
\boxed{3p^2 + 3p + 15}
\] make this smaller

Answer 1

To simplify the expression \((4p - 2p^2 + 8) + (5p^2 + 2p) + (7 - 3p)\), we first combine like terms in a more compact manner:

1. Write the expression directly: \[ 4p - 2p^2 + 8 + 5p^2 + 2p + 7 - 3p \]

2. Rearrange and combine like terms:

   • 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 all results: \[ 3p^2 + 3p + 15 \]

4. This expression can be factored further: \[ 3(p^2 + p + 5) \]

Thus, the simplified version of the results is: \[ \boxed{3(p^2 + p + 5)} \]