5. Find the sum.

Question

(4𝑝−2𝑝2+8)+(5𝑝2+2𝑝)+(7−3𝑝)

Answer 1

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

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: \[ \boxed{3p^2 + 3p + 15} \]