Question

A circular jacuzzi is surrounded by a circular deck. The radius of the jacuzzi is n − 3 and the radius of the full circle formed by the deck is n + 3. Write a polynomial that represents the area of just the deck itself, not including the space covered by the jacuzzi.

Answer 1

area of circle=pir^2

jacuzzi=pi(n-3)^2=pi(n²-6n+9)
deck=pi(n+3)²=pi(n²+6n+9)

deck-jacuzzi=what we need
pi(n²+6n+9)-pi(n²-6n+9)
pi(n²+6n+9-n²+6n-9)
pi(12n)
12npi is the area of jaccuzi not including deck