Question

A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool. (The area of a circle is given by A = πr ^2, where r represents the radius of the circle.)

Answer 1

A= π (n + 4) ^2
= π (n + 4) (n + 4) 

remember order of operations FOIL 

= π  (n^2 + 4n + 4n + 16)
= π (n^2 + 8n + 16)

A= πn^2 + 8πn + 16π

do the same for B just change the signs 

B = πn^2 - 8πn + 16π 

subtract the two 

(πn^2 + 8πn + 16π) - (πn^2 - 8πn + 16π) 

=16πn