Question

When factored completely the expression p^4-81 is equivalent to

Answer 1

   
$\displaystyle\\ p^4 - 81 =\\\\ =p^4-3^4 =\\\\ = \Big(p^2\Big)^2 - \Big(3^2\Big)^2 =\\\\ =\Big(p^2+3^2\Big)\Big(p^2-3^2\Big)=\\\\ =\boxed{\bf \Big(p^2+3^2\Big)\Big(p+3\Big)\Big(p-3\Big)}$