Evaluate \(a^3 - \dfrac{1}{a^3}\) if \(a - \dfrac{1}{a} = 4\).
a - 1/a = 4 square both sides
a^2 - 2 a(1/a) + 1/a^2 = 16
a^2 - 2 + 1/a^2 = 16
a^2 + 1/a^2 = 18
a^3 - 1/a^3 =
( a - 1/a) ( a^2 + a(1/a) + 1/a^2) =
(4) ( a^2 + 1/a^2 + 1) =
(4) ( 18 + 1) =
76
