If a - b = 6 and ab = 20, find the value of a3−b3.
a - b = 6, ab = 20
Cubing both sides,
(a−b)3=(6)3⇒ a3−b3−3ab(a−b)=216⇒ a3−b3−3×20×6=216⇒ a3−b3−360=216⇒ a3−b3=216+360=576∴ a3−b3=576