[tex](3\sqrt5-1)^3 = \\ \\ = (3\sqrt5-1)^{2+1} = \\ \\ = (3\sqrt5-1)^2\cdot (3\sqrt5-1) = \\ \\ = \Big((3\sqrt5)^2-2\cdot 3\sqrt5\cdot 1+1^2\Big)\cdot (3\sqrt5-1)= \\ \\ = (9\cdot 5-6\sqrt5+1) \cdot (3\sqrt5-1) = \\ \\ = (46-6\sqrt5)\cdot (3\sqrt5-1) = \\ \\ = 138\sqrt5-46-18\cdot 5+6\sqrt5 = \\ \\ = -46-90+138\sqrt5+6\sqrt5 = \\ \\ = -136+144\sqrt5[/tex]
