Factorise: 27x³ + y³ + z³ - 9xyz

27x³ + y³ + z³ - 9xyz = (3x)³ + (y)³ + z³ - 9xyz
Let a = 3x, b = y, c = z.
Then the expression becomes a³ + b³ + c³ - 3abc.
We know that a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca).
Substituting the values of a, b, and c, we get:
(3x + y + z)((3x)² + y² + z² - (3x)y - y(z) - z(3x))
= (3x + y + z)(9x² + y² + z² - 3xy - yz - 3xz)