Factorise: 27x3+y3+z3–9xyz

The given expression is 27x^3 + y^3 + z^3 - 9xyz.

This is a special type of cubic expression known as a sum of cubes. The general formula for the sum of cubes is a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca).

In this case, a = 3x, b = y, and c = z.

So, we can rewrite the expression as (3x)^3 + y^3 + z^3 - 3*(3x)yz.

Now, we can apply the formula to factorise the expression:

= (3x + y + z)[(3x)^2 + y^2 + z^2 - (3x)y - (3x)z - yz] = (3x + y + z)[9x^2 + y^2 + z^2 - 3xy - 3xz - yz]

So, the factorised form of the given expression is (3x + y + z)(9x^2 + y^2 + z^2 - 3xy - 3xz - yz).