Question

Factorise: 27x 3 +y 3 +z 3 -9 xyz.

Answer 1

27x^3 + y^3 + z^3 -9xyz

= (3x)^3 + (y)^3 + (z)^3 - 9xyz

= (3x)^3 + (y)^3 + (z)^3 - 3 x 3x x y x z

USING IDENTITY : a^3 + b^3 + c^3 - 3abc = (a + b + c) (a^2 + b^2 + c^2 - ab - bc - ca) putting a = 3x, b = y, c = z

= (3x + y + z) (9x^2 + y^2 + z^2 - 3xy - yz - 3zx)