Question

Factorise 27xcube+ycube+zcube-9xyz

Answer 1

$27 {x}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ = {(3x)}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ = (3x + y + z)( {(3x)}^{2} + {y}^{2} + {z}^{2} - (3x)y - yz - (3x)z) \\ = (3x + y + z)( 9{x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3xz)$