Factorize:

Concept Used:

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – xz)

Explanation:

27x³ + y³ + z³ – 9xyz = (3x)³ + y³ + z³ – 3 × 3xyz

Using identity,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – xz)

27x³ + y³ + z³ – 9xyz

= (3x + y + z) {(3x)² + y² + z² – 3xy – yz – 3xz}

= (3x + y + z) (9x² + y² + z² – 3xy – yz – 3xz)