Question

Factorise 27x³ + y³ + z³ – 9xyz using identity.

Answer 1

Given 27x³+ y³ + z³ – 9xyz

= (3x)³ + (y)³ + (z)³ – 3 (3x) (y) (z) 

= (3x + y + z)

[(3x)² + y² + z² – (3x) (y) – (y) (z) – (z) (3x)] 

[ ∵ (x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) = (3x + y + z) (9x² + y² + z² – 3xy – yz – 3xz)