Factorize:

x⁶ – 729

We know that,

a³ - b³ = (a - b) (a²+ a × b + b²)

Using this formula, we get

= (x²)³ – (9)³

= (x² – 9) [(x²)² + x²9 + (9)²]

= (x² – 9) (x⁴ + 9x² + 81)

= (x + 3) (x – 3) [(x² + 9)² – (3x)²]

= (x + 3) (x – 3) (x² + 3x + 9) (x² – 3x + 9)