Factorise x⁶ – y⁶

x⁶ – y⁶ = (x²)³ – (y²)³
          = (x² – y²)[(x²)² + x²y² +(y²)²]
          = (x + y)(x – y)(x⁴ + x²y² + y⁴)
(Here the third factor can be further factorised as shown)
          = (x + y)(x – y)(x⁴ + 2x²y² + y⁴ – x²y²)
         = (x + y)(x – y)[(x² + y²)² – x²y²]
         = (x + y)(x – y) (x² + y² + xy)(x² + y² – xy)