∵   x⁴ - (y + z)⁴ = [x²]² - [(y + z)²]²

                       = [(x²) + (y + z)²] [(x²) - (y + z)²]
                                                
                                                     [Using a² - b² = (a+b)(a-b)]

We can factorise [x² - (y + z)²] further as

       x² - (y + z)² = [(x) + (y + z)][(x) - (y + z)]

                         = (x + y + z)(x - y - z)

∴      x⁴ - (y + z)⁴ = (x + y + z)(x - y - z)[x² + (y + z)²]