Question

Factorise.

x⁴ − (x − z)⁴

Answer 1

x⁴ − (x − z)⁴ 

= (x²)² − [(x − z)²]² 

Using the identity a² − b² = (a − b) (a + b)

= [x² − (x − z)²] [x² + (x − z)²] 

= [x − (x − z)] [x + (x − z)] [x² + (x − z)²]

= z (2x − z) [x² + x² − 2xz + z²]

= z (2x − z) (2x² − 2xz + z²)