Question

Factorise.

x⁴ − (y + z)⁴

Answer 1

x⁴ − (y + z)⁴ 

= (x²)² − [(y + z)²]² 

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

= [x² − (y + z)²] [x² + (y + z)²] 

Again, using a² − b² = (a − b) (a + b)

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

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