Question

Factorise the following:

(x² + y² – z²)² – 4x²y²

Answer 1

(x² + y² – z²)² – 4x²y²

= (x² + y² – z²)² – (2xy)²

= (x² + y² – z² – 2xy) (x² + y² – z² + 2xy)

= [(x² + y² – 2xy) – z²] [(x² + y² + 2xy) – z²]

= [(x – y)² – z²] [(x + y)² – z²]

= [(x – y – z) (x – y + z)] [(x + y – z) (x + y + z)]

= (x – y – z) (x – y + z) (x + y – z) (x + y + z)