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).