Question

Factorise : \((x^2 + y^2 -z^2)^2 - 4x^2y^2\)

Answer 1

\((x^2 + y^2 -z^2)^2 - 4x^2y^2\) = \((x^2 + y^2 -z^2)^2 - (2xy)^2\)

= (x² + y² + z² + 2xy)(x² + y² -z² -2xy)      [∴ a² - b² = (a-b)(a+b)]

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

= [(x + y)² -z²] [(x + y)² -z²]

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