Question

Factorize : x⁴ + y⁴ – 11 x²y²

Answer 1

The factors of x⁴ + y⁴ – 11 x²y² are

{ (x + y) (x - y) + 3xy } { (x + y) (x - y) - 3xy }

•  x⁴ + y⁴ – 11 x²y²

= (x²)² + (y²)² - 2x²y² - 9x²y²  

[ Breaking - 11 x²y² into -2x²y² - 9x²y² ]

= { (x²)² + (y²)² - 2x²y² } - 9x²y²  

= (x² - y²)² - (3xy)²

[Applying a² + b² - 2ab = (a - b)², and writing 9x²y² = (3xy)² ]

= (x² - y² + 3xy) (x² - y² - 3xy)

[ Applying a² - b² = (a + b) (a - b).

Here, a = x² - y², and b = 3xy ]

= { (x + y) (x - y) + 3xy } { (x + y) (x - y) - 3xy }

[ Applying a² - b² = (a + b) (a - b).

Here, a = x, b = y ]

Answer 2

HOPE IT HELPS YOU

PLS MARK ME BRAINLIST