Question

Expand (x²-y²)²+(2xy)² and identify the resulting identity

Answer 1

(x²)² + (y²)² - 2x²y² + 2x²y²

= x⁴ + y⁴

= (x² + y²)² - (√2xy)²

= (x² + y² - √2xy) (x² + y² + √2xy).

The identity is a² - b² = (a-b) (a+b).