Factories the following

x⁴ – 2x²y² + y⁴

In the given expression

1^st and last terms are perfect square

⇒ x⁴ = x² × x²

⇒ y⁴ = y² × y²

And the middle expression is in form of 2ab

2x²y² = 2 × x² × y²

∴ x² × x² - 2 × x² × y² + y² × y²

Gives (a-b)² = a²-2ab + b²

⇒ x⁴ – 2x²y² + y⁴

a = x² and b = y²;

∴ x⁴ – 2x²y² + y⁴ = (x² – y²) (x² + y²)

Hence the factors of x⁴ – 2x²y² + y⁴ are (x² – y²) and (x² + y²)