Question

Factorise.

a⁴ − 2a²b² + b⁴

Answer 1

a⁴ − 2a²b² + b⁴

= (a²)² − 2a²b² + (b²)²

Using the identity (a − b)² = a² − 2ab + b²

= (a² − b²)²

Using the identity a² − b² = (a − b) (a + b)

= [(a − b) (a + b)]² 

= (a − b)² (a + b)²