Question

Factorise.

p⁴ − 81

Answer 1

 p⁴ − 81

= (p²)² − (9)² 

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

= (p² − 9) (p² + 9)

= (p² − 3²) (p² + 9)

Again, using a² − b² = (a − b) (a + b)

= (p − 3) (p + 3) (p² + 9)