Question

Factorise: 
a raise to 4 + a² + 1

Answer 1

a^4 + a² + 1
Adding and subtracting a²,

(a^4 + 2a² + 1) - a²
= (a² + 1)² - (a)²
[x² - y² = (x + y)(x - y). Here x = (a² + 1) and y = a]
= (a² + a + 1)(a² - a + 1)