a(a + 1)(a + 2)(a + 3) + 1
= a(a + 3)(a + 1)(a + 2) + 1
= (a² + 3a)(a² + 3a + 2) + 1
= (a² + 3a)² + 2(a² + 3a) + 1
= (a² + 3a + 1)²