a^4 + (1-a)(1+a)(a+a^2)
=a^4 - (a - 1)(a + 1)(a^2 + 1)
=a^4 - (a^2 - 1)(a^2 + 1)
=a^4 - (a^4 - 1)
=a^4 - a^4 + 1
=1