(1-a)(1+a)(1+a²)-(a+3)(a²-3a+9)
Expanding the first term:
= (1 + a - a - a^2)(1 + a^2)
= (1 - a^2)(1 + a^2)
= 1 + a^2 - a^2 - a^4

Expanding the second term:
= a(a^2 - 3a + 9) - 3(a^2 - 3a + 9)
= a^3 - 3a^2 + 9a - 3a^2 + 9a - 27
= a^3 - 6a^2 + 18a - 27

Putting both expansions together:
= (1 + a^2 - a^2 - a^4) - (a^3 - 6a^2 + 18a - 27)
= 1 + a^2 - a^2 - a^4 - a^3 + 6a^2 - 18a + 27
= 1 - a^4 - a^3 + 5a^2 - 18a + 27

So, the final expression is:
1 - a^4 - a^3 + 5a^2 - 18a + 27