Let's simplify the given expression step by step:
(3a - a^2)^2 - a^2(a - 2)(a + 2) + 2a(7 + 3a^2)
= (3a - a^2)(3a - a^2) - a^2(a^2 - 4) + 2a(7 + 3a^2)
= (9a^2 - 6a^3 + a^4) - (a^4 - 4a^2) + 14a + 6a^3
= 9a^2 - 6a^3 + a^4 - a^4 + 4a^2 + 14a + 6a^3
= 13a^2 + 8a
Therefore, (3a - a^2)^2 - a^2(a - 2)(a + 2) + 2a(7 + 3a^2) simplifies to 13a^2 + 8a.
Let's simplify the given expression step by step:
(3a - a^2)^2 - a^2(a - 2)(a + 2) + 2a(7 + 3a^2)
= (3a - a^2)(3a - a^2) - a^2(a^2 - 4) + 2a(7 + 3a^2)
= (9a^2 - 6a^3 + a^4) - (a^4 - 4a^2) + 14a + 6a^3
= 9a^2 - 6a^3 + a^4 - a^4 + 4a^2 + 14a + 6a^3
= 13a^2 + 8a
Therefore, (3a - a^2)^2 - a^2(a - 2)(a + 2) + 2a(7 + 3a^2) simplifies to 13a^2 + 8a.