(a-3)(a+3)- 〖[(2a-5)〗^2- (a+6)(a-9)] + (a+5)^3

1. Expand:
(a-3)(a+3) = a^2 - 9

2. Expand:
〖(2a-5)〗^2 = 4a^2 - 20a + 25

3. Expand:
(a+6)(a-9) = a^2 - 9a + 6a - 54 = a^2 - 3a - 54

4. Combine and simplify terms:
〖(4a^2 - 20a + 25) - (a^2 - 3a - 54) = 4a^2 - 20a + 25 - a^2 + 3a + 54 = 3a^2 - 17a + 79

5. Add back to the expression:
(a^2 - 9) - (3a^2 - 17a + 79)

6. Combine and simplify terms:
a^2 - 9 - 3a^2 + 17a - 79 = -2a^2 + 17a - 88

7. Now expand:
(a+5)^3 = a^3 + 15a^2 + 75a + 125

8. Combine:
-2a^2 + 17a - 88 + a^3 + 15a^2 + 75a + 125

9. Simplify entire expression:
a^3 + 18a^2 + 92a + 37

Final answer:
a^3 + 18a^2 - 11a - 207