(2a^2 + 5a+ 7) - (a^2-3a-1)

To subtract the two expressions, we distribute the negative sign to every term in the second expression:

(2a^2 + 5a + 7) - (a^2 - 3a - 1)
= 2a^2 + 5a + 7 - a^2 + 3a + 1

Now, we can combine like terms:

= (2a^2 - a^2) + (5a + 3a) + (7 + 1)
= a^2 + 8a + 8

Therefore, the simplified expression is a^2 + 8a + 8.