Answer:

The difference between the two expressions is 2r^2 + 3s^2 + 4r + 2s - 1.

Step-by-step explanation:

We can subtract the two expressions as follows:

(3r^2 - s^2 + 4r + 3s) - (r^2 + 2s^2 + 1) =

3r^2 - r^2 - s^2 + 2s^2 + 4r + 3s - 1 =

2r^2 + 3s^2 + 4r + 2s - 1 =

2r^2 + 3s^2 + 4r + 2s - 1