The problem is to simplify the expression $(r^2 - 7s^2) + (2r^2 + 3s^2)$.

1. Problem Description

The problem is to simplify the expression $(r^2 - 7s^2) + (2r^2 + 3s^2)$.

2. Solution Steps

First, remove the parentheses:

$r^2 - 7s^2 + 2r^2 + 3s^2$

Next, group like terms:

$(r^2 + 2r^2) + (-7s^2 + 3s^2)$

Then, combine the like terms:

$1r^2 + 2r^2 = 3r^2$

$-7s^2 + 3s^2 = -4s^2$

Therefore, the simplified expression is:

$3r^2 - 4s^2$

3. Final Answer

$3r^2 - 4s^2$