The given expression is:

$(x^2 + 6xy - 3y^2) + (2x^2 + 5xy - 3y^2)$

Let's simplify it step by step:

1. Combine like terms:
   • Combine the $x^2$ terms: $x^2 + 2x^2 = 3x^2$
   • Combine the $xy$ terms: $6xy + 5xy = 11xy$
   • Combine the $y^2$ terms: $-3y^2 - 3y^2 = -6y^2$

Thus, the simplified expression is:

$3x^2 + 11xy - 6y^2$

Would you like further details on how the terms were combined, or any specific explanation?

Here are some related questions you might find helpful:

1. How do you identify like terms in a polynomial?
2. Can you factor the expression $3x^2 + 11xy - 6y^2$?
3. What are the general steps for simplifying polynomial expressions?
4. How does this simplification change if the signs of some terms are reversed?
5. How do you visualize a quadratic expression in two variables?

Tip: Always group like terms (with the same variables and exponents) when simplifying polynomials.