To simplify the algebraic expression by combining like terms from the uploaded image, we have:

$3a^2 - 9ab + 7b^2 - 7a^2 - 2ab + 2b^2$

We combine the like terms as follows:

1. Terms with $a^2$:

   • $3a^2 - 7a^2 = -4a^2$

2. Terms with $ab$:

   • $-9ab - 2ab = -11ab$

3. Terms with $b^2$:

   • $7b^2 + 2b^2 = 9b^2$

Thus, the simplified expression is:

$\boxed{-4a^2 - 11ab + 9b^2}$

Would you like further details on how these terms are combined or have other questions?

Here are some related questions:

1. What happens if the signs of the terms are changed?
2. How can we further factorize this expression if possible?
3. How would adding another term, like $5a^2$ or $-3b^2$, affect the simplified result?
4. Can this method of simplification be applied to expressions with three variables?
5. What are some real-life applications of combining like terms?

Tip: When combining like terms, it helps to underline or highlight terms that contain the same variables and powers, so you don't miss any during the simplification process.