https://file.aiquickdraw.com/mathbot/file/1725950150388ivma83ue.jpg

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.

Simplify the following expression by combining the like terms: 3a^2 - 9ab + 7b^2 - 7a^2 - 2ab + 2b^2

Learn how to simplify the expression 3a^2 - 9ab + 7b^2 - 7a^2 - 2ab + 2b^2 by combining like terms. This problem covers key algebraic concepts like simplification, the commutative property, and associative property, making it suitable for students in Grades 9-11.

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