Final answer:
To simplify the expression, combine like terms for each variable to get 1a² - 11ab + 7b².
Step-by-step explanation:
The student question asks to simplify the algebraic expression 9a²-8ab+4b²-8a²-3ab+3b² by combining like terms. In order to do this, we will identify terms that contain the same variables raised to the same power and combine them.
Combining like terms:
The like terms for a² would be 9a² and -8a², which gives us 9a²-8a² = 1a² or simply a².
The like terms for ab would be -8ab and -3ab, which gives us -8ab-3ab = -11ab.
The like terms for b² would be 4b² and 3b², which gives us 4b²+3b² = 7b².
Therefore, after combining like terms, our simplified expression is a² - 11ab + 7b².