Final answer:
To combine like terms in the expression 5x^2 + 3x + 4 - x^2 - 6x - 7, identify and group like terms, resulting in the simplified expression 4x^2 - 3x - 3 after combining them accordingly.
Step-by-step explanation:
To combine like terms in an algebraic expression, you should group terms with the same variables and exponents. The given expression has terms that can be combined: 5x^2 + 3x + 4 - x^2 - 6x - 7. Here, 5x^2 and -x^2 are like terms, as are 3x and -6x, and the constant terms 4 and -7.
Let's combine them step by step:
After combining these like terms, the simplified expression is 4x^2 - 3x - 3. It's important to always check if the answer is reasonable by ensuring that all like terms have been accurately combined and no terms have been inadvertently altered or omitted during the process. In this case, simplification has been correctly performed, as there are no remaining like terms to combine.