Final answer:
To simplify the algebraic expression (3x^2 + 5x + 7) - (-4x^2 + 3x - 6), we change the signs of the terms inside the second parenthesis, combine like terms, and end up with a simplified expression of 7x^2 + 2x + 13.
Step-by-step explanation:
To simplify the expression (3x^2 + 5x + 7) − (−4x^2 + 3x − 6), you need to distribute the negative sign through the second parenthesis which changes the signs of the terms inside.
Here's the simplification step-by-step:
- Remove the parentheses and change the signs of the second set of terms: 3x^2 + 5x + 7 + 4x^2 - 3x + 6.
- Combine like terms: (3x^2 + 4x^2) + (5x - 3x) + (7 + 6).
- Simplify each group of like terms: 7x^2 + 2x + 13.
After eliminating terms wherever possible and combining like terms, the simplified algebraic expression is
7x^2 + 2x + 13.
To check if the simplification is reasonable, ensure that all like terms have been combined correctly and that no arithmetic mistakes have been made.