Final answer:
The expression (2x^2 + 7x + 10) - (x^2 + 2x - 9) simplifies to x^2 + 5x + 19 by subtracting the terms of the second polynomial from the first and combining like terms.
Step-by-step explanation:
To simplify the expression (2x^2 + 7x + 10) - (x^2 + 2x - 9), we need to subtract the second polynomial from the first. Perform subtraction by changing the sign of each term in the second polynomial and then combining like terms.
Change the signs of the terms in the second polynomial: -x^2 - 2x + 9.
Add this to the first polynomial: 2x^2 + 7x + 10 + (-x^2 - 2x + 9).
Combine like terms: (2x^2 - x^2) + (7x - 2x) + (10 + 9).
Simplify each group of like terms: x^2 + 5x + 19.
The simplified expression is x^2 + 5x + 19.