Final answer:
To subtract and combine like terms for (-x² + 4x - 7) - (x² - 5x + 3), distribute the negative sign across the second parenthesis, and then combine like terms. The final simplified expression is -2x² + 9x - 10, which corresponds to Option A.
Step-by-step explanation:
To use the distributive property to subtract and combine like terms for the expression (-x² + 4x - 7) - (x² - 5x + 3), we must first distribute the subtraction sign across the terms in the second parenthesis, effectively changing the sign of each term within that parenthesis. This step is crucial to ensure proper subtraction of like terms.
We rewrite the expression as follows:
-x² + 4x - 7 - x² + 5x - 3
Next, we combine like terms:
Combine the x² terms: (-x² - x²) = -2x²
Combine the x terms: (4x + 5x) = 9x
Combine the constant terms: (-7 - 3) = -10
The final expression after combining like terms is:
-2x² + 9x - 10
Therefore, the correct answer is Option A: -2x² + 9x - 10.