Final answer:
To simplify the expression (3p^2 - 6pq + 7q^2) - (p^2 - 5pq + 9q²), distribute the negative sign to each term inside the parentheses. Combine like terms by adding the coefficients of the same variable. The simplified expression is 2p² - pq - 2q². Therefore, the correct option is A.
Step-by-step explanation:
To simplify the expression (3p^2 - 6pq + 7q^2) - (p^2 - 5pq + 9q²), we need to perform the subtraction operation between the two sets of terms. This can be done by distributing the negative sign to each term inside the parentheses.
Expanding the expression, we have 3p^2 - 6pq + 7q^2 - p^2 + 5pq - 9q². Now, we can combine like terms by adding the coefficients of the same variable.
Combining the like terms gives us 2p^2 - pq - 2q^2. Therefore, the correct answer is Option 1: 2p² - pq - 2q².