Answer: 6x² - 3xy - 4y²
Explanation:
The sum of x² - 2xy + y² and 3x² + 4xy - y² is:
(x² - 2xy + y²) + (3x² + 4xy - y²)
Simplifying and combining like terms, we get:
4x² + 2xy
Now, we need to subtract -2x² + 5xy + 4y² from this sum. To do this, we can change the sign of each term in -2x² + 5xy + 4y² and then add:
4x² + 2xy + (2x² - 5xy - 4y²)
Simplifying and combining like terms, we get:
6x² - 3xy - 4y²
Therefore, the answer is 6x² - 3xy - 4y².