(4x² - 2xy + y²) + (- 8x² -9xy – y²) + (x² + xy -8y²)

(4X^2-2XY+Y^2)+(-8X^2-9XY-6Y^2)+(X^2+8XY-8Y^2).

Combine like-terms:
-3X^2 - 3XY - 8Y^2.

To simplify the given expression, we can combine like terms by adding or subtracting the coefficients of the same variables in each expression.

The expression given is:
(4x² - 2xy + y²) + (-8x² - 9xy - y²) + (x² + xy - 8y²)

Step 1: Group like terms.
(4x² - 8x² + x²) + (-2xy - 9xy + xy) + (y² - y² - 8y²)

Step 2: Combine like terms within each group.
(-3x²) + (-10xy) + (-7y²)

The simplified expression is -3x² - 10xy - 7y².