(xy2-x2-xy)(y2-2)

To multiply the expression (xy^2 - x^2 - xy) and (y^2 - 2), we can use the distributive property.

Step 1: Distribute the first term of the first expression (xy^2) to both terms of the second expression (y^2 - 2):

(xy^2)(y^2) - (xy^2)(2) = xy^4 - 2xy^2

Step 2: Distribute the middle term of the first expression (-x^2) to both terms of the second expression (y^2 - 2):

(-x^2)(y^2) - (-x^2)(2) = -x^2y^2 + 2x^2

Step 3: Distribute the last term of the first expression (-xy) to both terms of the second expression (y^2 - 2):

(-xy)(y^2) - (-xy)(2) = -xy^3 + 2xy

Combining all the terms gives us the final result:

xy^4 - 2xy^2 - x^2y^2 + 2x^2 - xy^3 + 2xy

Simplifying further:

xy^4 - x^2y^2 - xy^3 - 2xy^2 + 2x^2 + 2xy