-2ху(х^2+2ху-у^2)

To simplify the expression \(-2xy(x^2 + 2xy - y^2)\), you can distribute \(-2xy\) across the polynomial inside the parentheses.

Here's how you would do that step by step:

1. Distribute \(-2xy\): \[ -2xy \cdot x^2 + (-2xy) \cdot 2xy + (-2xy) \cdot (-y^2) \]

2. Calculate each term:

   • \(-2xy \cdot x^2 = -2x^3y\)
   • \(-2xy \cdot 2xy = -4x^2y^2\)
   • \(-2xy \cdot (-y^2) = 2xy^3\)

3. Combine the results: \[ -2x^3y - 4x^2y^2 + 2xy^3 \]

So the simplified expression is: \[ -2x^3y - 4x^2y^2 + 2xy^3 \]