4xy(2x+0,5y-xy)

To simplify the expression \( 4xy(2x + 0.5y - xy) \), we will distribute \( 4xy \) to each term inside the parentheses.

1. Distribute \( 4xy \) to \( 2x \): \[ 4xy \cdot 2x = 8x^2y \]

2. Distribute \( 4xy \) to \( 0.5y \): \[ 4xy \cdot 0.5y = 2xy^2 \]

3. Distribute \( 4xy \) to \( -xy \): \[ 4xy \cdot -xy = -4x^2y^2 \]

Now, we combine all the terms: \[ 8x^2y + 2xy^2 - 4x^2y^2 \]

So the simplified expression is: \[ 8x^2y + 2xy^2 - 4x^2y^2 \]