multiply. \( -8 x^{3} y\left(5 x^{2} y-4 x y^{2}+8 x y\right) \)

To multiply the expression \( -8 x^{3} y\left(5 x^{2} y-4 x y^{2}+8 x y\right) \), you distribute \( -8 x^{3} y \) to each term inside the parentheses. 1. For the first term: \( -8 x^{3} y \cdot 5 x^{2} y = -40 x^{5} y^{2} \) 2. For the second term: \( -8 x^{3} y \cdot -4 x y^{2} = 32 x^{4} y^{3} \) 3. For the third term: \( -8 x^{3} y \cdot 8 x y = -64 x^{4} y^{2} \) Now combine those results: So, the final expression after distributing is: \[ -40 x^{5} y^{2} + 32 x^{4} y^{3} - 64 x^{4} y^{2} \] You can also combine like terms: \[ -40 x^{5} y^{2} + (32 x^{4} y^{3} - 64 x^{4} y^{2}) \] Thus, the final answer is: \[ -40 x^{5} y^{2} + 32 x^{4} y^{3} - 64 x^{4} y^{2} \]