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

When you multiply \( -4xy^{2} \) by each term in the polynomial \( (3x^{2} + 5xy^{2} - 8xy) \), you distribute \( -4xy^{2} \) to each term: 1. \( -4xy^{2} \cdot 3x^{2} = -12x^{3}y^{2} \) 2. \( -4xy^{2} \cdot 5xy^{2} = -20x y^{4} \) 3. \( -4xy^{2} \cdot (-8xy) = 32x^{2}y^{3} \) Now, combine all the terms together: \[ -12x^{3}y^{2} - 20xy^{4} + 32x^{2}y^{3} \] So, the final result of multiplying \( -4xy^{2}(3x^{2}+5xy^{2}-8xy) \) is: \[ -12x^{3}y^{2} + 32x^{2}y^{3} - 20xy^{4} \]