Chapter 5 - Section 5.5 - Multiplying Polynomials - Exercise Set - Page 379: 27

$-4x^{3}y+7x^{2}y^{2}-xy^{3}-3y^{4}$

$-y(4x^{3}-7x^{2}y+xy^{2}+3y^{3})=(-y)(4x^{3})+(-y)(-7x^{2}y)+(-y)(xy^{2})+(-y)(3y^{3})=(-4x^{3}y)+7x^{2}y^{1+1}+(-xy^{1+2})+(-3y^{1+3})=(-4x^{3}y)+7x^{2}y^{2}+(-xy^{3})+(-3y^{4})=-4x^{3}y+7x^{2}y^{2}-xy^{3}-3y^{4}$