Chapter 8 - Polynomials and Factoring - 8-2 Multiplying and Factoring - Practice and Problem-Solving Exercises - Page 495: 14

$-56y^{5}+32y^{4}+8y^{3}$

We start with the given expression: $-8y^3(7y^2-4y-1)$ We apply the distributive property to multiply the monomial by the binomial: $(-8y^3)(7y^2)+(-8y^3)(-4y)+(-8y^3)(-1)$ We multiply the coefficients and add the exponents on each term to arrive at our answer: $$-56y^{3+2}+32y^{1+3}+8y^{3}$$$$-56y^{5}+32y^{4}+8y^{3}$$