Chapter 5 - Section 5.4 - Multiplying Polynomials - Exercise Set - Page 289: 52

$-27x^{3}y^{2}+18x^{2}y^{2}-90xy^2$

Using the Distributive Property, the given expression is equivalent to \begin{align*} & -9xy^2(3x^2-2x+10) \\\\&= -27x^{1+2}y^{2}+18x^{1+1}y^{2}-90xy^2 \\\\&= -27x^{3}y^{2}+18x^{2}y^{2}-90xy^2 .\end{align*}