Chapter R - Review of Basic Concepts - R.2 Real Numbers and Their Properties - R.2 Exercises - Page 22: 110

$x=(+),y=(+)$ or $x=(-),y=(+)$

The question asks what signs on values $x$ and $y$ would make the statement $x^{2}y>0$ true. We are given the fact that $x$ and $y$ are nonzero values. A positive $x$ value that is squared will give a positive $x$ value. Multiplying this by a positive $y$ value will give a positive product greater than $0$. A negative $x$ value that is squared will give a positive $x$ value (negative times negative is a positive). Multiplying this by a positive $y$ value will give a positive product greater than $0$.