The term $-8x^{2}y$ is a product of factors. Which product is correct?

A term is built by MULTIPLYING its factors, and $x^2$ means $x\times x$. So $-8x^{2}y=-8\times x\times x\times y$. Writing only one $x$ loses a factor; joining the pieces with + turns one term into a three-term expression; dropping the minus changes the coefficient from −8 to 8.