For a given operation $\circ$, let $z = x \circ y$.
Then $z$ is called the product of $x$ and $y$.
The left-hand product of $x$ by $y$ is the product $y \circ x$.
The right-hand product of $x$ by $y$ is the product $x \circ y$.
Also known as
The product of $a$ and $b$ is sometimes seen referred to as their sum.
This can be confusing and is therefore endorsed on this site only when referring to ring addition.