Answer
False
Work Step by Step
The equation $(x+y)(x-y)$ defines the two equations $y=-x$ and $y=x$ for all $x$. However, the function $|x|$ only defines $y=-x$ for all negative $x$ and $y=x$ for all positive $x$. Thus, the equation $(x+y)(x-y)$ does is not defined implicitly by $(x+y)(x-y)=0$.
