User:Sapphiredove41

Proof that $(x + y)^2$ and $x^2 + y^2$ are the same when $x$ or $y$ is $0$ : $(x+y)^2$ factored out is $x^2+2xy+y^2$ , so if we want to make the statement $(x+y)^2=x^2+y^2$ true, $2xy$ must be equal to $0$ . This means that either $x$ or $y$ has to be $0$ for this to work. We can see this if we substitute $0$ in for $y$ $(x+0)^2=x^2$ $x^2+0^2=x^2+0=x^2$