Can you explain the simplification, addition of two squares.

Question

$(x^2+y^2) = (x-y)^2 + 2xy$

How did it get simplified such that $(x^2+y^2)$ became $(x-y)^2 + 2xy$

Many Thanks :)

Answer 1

$(x-y)^2$ can be written as $x^2-2xy+y^2$. Indeed, if you multiply $(x-y)\times (x-y)$, the terms are $x^2-yx-xy+y^2$.

So $(x-y)^2+2xy=(x^2-2xy+y^2)+2xy=x^2+y^2$.