TITLE: Prove the following $x^2−y^2=(x−y)(x+y)$
QUESTION [5 upvotes]: I'm going through the book Calculus by Michael Spivak, not sure on how to go about the first problem. If anyone can just go through it with a solution I think I can handle myself from there. Thanks.
Prove the following: 
$x^2−y^2=(x−y)(x+y)$

REPLY [2 votes]: Treat $x^2-y^2=0 $as a quadratic equation in variable $x$. Use $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ so that 
$x=\frac{0\pm\sqrt{0+4y^2}}{2}=\pm y$
So $x^2-y^2=(x+y)(x-y)$