TITLE: Basic absolute value property
QUESTION [6 upvotes]: Hello all I am wondering if anyone has the correct proof that I should use for Spivak calculus ( chapter 1, question 12 )  that says
$$|xy|=|x| \cdot |y|$$
from past times I know it is true , but I am not sure the best way to prove it, and I need this property to use in the rest of the proofs as well.
Should I write something like 
$|xy|= xy$ , for  $xy \ge 0$ and $|xy|= -(xy)$ if $xy \le 0 ?$
Or should I write $$|xy|=\sqrt{(xy)^{2}}$$ and expand from that or what?
Thanks a lot everyone, I just want to make sure I have covered it all correctly. 
Preferably the answer will be from someone that is familiar with Spivak , because I would like to be able to prove it the way he would have wanted, i.e., only using what we had learnt up to this point.
Thanks!

REPLY [2 votes]: A bit shorter: Since $|x| = |-x|$ (more or less by definition), changing the sign of $x$ (or $y$) leaves both sides of the tentative equality unchanged. Hence, we may as well assume that $x$ and $y$ are both positive, in which case the equality is obvious.