How can I prove that if $|x| > |y|$ then $x^2 > y^2$

Question

How can I prove that if $|x| > |y|$ then $x^2 > y^2$ using proofs such as contradiction, direct proof.

Answer 1

Faster, if you assume that $t \mapsto t^2$ is strictly growing on $[0 , \infty)$, then $x^2 < y^2$ if $|x| < |y|$.

Answer 2

$|x| < |y| \implies |x||x| = |x|^2 = x^2 < |x||y| < |y||y| = |y|^2 = y^2$

Answer 3

Direct Proof. Assume that $|x|>|y|$. Then $$x^2=|x^2|=|xx|=|x|\cdot|x|>|y|\cdot|y|=|y|^2=|y^2|=y^2.$$