# "If x is a difference of squares, prove that 3x is a difference of squares as well."

Prove that if $$x$$ is a difference of integer squares, then $$3x$$ is a difference of integer squares as well.
Write $$x=u^2-v^2$$ with $$u,v\in \Bbb Z$$, then $$3x=3(u^2-v^2)=3(u+v)(u-v)=(3u+3v)(u-v)=((2u+v)+(u+2v))((2u+v)-(u+2v))=(2u+v)^2-(u+2v)^2$$