How do you convert this Polar equation into it's Cartesian equivalent

the polar equation is;

r^2 = 4cos2θ

the r^2 really throws me off, no idea what to do :|

I'm using ¥ instead of theta because I'm using my phone.

First note cos2¥=(cos¥)^2-(sin¥)^2.
now
r^2 is just x^2+y^2
cos¥ = x / (sqroot(x^2 + y^2))
sin¥ = y / (sqroot(x^2 + y^2))

Substitue all this stuff into your initial equation and you have something with x and y's which you can rearrange.