Let $\displaystyle F_2$ be the free group on two generators $\displaystyle F_2=<x,y>$. Prove that the free group on 3 generators $\displaystyle F_3$ is a subgroup of $\displaystyle F_2$.

Not completely sure how to go about doing this. So$\displaystyle F_3=<x,y,z>$. Can I show that z can be written as the the product of $\displaystyle x$'s and $\displaystyle y$'s and their inverses?

Or is there some other method I should try?