Steenrod squares on real projective space (${\mathrm{Sq}}^j(x^r)=\left(\genfrac{}{}{0ex}{}{r}{j}\right)x^{r+j}$)

For the degree-one mod-two generator, ${\mathrm{Sq}}^{1}x=x^2$ and higher squares of $x$ vanish by instability. The Cartan formula gives the displayed binomial identity. Naturality applies it to relative classes of a stunted real projective space.