First Stiefel–Whitney class of a tensor product of real line bundles (source code)

= First Stiefel–Whitney class of a tensor product of real line bundles
{c}
{title2=$w_1(L\otimes L')$}

Real line bundles are classified by $H^1(X;\mathbb F_2)$, and tensor product corresponds to addition:
$$
w_1(L\otimes L')=w_1(L)+w_1(L').
$$