I have the following form $$\omega = dx_1 \wedge dx_2 + dx_3 \wedge dx_4$$
and I want to compute the interior product : $g^*(\omega,\omega)$ (I think $g^*$ is not standard notation but it is just to indicate the interior product on forms).
I have the first step of the solution: $$g^*(\omega,\omega) = g^*(dx_1 \wedge dx_2, dx_1 \wedge dx_2) + 2g^*(dx_1 \wedge dx_2, dx_3 \wedge dx_4) + g^*(dx_3 \wedge dx_4, dx_3 \wedge dx_4)$$
But I don't really understand how to get it. Can someone help me ?