I'm asked to consider three Ito processes $(X(t), t \ge 0)$, $(Y(t), t \ge 0)$, and $(Z(t), t \ge 0)$.
I am asked to show:
$$d(X(t)Y(t)Z(t)) = X(t)Y(t)dZ(t) + X(t)Z(t)dY(t) + Y(t)Z(t)dX(t) + X(t)dY(t)dZ(t) + Y(t)dX(t)dZ(t) + Z(t)dX(t)dY(t)$$
My work: I let $A(t) = X(t)$ and $B(t) = Y(t)Z(t)$ the product of two Ito processes is also Ito, so I just used Ito's product formula on $d(A(t),B(t))$ and $d(Y(t),Z(t))$ and plugged in the latter. However, doing so I get an extra term, $$dX(t)dY(t)dZ(t)$$ and I'm not sure why this necessarily vanishes.