Original sentence: Plugging in the subscripted x's into the induced 4D metric, embedding the de Sitter space in the five-dimensional Minkowski space R1,4, and being careful to use the Leibniz rule in differentials in , we find resulting cross terms there vanish on the sphere and one of the remaining squares of sum hypertrig collapse with  to produce , so the metric in these coordinates (t plus some set of coordinates on Sn−1) is given by
Edited sentence: Plugging in the subscripted x's into the induced 4D metric, embedding the de Sitter space in the five-dimensional Minkowski space R1,4, and carefully employing the Leibniz rule in differentials in , we find resulting cross terms there vanish on the sphere and one of the remaining squares of sum hypertrig collapse with  to produce , so the metric in these coordinates (t plus some set of coordinates on Sn−1) is given by