10:3 make a covenant. This was not an entirely new covenant, but the renewal of the Mosaic covenant in terms of an oath (v. 5) to keep the stipulation regarding intermarriage (Deut. 7:3; cf. Jer. 34:8–22 for a similar covenant renewal).
to put away. This is not the usual Hebrew phrase for divorce, and is used only here for putting away a wife. The Hebrew expression in v. 2 (“have married . . . women”) is not the usual phrase for marriage, and is used in the same way only in Neh. 13, in an analogous situation. The author’s choice of language seems to indicate that he did not regard the unions as legitimate marriages, nor the sending away as actual divorce.
according to the Law. The law does not provide explicitly for this exact situation. The phrase may refer to sending a woman away with her children, some provisions (Gen. 21:14), and certain legal rights (Deut. 21:10–14).