Commentaries:
Barnes' Notes
    There shall no strange god be in thee -  Worshipped by thee; or recognized and regarded as a god. This was a condition of his favor and friendship. Compare Deuteronomy 32:12; Isaiah 43:12. The word here rendered "strange" -  zār  - has reference to one of a foreign nation; and the meaning is, that they were not to worship or adore the gods that were worshipped by foreigners. This was a fundamental law of the Hebrew commonwealth.
    Neither shalt thou worship any strange god -  The Hebrew word here is different -  nêkâr  - but means substantially the same thing. The allusion is to gods worshipped by foreign nations.
 
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