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divide and conquer

Also, divide and govern or rule. Win by getting one's opponents to fight among themselves. For example, Divide and conquer was once a very successful policy in sub-Saharan Africa. This expression is a translation of the Latin maxim, Divide et impera (“divide and rule”), and began to appear in English about 1600.

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The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.