Is there a word to replace "balck people" in more polite way ?

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"Black people" is acceptable here, in fact, where I live (an area that is mostly black) when talking to real people in real situations, "black" is preferred.  The black people I know rarely ever say "African-American" but say "black" constantly (same with white people.)  You will still hear it in business contexts and the news and especially in governmental usage, though you will also hear "black" in these contexts, though possibly less often (especially less often in governmental contexts.)

I've had multiple black people tell me that they don't like the term "African-American" and so I don't use it anymore.  I've never had an issue with somebody being offended by the word "black," (though I'm sure such people are indeed out there) though in an extremely formal context, or if I was working for the government, I would probably still say "African-American" simply to avoid offending somebody.  It's better to sound silly to the people who don't like the term "African-American" than offensive to the people who are offended by the term "black."

Eliot is correct that race is ridiculously and constantly in the foreground here.  It's a constant presence that seems to have to be discussed constantly.  I think this will change eventually but I think it will take a long time.

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In England, we call them "people". Another word is "human being". It's only in America where they have this division between the colours.

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In America, most people would say "African-American"

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is there a polite way to 'replace black people'? hahahah

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It's not an answer to your question, just a thought...
What's the problem to name black people "black"? Is it something offensive? Or is it indecent to have black skin? What about calling people blonds or brunes depending on theire hair's color? 
  I think, to restrain people depending on color, or sex, or nationality is immoral and silly,  but not to call things by their proper names. imho.

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