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Which is the term of the expanasion (x-1)^13, which doesn't have the unknown x?
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Middle School Teacher
The full expansion of (x-1)^13 is:
x^13 - 13x^12 + 78x^11 - 286x^10 + 715x^9 - 1287x^8 + 1716x^7 - 1716x^6 + 1287x^5 - 715x^4 + 286x^3 - 78x^2 +
13x - 1
It's not really necessary to do the full expansion to know that the x-free term will be either + or - 1 -- there is no other number possible when all you are doing is multiplying -1 times itself repeatedly.
To figure out the + or -, think about the pattern.
-1 x -1 = 1 one time
1 x -1 = -1 two times
-1 x -1 = 1 three times
Since there are 13 (x-1)s in a row, you are multiplying by -1 a total of 12 times (the first (x-1) is the starting point). As you can see above, when you multiply an even number of times you end up with -1.
Posted by cburr on April 18, 2009 at 1:39 AM (Answer #1)
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