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Dalia S.

asked • 04/01/14

Which term of the expansion contains x^8

Which term of the expansion of (x+5)10 contains x8?
the term number that contains x8 is?
 

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Philip P. answered • 04/01/14

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Dalia S.

i have followed the steps that you provided, however, my answer still seems to be incorrect 
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04/01/14

Philip P.

In your case, (x + 5)10, a=x, b=5, n=10. What do you have to set k to to get xn-k = x8? The term number, then is r = k+1.
 
OK, to make x10-k = x8, k must = 2.  The term number is r = k +1 = 2 + 1 = 3.  Is that what you got?
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04/01/14

Philip P.

The actual term itself (vice just the number of the term) can be determined from the following formula:

(n!/(n-k)!k!)*an-kbk = 10!/(10-2)!(2!) * x852 = 1125x8

Where n = 10, k = 2, a = x, b = 5.
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04/01/14

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