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If m and n are odd integers, how many terms in the expansion of $(m+n)^8$ are odd?

 Oct 30, 2021
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If m and n are odd integers, how many terms in the expansion of $(m+n)^8$ are odd?

 

an odd times an odd is odd  so  m^k is odd and n^(8-k) is odd so times them together and they are odd

 

But all the coefficients except for the 1 at each end are even.  An even time an odd = even

 

So there are 9 terms in total and 7 of them will be even, the first and the last will be odd

 

 Oct 30, 2021
edited by Melody  Oct 30, 2021
edited by Melody  Oct 30, 2021

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