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

 May 14, 2021
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The expansion of  (m + n)8 

      =  1m0n8  +  8m1n7  +  28m2n6  +  56m3n5  +  70m4n4  +  56m5n3  +  28m6n2  +  8m7n1  +  1m0n8

 

The terms will be odd if both the m-term and the n-term are odd.

These terms will be odd if both of their exponents are odd.

 

Therefore, there will be  8  +  56  +  56  +  8  odd terms.

 May 14, 2021

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