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