^(8)1−(y)/(x)(x+y)的展开式中_(xy)26的系数为________________(用数字作答).
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答案
-28
解析
^(8)1−(y)/(x)(x+y)可化为(x+y)^(88)−(y)/(x)(x+y),结合二项式展开式的通项公式求解. 因为^(888)1−(y)/(x)(x+y)=(x+y)−(y)/(x)(x+y), 所以^(8)1−(y)/(x)(x+y)的展开式中含_(xy)26的项为C8^(62653526)xy−(y)/(x)C8xy=−28xy, ^(8)1−(y)/(x)(x+y)的展开式中_(xy)26的系数为-28 故答案为:-28