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求二项式的展开式中指定项的系数是二项式定理中较基础的题型,也是近年来高考常考题型之一,难度不大。针对二项式定理试题中求展开式指定项的系数问题,本文特别进行了归类与解析,并提出了对应的策略,供同学们复习时参考。一、(a+b)~n(n∈N~*)型直接套用二项展开式的通项公式来求二项展开式中指定项的系数,并由待定系数法确定参数的值。例1(x-2~(1/2)y)~(10)的展开式中x~6y~4项的系数是()A.840 B.-840C.210 D.-210解析在通项公式T_(r+1)=C_(10)~r(-2~(1/2)y)~r x~(10-r)中,
Find the binomial expansions in the specified item coefficient is the Binomial theorem in the more basic questions, but also the entrance exam in recent years often one of the exam questions, not difficult. In order to solve the problem of binomial theorem expansions, this article has carried on the classification and the analysis in particular, and put forward the corresponding tactics, for the students to review for reference. First, (a + b) ~ n (n ∈ N ~ *) type directly apply the binomial expansion of the general formula to find the binomial expansion coefficient of the specified items, and the pending coefficient method to determine the value of the parameter. The coefficients of x ~ 6y ~ 4 in the expansions of Example 1 (x-2 ~ (1/2) y) ~ (10) are () A.840 B.-840C.210 D.- In the formula T_ (r + 1) = C_ (10) ~ r (-2 ~ (1/2) y) ~ rx ~ (10-r)