11.(5分)$(x^{3}-\dfrac{1}{x})^{4}$的展开式中常数项是____. 分析:利用二项展开式的通项公式$T_{r+1}={C}_{4}^{r}\cdot (x^{3})^{4-r}\cdot {(-\dfrac{1}{x})}^{r}$即可求得展开式中的常数项. 解:设${({x}^{3}-\dfrac{1}{x})}^{4}$展开式的通项为$T_{r+1}$,则$T_{r+1}={C}_{4}^{r}\cdot (x^{3})^{4-r}\cdot {(-\dfrac{1}{x})}^{r}=(-1)^{r}\cdot {C}_{4}^{r}\cdot x^{12-4r}\cdot$ 令$12-4r=0$得$r=3$. $\therefore$开式中常数项为:$(-1)^{3}\cdot {C}_{4}^{3}=-4$. 故答案为:$-4$. 点评:本题考查二项式系数的性质,利用通项公式化简是关键,属于中档题.
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