Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - Guided Practice for Example 7 - Page 694: 11

$189$

Using the Binomial Theorem, we know that in the expansion of $(a+b)^n$ each term has the form $_nC_ra^{n-r}b^r$ where $0\leq r\leq n$ and $r$ is an integer. Hence here $n=7,a=x,b=-3,r=2$, thus: $_nC_ra^{n-r}b^r=_7C_2\cdot x^5\cdot(-3)^2=21\cdot9\cdot x^5=189x^5$