Chapter 10 Counting Methods and Probability - 10.2 Use Combinations and the Binomial Theorem - Guided Practice for Example 7 - Page 694: 12

$1400000x^3$

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 $n=8,a=2x,b=5,r=5$, thus: $_nC_ra^{n-r}b^r=_8C_5\cdot (2x)^3\cdot5^5=56\cdot8x^3\cdot 3125=1400000x^3$