Chapter 14.1, Problem 19E

To determine

To find: Thesecond term of ${\left(c-2d\right)}^7$ .

Answer to Problem 19E

The second term is $-14c^{6}d$ .

Explanation of Solution

Given:

The given expressionis ${\left(c-2d\right)}^7$ .

Calculation:

Consider the given expression,

  ${\left(c-2d\right)}^7$

Consider the $r^{th}$ term of the expansion ${\left(x+y\right)}^n$ is,

  $T_r=C\left(n,r-1\right)x^{n-p+1}{y}^{r-1}$

Then, the second term of the expansion is,

  $\begin{array}{c}{T}_r=C\left(7,2-1\right){\left(c\right)}^{7-2+1}{\left(-2d\right)}^{2-1}\\ =C\left(7,2\right)c^6\left(-2d\right)\\ =7c^6\left(-2d\right)\\ =-14c^{6}d\end{array}$