Chapter 11, Problem 19PT

To determine

Find the 4^th term of expansion ${(c+d)}^9$

Answer to Problem 19PT

The 4^th term of the expansion is $84c^6·d^3$ .

Explanation of Solution

Given:

The expansion: ${(c+d)}^9$

Concept Used:

In ${(a+b)}^n$ , the $rth$ term of the expansion is ${}^n{\text{C}}_{r-1}·a^{n-r+1}·b^{r-1}$

Calculation:

Find the 4^th term of the expansion: ${(c+d)}^9$

  $\begin{array}{}$ {(c+d)}^{°}$$ {}^n{C}_{r-1}\cdot a^{n-r+}\cdot b^{r-4}\Rightarrow n=9,r=4,a=c,b=d$$ {}^2{C}_{4-1}\cdot c^{8-4+1}\cdot {(3n)}^{4-1}{=}^2{C}_2\cdot c^6\cdot {(d)}^2=84\cdot c^6\cdot d^3=84c^6\cdot a^2$\end{array}$

Thus, the 4^th term of the expansion is $84c^6·d^3$ .