Chapter 11.7, Problem 16WE

To determine

To Find: The ninth term of the form ${(p-q)}^{15}$ .

Answer to Problem 16WE

The required 9^th term of the binomial form ${(p-q)}^{15}$ is $6435p^7{q}^8$ .

Explanation of Solution

Given Information:

The eight term is $-6435p^8{q}^7$ .

In this given case the term 8^th and the term 9^th have same coefficient, as there are 16 terms in the expansion of the form.

It is also to be noted that the powers of the binomial expansion also get switched symmetrically. The alternating minus sign is not at all treated as a part of the coefficient.

So, the alternating minus sign will come about because of changing power on $(-q)$ .

Hence, the 9^th term of the binomial form ${(p-q)}^{15}$ is $6435p^7{q}^8$ .