Chapter 11, Problem 11CT

To determine

To calculate:

The ${12}^{th}$ term in the following expansion ${\left(2x-y\right)}^{13}$

Answer to Problem 11CT

The ${12}^{th}$ term of the expansion is $-312x^2{y}^{11}$ .

Explanation of Solution

Given information:

  ${\left(2x-y\right)}^{13}$

Formula used:

  $t_{r+1}=C{}_r\times a^{n-r}\times b^r$

Calculation:

Consider the expansion:

  ${\left(2x-y\right)}^{13}$

By using this formula:

  $\begin{array}{l}{t}_{r+1}=C{}_r\times a^{n-r}\times b^r\\ t_{12}=C{}_{11}\times x^{13-11}\times {\left(-y\right)}^{11}\\ t_{12}=312\times x^{13-11}\times {\left(-y\right)}^{11}\\ t_{12}=-312x^2{y}^{11}\end{array}$

The ${12}^{th}$ term of the expansion is $-312x^2{y}^{11}$ .