Chapter 12, Problem 59RE

To determine

To expand: The given expression using Binomial theorem.

Answer to Problem 59RE

The expanded expression is $32x^5+240x^4+720x^3+1080x^2+810x+243$ .

Explanation of Solution

Given: ${\left(x+2\right)}^5$

The given expression is expanded as

  $\begin{array}{c}{\left(2x+3\right)}^5=\left[\begin{array}{l}\left(\begin{array}{l}5\\ 0\end{array}\right){\left(2x\right)}^5+\left(\begin{array}{l}5\\ 1\end{array}\right){\left(3\right)}^1{\left(2x\right)}^{5-1}+\left(\begin{array}{l}5\\ 2\end{array}\right){\left(3\right)}^2{\left(2x\right)}^{5-2}+\\ \left(\begin{array}{l}5\\ 3\end{array}\right){\left(3\right)}^3{\left(2x\right)}^{5-3}+\left(\begin{array}{l}5\\ 4\end{array}\right){\left(3\right)}^4{\left(2x\right)}^{5-4}+\left(\begin{array}{l}5\\ 5\end{array}\right){\left(3\right)}^5{\left(2x\right)}^{5-5}\end{array}\right]\\ =32x^5+240x^4+720x^3+1080x^2+810x+243\end{array}$

Therefore, the expanded expression is shown above.