Chapter 12, Problem 60RE

To determine

To expand: The given expression using Binomial theorem.

Answer to Problem 60RE

The expanded expression is $81x^4+432x^3+864x^2+768x+256$ .

Explanation of Solution

Given: ${\left(3x-4\right)}^4$

The given expression is expanded as

  $\begin{array}{c}{\left(3x-4\right)}^4=\left(\begin{array}{l}4\\ 0\end{array}\right){\left(3x\right)}^4+\left(\begin{array}{l}4\\ 1\end{array}\right){\left(-4\right)}^1{\left(3x\right)}^{4-1}+\left(\begin{array}{l}4\\ 2\end{array}\right){\left(-4\right)}^2{\left(3x\right)}^{3-2}+\left(\begin{array}{l}4\\ 3\end{array}\right){\left(-4\right)}^3{\left(3x\right)}^{4-3}+\left(\begin{array}{l}4\\ 4\end{array}\right){\left(-4\right)}^4{\left(3x\right)}^{4-4}\\ =81x^4+432x^3+864x^2+768x+256\end{array}$

Therefore, the expanded expression is shown above.