Chapter 12, Problem 58RE

To determine

To expand: The given expression using Binomial theorem.

Answer to Problem 58RE

The expanded expression is $x^4+12x^3+54x^2+108x+81$ .

Explanation of Solution

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

The given expression is expanded as

  $\begin{array}{c}{\left(x-3\right)}^4=\left(\begin{array}{l}4\\ 0\end{array}\right)x^4+\left(\begin{array}{l}4\\ 1\end{array}\right){\left(-3\right)}^1{x}^{4-1}+\left(\begin{array}{l}4\\ 2\end{array}\right){\left(-3\right)}^2{x}^{3-2}+\left(\begin{array}{l}4\\ 3\end{array}\right){\left(-3\right)}^3{x}^{4-3}+\left(\begin{array}{l}4\\ 4\end{array}\right){\left(-3\right)}^4{x}^{4-4}\\ =x^4+12x^3+54x^2+108x+81\end{array}$

Therefore, the expanded expression is shown above.