Question

In the following exercises, expand each binomial.

$(x-2{)}^4$

Short answer

Expansion is$x^4-8x^3+24x^2-32x+16$

Step-by-step solution

Given Information

Expand$(x-2{)}^4$

Solution

We have

$$\begin{gathered} (x-2{)}^4=\left(\begin{array}{c}4\\ 0\end{array}\right)x^{4-0}{(-2)}^{4-4}+\left(\begin{array}{c}4\\ 1\end{array}\right)x^{4-1}{(-2)}^{4-3}+\left(\begin{array}{c}4\\ 2\end{array}\right)x^{4-2}{(-2)}^{4-2}+\left(\begin{array}{c}4\\ 3\end{array}\right)x^{4-3}{(-2)}^{4-1}+\left(\begin{array}{c}4\\ 4\end{array}\right)x^{4-4}{(-2)}^{4-0} \\ =x^4-8x^3+24x^2-32x+16 \end{gathered}$$