College Algebra, Chapter 9, Review Exercises, Section Review Exercises, Problem 76

Expand the expression $(x - 2)^5$
By using Pascal's Triangle, we find the expansion of $(a + b)^5$ as $(a + b)^5 = a^5 + 5a^4 b + 10a^3 b^2 + 10a^2 b^3 + 5ab^4 + b^5$

Substituting $a = x$ and $b = -2$ gives

$
\begin{equation}
\begin{aligned}
(x - 2)^5 &= x^5 + 5 (x)^4(-2) + 10 (x)^3(-2)^2 + 10 (x)^2(-2)^3 + 5 (x)(-2)^4 + (-2)^5\\
\\
&= x^5 - 10x^4 + 40x^3 - 80x^2 + 80x - 32
\end{aligned}
\end{equation}
$