Answer
$A^3-3A^2B+3AB^2-B^3$
Work Step by Step
We are given the expression $(A-B)^3$.
For expanding it we will use the $\textit{Binomial Theorem}$:
$$\begin{align}(a+b)^n=\binom{n}{0}a^n+\binom{n}{1}a^{n-1}b+\binom{n}{2}a^{n-2}b^2+\cdots+\binom{n}{n}b^n.\end{align}\tag1$$
Substitute $a=A$, $b=-B$, $n=3$ in Eq. $(1)$:
$$\begin{align*}
(A-B)^3&=\binom{3}{0}A^3+\binom{3}{1}A^2(-B)+\binom{3}{2}A(-B)^2+\binom{3}{3}(-B)^3\\
&=A^3-3A^2B+3AB^2-B^3.
\end{align*}$$
The expansion is:
$$(A-B)^3=A^3-3A^2B+3AB^2-B^3.$$
