Answer
$ A^{3}-3A^{2}B+3AB^{2}-B^{3}$
Work Step by Step
The Binomial Theorem$:$
$(a+b)^{n}=\left(\begin{array}{l}
n\\
0
\end{array}\right)a^{n}+\left(\begin{array}{l}
n\\
1
\end{array}\right)a^{n-1}b+\left(\begin{array}{l}
n\\
2
\end{array}\right)a^{n-2}b^{2}+\cdots+\left(\begin{array}{l}
n\\
n
\end{array}\right)b^{n}$
----------------
$\left(\begin{array}{l}
3\\
0
\end{array}\right)a^{3}b^{0}+\left(\begin{array}{l}
3\\
1
\end{array}\right)a^{2}b^{1}+\left(\begin{array}{l}
3\\
2
\end{array}\right)a^{1}b^{2}+\left(\begin{array}{l}
3\\
3
\end{array}\right)a^{0}b^{3}$
replace $a=A, b=-B$
$=1\cdot A^{3}(-B)^{0}+3A^{2}(-B)^{1}+3A^{1}(-B)^{3}+1\cdot A^{0}(-B)^{3}$
$= A^{3}-3A^{2}B+3AB^{2}-B^{3}$
