Answer
$1-5x+10x^{2}-10x^{3}+5x^{4}-x^{5}$
Work Step by Step
$(a+b)^{n}=\left(\begin{array}{l}
n\\
0
\end{array}\right)a^{n}+\left(\begin{array}{l}
n\\
1
\end{array}\right)a^{n-1}b+\left(\begin{array}{l}
n\\
2
\end{array}\right)a^{n-2}b^{2}+\cdots+\left(\begin{array}{l}
n\\
n
\end{array}\right)b^{n}$
-----------------
$(1 -x)^{5}= (1 +(-x))^{5}=$
$\left(\begin{array}{l}
5\\
0
\end{array}\right)(1)^{5}(-x)^{0}+ \left(\begin{array}{l}
5\\
1
\end{array}\right)(1)^{4}(-x)^{1}+ \left(\begin{array}{l}
5\\
2
\end{array}\right)(1)^{3}(-x)^{2}+$
$+ \left(\begin{array}{l}
5\\
3
\end{array}\right)(1)^{2}(-x)^{3}+ \left(\begin{array}{l}
5\\
4
\end{array}\right)(1)^{1}(-x)^{4}+ \left(\begin{array}{l}
5\\
5
\end{array}\right)(1)^{0}(-x)^{5}$
$\left(\begin{array}{l}
5\\
0
\end{array}\right)=1=\left(\begin{array}{l}
5\\
5
\end{array}\right)$
$\left(\begin{array}{l}
5\\
1
\end{array}\right)=5=\left(\begin{array}{l}
5\\
4
\end{array}\right)$
$\displaystyle \left(\begin{array}{l}
5\\
2
\end{array}\right)=\frac{5\times 4}{1\times 2}=10=\left(\begin{array}{l}
5\\
3
\end{array}\right)$
$=1-5x+10x^{2}-10x^{3}+5x^{4}-x^{5}$
