Answer
Fill the blanks with
$\left(\begin{array}{l}
4\\
0
\end{array}\right),\ \left(\begin{array}{l}
4\\
1
\end{array}\right),\ \left(\begin{array}{l}
4\\
2
\end{array}\right),\ \left(\begin{array}{l}
4\\
2
\end{array}\right)$
Work Step by Step
The Binomial Theorem (p. 883)
$(a+b)^{n}=\left(\begin{array}{l}
n\\
0
\end{array}\right)a^{n}+\left(\begin{array}{l}
n\\
1
\end{array}\right)a^{n-1}b+\left(\begin{array}{l}
n\\
2
\end{array}\right)a^{n-2}b^{2}+\cdots+\left(\begin{array}{l}
n\\
n
\end{array}\right)b^{n}$
------------------
$(a+b)^{4}=\left(\begin{array}{l}
4\\
0
\end{array}\right)a^{4}+\left(\begin{array}{l}
4\\
1
\end{array}\right)a^{3}b+\left(\begin{array}{l}
4\\
2
\end{array}\right)a^{2}b^{2}+\left(\begin{array}{l}
4\\
1
\end{array}\right)ab^{3}+\left(\begin{array}{l}
4\\
0
\end{array}\right)b^{4}$
