Answer
$3520\sqrt{2}y^{3}$
Work Step by Step
(See p. 884)
The term that contains $a^{r}$
in the expansion of $(a+b)^{n}$ is$ \left(\begin{array}{l}
n\\
r
\end{array}\right)a^{r}b^{n-r}$.
Property of bin. coefficients: $\left(\begin{array}{l}
n\\
r
\end{array}\right)=\left(\begin{array}{l}
n\\
n-r
\end{array}\right)$
---------------
$a=\sqrt{2}, b=y, n=12$
If the exponent of b is 3,
then the exponent of a is $12-3=9$
The term is
$\left(\begin{array}{l}
12\\
9
\end{array}\right)a^{9}b^{12-9}=\left(\begin{array}{l}
12\\
12-9
\end{array}\right)a^{9}b^{12-9}$
$=\displaystyle \frac{12\cdot 11\cdot 10}{1\cdot 2\cdot 3}\cdot a^{9}b^{3}$
$=220(\sqrt{2})^{9}y^{3}$
$=220\cdot 2^{4}\sqrt{2}\cdot y^{3}$
$=3520\sqrt{2}y^{3}$
