Answer
$495a^{8}b^{8}$
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: $\left(\begin{array}{l}
n\\
r
\end{array}\right)=\left(\begin{array}{l}
n\\
n-r
\end{array}\right)$
---------------
We are searching for the term $\left(\begin{array}{l}
12\\
r
\end{array}\right)(a)^{r}(b^{2})^{12-r}$
in which $(b^{2})^{12-r}=b^{8}$
$b^{24-2r}=b^{8}$
$24-2r=8$
$2r=16$
$r=8$
So the term is
$\left(\begin{array}{l}
12\\
8
\end{array}\right)(a)^{8}(b^{2})^{12-8}=\left(\begin{array}{l}
12\\
12-8
\end{array}\right)(a)^{8}(b^{2})^{12-8}=$
$= \displaystyle \frac{12\cdot 11\cdot 10\cdot 9}{1\cdot 2\cdot 3\cdot 4}\cdot a^{8}b^{8}$
$=495a^{8}b^{8}$
