Answers to the Extended Problems are below in random order.
\(\begin{align}&26\ \text{terms}\ & \ \ &
19,496,960{x}^{13}{y}^{4}\ & \ \ &
25th\\\\
&9,289,728{x}^{9}{y}^{6}\ & \ \ &
7th\ \text{term}\ & \ \ &
-4,560,192{a}^{5}{b}^{25}\\\\
&32{x}^{5}-80{x}^{4}y+80{x}^{3}{y}^{2}-40{x}^{2}{y}^{3}+10x{y}^{4}-{y}^{5}\ & \ \ &
480,700{x}^{18}{y}^{7}\end{align}\)
\(\begin{align}&26\ \text{terms}\ & \ \ &
19,496,960{x}^{13}{y}^{4}\ & \ \ &
25th\\\\
&9,289,728{x}^{9}{y}^{6}\ & \ \ &
7th\ \text{term}\ & \ \ &
-4,560,192{a}^{5}{b}^{25}\\\\
&32{x}^{5}-80{x}^{4}y+80{x}^{3}{y}^{2}-40{x}^{2}{y}^{3}+10x{y}^{4}-{y}^{5}\ & \ \ &
480,700{x}^{18}{y}^{7}\end{align}\)