Đáp án:
$\begin{array}{l}
1){\left( {xy + \frac{1}{y}} \right)^5} = \sum\limits_{k = 0}^5 {C_5^k.{{\left( {xy} \right)}^{5 - k}}.{y^{ - k}}} = \sum\limits_{k = 0}^5 {C_5^k.{x^{5 - k}}.{y^{5 - k - k}}} \\
{x^3}y \Rightarrow \left\{ \begin{array}{l}
5 - k = 3\\
5 - k - k = 1
\end{array} \right. \Rightarrow k = 2\\
\Rightarrow Số\,hạng\,chứa\,{x^3}y:C_5^2.{x^3}y = 10{x^3}y\\
2)\\
C_n^0 + C_n^1 + ... + C_n^n = 1024\\
\Rightarrow {2^n} = 1024\\
\Rightarrow n = 10\\
\Rightarrow {\left( {\frac{1}{x} + {x^3}} \right)^{10}} = \sum\limits_{k = 0}^{10} {C_{10}^k.{x^{ - \left( {10 - k} \right)}}{x^{3k}}} = \sum\limits_{k = 0}^{10} {C_{10}^k.{x^{4k - 10}}} \\
{x^6} \Rightarrow 4k - 10 = 6 \Rightarrow k = 4\\
\Rightarrow Hệ\,số:{x^6}\,la:C_{10}^6 = 210
\end{array}$
