Đáp án:
$\begin{array}{l}
a){x^5}.y + 3{x^5}y + 5{x^5}y + ... + 2021.{x^5}y\\
= {x^5}.y.\left( {1 + 3 + 5 + ... + 2021} \right)\\
= {x^5}.y.\frac{{\left( {2021 + 1} \right).1011}}{2}\\
= 1022121.{x^5}y\\
b)2{x^5} + {2^2}.{x^5} + {2^3}.{x^5} + ... + {2^{101}}.{x^5}\\
= {x^5}.\left( {2 + {2^2} + {2^3} + ... + {2^{101}}} \right)\\
Đặt:2 + {2^2} + {2^3} + ... + {2^{101}} = A\\
\Rightarrow 2A = {2^2} + {2^3} + {2^4} + ... + {2^{102}}\\
\Rightarrow 2A - A = {2^{102}} - 2\\
\Rightarrow A = {2^{102}} - 2\\
\Rightarrow 2{x^5} + {2^2}.{x^5} + {2^3}.{x^5} + ... + {2^{101}}.{x^5}\\
= {x^5}.\left( {{2^{102}} - 2} \right)
\end{array}$
