Đáp án:

 a) 0; b)7775

Giải thích các bước giải:

\[\begin{array}{l}
a){x^5}y - x{y^5} = xy\left( {{x^4} - {y^4}} \right)\\
\left\{ \begin{array}{l}
x - y = 2\\
{x^2} + {y^2} = 4
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
{\left( {x - y} \right)^2} = 4\\
{x^2} + {y^2} = 4
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
{x^2} + {y^2} - 2xy = 4\\
{x^2} + {y^2} = 4
\end{array} \right. \Rightarrow xy = 0\\
 \Rightarrow {x^5}y - x{y^5} = xy\left( {{x^4} - {y^4}} \right) = 0\\
b){x^5} - 32{y^5}\\
 = {x^5} - {\left( {2y} \right)^5}\\
 = \left( {x - 2y} \right)\left( {{x^4} + {x^3}.2y + {x^2}.{{\left( {2y} \right)}^2} + x.{{\left( {2y} \right)}^3} + {{\left( {2y} \right)}^4}} \right)\\
 + ){x^4} + {x^3}.2y + {x^2}.{\left( {2y} \right)^2} + x.{\left( {2y} \right)^3} + {\left( {2y} \right)^4}\\
 = \left( {{x^4} + 2{x^2}.{{\left( {2y} \right)}^2} + {{\left( {2y} \right)}^4}} \right) - {x^2}.{\left( {2y} \right)^2} + {x^3}.2y + x.{\left( {2y} \right)^3}\\
 = {\left( {{x^2} + {{\left( {2y} \right)}^2}} \right)^2} + 2xy\left( {{x^2} - 2xy + 4{y^2}} \right)\\
 = {\left( {{{\left( {x + 2y} \right)}^2} - 2.x.2y} \right)^2} + 2xy\left( {{{\left( {x + 2y} \right)}^2} - 6xy} \right)\\
 = {\left( {{7^2} - 4.3} \right)^2} + 2.3.\left( {{7^2} - 6.3} \right)\\
 = 1555\\
 + )x + 2y = 7\\
 \Rightarrow {\left( {x + 2y} \right)^2} = 49\\
 \Leftrightarrow {x^2} + 4xy + 4{y^2} = 49\\
 \Leftrightarrow {x^2} - 4xy + 4{y^2} + 8xy = 49\\
 \Leftrightarrow {\left( {x - 2y} \right)^2} + 8xy = 49\\
 \Leftrightarrow {\left( {x - 2y} \right)^2} = 49 - 8.3 = 25\\
 \Leftrightarrow x - 2y = 5\left( {x > 2y \Rightarrow x - 2y > 0} \right)\\
 \Rightarrow {x^5} - 32{y^5} = 5.1555 = 7775
\end{array}\]