Đáp án:
$\begin{array}{l}
21)\left( {5x - y} \right)\left( {25{x^2} + 5xy + {y^2}} \right) - {\left( {x - 2y} \right)^3} - 3{\left( {2x + y} \right)^3}\\
= 125{x^3} - {y^3} - {x^3} + 6{x^2}y - 12x{y^2} + 8{y^3}\\
- 24{x^3} + 36{x^2}y - 18x{y^2} + 3{y^3}\\
= 100{x^3} + 10{y^3} + 42{x^2}y - 30x{y^2}\\
22) - 4{\left( {x + 3y} \right)^3} + \left( {x - 3y} \right)\left( {x + y} \right)\left( {x - y} \right)\\
- {\left( {2x - y} \right)^3}\\
= - 4\left( {{x^3} + 9{x^2}y + 27x{y^2} + 27{y^3}} \right)\\
+ \left( {x - 3y} \right)\left( {{x^2} - {y^2}} \right) - \left( {8{x^3} - 12{x^2}y + 6x{y^2} - {y^3}} \right)\\
= - 4{x^3} - 36{x^2}y - 108x{y^2} - 108{y^3}\\
+ {x^3} - x{y^2} - 3{x^2}y + 3{y^3} - 8{x^3} + 12{x^2}y - 6x{y^2} + {y^3}\\
= - 11{x^3} - 104{y^3} - 27{x^2}y - 115x{y^2}\\
23)\\
{\left( {3x + y} \right)^3} - \left( {5x - y} \right)\left( {25{x^2} + 5xy + {y^2}} \right) + {\left( {x + 2y} \right)^3}\\
= 27{x^3} + 27{x^2}y + 9x{y^2} + {y^3}\\
- {\left( {5x} \right)^3} + {y^3} + {x^3} + 6{x^2}y + 12x{y^2} + 8{y^3}\\
= 23{x^3} + 10{y^3} + 33{x^2}y + 21x{y^2}
\end{array}$
