Đáp án: $P = \dfrac{7}{3}$
Giải thích các bước giải:
$\begin{array}{l}
P = {\left( {3x + y} \right)^3} - \left( {2x - y} \right)\left( {2x + y} \right) + {\left( {x - 3y} \right)^3}\\
Khi:x = \dfrac{1}{3};y = - \dfrac{1}{3}\\
\Leftrightarrow P = {\left( {3.\dfrac{1}{3} - \dfrac{1}{3}} \right)^3} - \left( {2.\dfrac{1}{3} + \dfrac{1}{3}} \right).\left( {2.\dfrac{1}{3} - \dfrac{1}{3}} \right)\\
+ {\left( {\dfrac{1}{3} - 3.\dfrac{{ - 1}}{3}} \right)^3}\\
= {\left( {1 - \dfrac{1}{3}} \right)^3} - 1.\dfrac{1}{3} + {\left( {\dfrac{1}{3} + 1} \right)^3}\\
= {\left( {\dfrac{2}{3}} \right)^3} - \dfrac{1}{3} + {\left( {\dfrac{4}{3}} \right)^3}\\
= \dfrac{8}{{27}} - \dfrac{1}{3} + \dfrac{{64}}{{27}}\\
= \dfrac{7}{3}
\end{array}$
