Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
a,\\
M = \left( {\sqrt[3]{9} + \sqrt[3]{6} + \sqrt[3]{4}} \right).\left( {\sqrt[3]{3} - \sqrt[3]{2}} \right)\\
= \left( {\sqrt[3]{3} - \sqrt[3]{2}} \right).\left( {{{\sqrt[3]{3}}^2} + \sqrt[3]{3}.\sqrt[3]{2} + {{\sqrt[3]{2}}^2}} \right)\\
= {\sqrt[3]{3}^3} - {\sqrt[3]{2}^3}\\
= 3 - 2\\
= 1\\
b,\\
N = \sqrt[3]{{7 + 4\sqrt 3 }}.\sqrt[3]{{7 - 4\sqrt 3 }} + \sqrt[3]{{72 + 32\sqrt 5 }}.\sqrt[3]{{9 - 4\sqrt 5 }}\\
= \sqrt[3]{{\left( {7 + 4\sqrt 3 } \right).\left( {7 - 4\sqrt 3 } \right)}} + \sqrt[3]{{\left( {72 + 32\sqrt 5 } \right).\left( {9 - 4\sqrt 5 } \right)}}\\
= \sqrt[3]{{{7^2} - {{\left( {4\sqrt 3 } \right)}^2}}} + \sqrt[3]{{8.\left( {9 + 4\sqrt 5 } \right).\left( {9 - 4\sqrt 5 } \right)}}\\
= \sqrt[3]{{49 - 48}} + \sqrt[3]{{8.\left( {{9^2} - {{\left( {4\sqrt 5 } \right)}^2}} \right)}}\\
= 1 + \sqrt[3]{{8.1}}\\
= 3\\
c,\\
P = \sqrt[3]{{ - 27{x^3}{y^{12}}{z^9}}}\\
= \sqrt[3]{{{{\left( { - 3x{y^4}{z^3}} \right)}^3}}}\\
= - 3x{y^4}{z^3}
\end{array}\)
