A=(∛(a^4 )+∛(a^2 b^2 )+∛(b^4 ))/(∛(a^2 )+∛ab+∛(b^2 ))

Giải thích các bước giải:

\[\begin{array}{l}
A = \frac{{\sqrt[3]{{{a^4}}} + \sqrt[3]{{{a^2}{b^2}}} + \sqrt[3]{{{b^4}}}}}{{\sqrt[3]{{{a^2}}} + \sqrt[3]{{ab}} + \sqrt[3]{{{b^2}}}}} = \frac{{\left( {\sqrt[3]{{{a^2}}} - \sqrt[3]{{{b^2}}}} \right)\left( {\sqrt[3]{{{a^4}}} + \sqrt[3]{{{a^2}{b^2}}} + \sqrt[3]{{{b^4}}}} \right)}}{{\left( {\sqrt[3]{{{a^2}}} - \sqrt[3]{{{b^2}}}} \right)\left( {\sqrt[3]{{{a^2}}} + \sqrt[3]{{ab}} + \sqrt[3]{{{b^2}}}} \right)}} = \frac{{{{\left( {\sqrt[3]{{{a^2}}}} \right)}^3} - {{\left( {\sqrt[3]{{{b^2}}}} \right)}^3}}}{{\left( {\sqrt[3]{a} + \sqrt[3]{b}} \right)\left[ {\left( {\sqrt[3]{a} - \sqrt[3]{b}} \right)\left( {\sqrt[3]{{{a^2}}} + \sqrt[3]{{ab}} + \sqrt[3]{{{b^2}}}} \right)} \right]}}\\
 = \frac{{{a^2} - {b^2}}}{{\left( {\sqrt[3]{a} + \sqrt[3]{b}} \right)\left( {a - b} \right)}} = \frac{{a + b}}{{\left( {\sqrt[3]{a} + \sqrt[3]{b}} \right)}} = \left( {\sqrt[3]{{{a^2}}} + \sqrt[3]{{ab}} + \sqrt[3]{{{b^2}}}} \right)
\end{array}\]