Rút gọn phép tính : ( a ^ 2/3 + 1 ) ( a ^ 4/9 + a ^ 2/9 + 1)

7/22

Rút gọn : \(\left( {{a^{\frac{2}{3}}} + 1} \right)\left( {{a^{\frac{4}{9}}} + {a^{\frac{2}{9}}} + 1} \right)\left( {{a^{\frac{2}{9}}} - 1} \right)\) ta được.

\({a^{\frac{1}{3}}} + 1\).

\({a^{\frac{1}{3}}} - 1\).

\({a^{\frac{4}{3}}} + 1\).

\({a^{\frac{4}{3}}} - 1\).

Giải thích

Ta có: \[\left( {{a^{\frac{2}{3}}} + 1} \right)\left( {{a^{\frac{4}{9}}} + {a^{\frac{2}{9}}} + 1} \right)\left( {{a^{\frac{2}{9}}} - 1} \right) = \left( {{a^{\frac{2}{3}}} + 1} \right)\left[ {{{\left( {{a^{\frac{2}{9}}}} \right)}^3} - 1} \right] = \left( {{a^{\frac{2}{3}}} + 1} \right)\left( {{a^{\frac{2}{3}}} - 1} \right) = {a^{\frac{4}{3}}} - 1\].