展开 (p^{2/3}-q^{1/3})^3

解答

展开

(p^{\frac{2}{3}} - q^{\frac{1}{3}})^{3}

p^{2} - 3 p^{\frac{4}{3}} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} q^{\frac{2}{3}} - q

求解步骤

(p^{\frac{2}{3}} - q^{\frac{1}{3}})^{3}

使用完全立方公式:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(p^{\frac{2}{3}} - q^{\frac{1}{3}})^{3} = (p^{\frac{2}{3}})^{3} - 3 (p^{\frac{2}{3}})^{2} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} (q^{\frac{1}{3}})^{2} - (q^{\frac{1}{3}})^{3}

= (p^{\frac{2}{3}})^{3} - 3 (p^{\frac{2}{3}})^{2} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} (q^{\frac{1}{3}})^{2} - (q^{\frac{1}{3}})^{3}

(p^{\frac{2}{3}})^{3} = p^{2}

(p^{\frac{2}{3}})^{2} = p^{\frac{4}{3}}

(q^{\frac{1}{3}})^{2} = q^{\frac{2}{3}}

(q^{\frac{1}{3}})^{3} = q

= p^{2} - 3 p^{\frac{4}{3}} q^{\frac{1}{3}} + 3 p^{\frac{2}{3}} q^{\frac{2}{3}} - q

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