展开 (x^{9/5}-4x^{4/5})^2

解答

展开

(x^{\frac{9}{5}} - 4 x^{\frac{4}{5}})^{2}

x^{\frac{18}{5}} - 8 x^{\frac{13}{5}} + 16 x^{\frac{8}{5}}

求解步骤

(x^{\frac{9}{5}} - 4 x^{\frac{4}{5}})^{2}

使用完全平方公式:

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

(x^{\frac{9}{5}} - 4 x^{\frac{4}{5}})^{2} = (x^{\frac{9}{5}})^{2} - 2 x^{\frac{9}{5}} \cdot 4 x^{\frac{4}{5}} + (4 x^{\frac{4}{5}})^{2}

= (x^{\frac{9}{5}})^{2} - 2 x^{\frac{9}{5}} \cdot 4 x^{\frac{4}{5}} + (4 x^{\frac{4}{5}})^{2}

(x^{\frac{9}{5}})^{2} = x^{\frac{18}{5}}

2 x^{\frac{9}{5}} \cdot 4 x^{\frac{4}{5}} = 8 x^{\frac{13}{5}}

(4 x^{\frac{4}{5}})^{2} = 16 x^{\frac{8}{5}}

= x^{\frac{18}{5}} - 8 x^{\frac{13}{5}} + 16 x^{\frac{8}{5}}

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