展开 (x^{3/2}-4)^3

解答

展开

(x^{\frac{3}{2}} - 4)^{3}

x^{\frac{9}{2}} - 12 x^{3} + 48 x^{\frac{3}{2}} - 64

求解步骤

(x^{\frac{3}{2}} - 4)^{3}

使用完全立方公式:

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

(x^{\frac{3}{2}} - 4)^{3} = (x^{\frac{3}{2}})^{3} - 3 (x^{\frac{3}{2}})^{2} \cdot 4 + 3 x^{\frac{3}{2}} \cdot 4^{2} - 4^{3}

= (x^{\frac{3}{2}})^{3} - 3 (x^{\frac{3}{2}})^{2} \cdot 4 + 3 x^{\frac{3}{2}} \cdot 4^{2} - 4^{3}

(x^{\frac{3}{2}})^{3} = x^{\frac{9}{2}}

3 (x^{\frac{3}{2}})^{2} \cdot 4 = 12 x^{3}

3 x^{\frac{3}{2}} \cdot 4^{2} = 48 x^{\frac{3}{2}}

4^{3} = 64

= x^{\frac{9}{2}} - 12 x^{3} + 48 x^{\frac{3}{2}} - 64

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