展开 (1-x^{1/2})^3

解答

展开

(1 - x^{\frac{1}{2}})^{3}

1 - 3 x^{\frac{1}{2}} + 3 x - x^{\frac{3}{2}}

求解步骤

(1 - x^{\frac{1}{2}})^{3}

使用完全立方公式:

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

(1 - x^{\frac{1}{2}})^{3} = 1^{3} - 3 \cdot 1^{2} x^{\frac{1}{2}} + 3 \cdot 1 \cdot (x^{\frac{1}{2}})^{2} - (x^{\frac{1}{2}})^{3}

= 1^{3} - 3 \cdot 1^{2} x^{\frac{1}{2}} + 3 \cdot 1 \cdot (x^{\frac{1}{2}})^{2} - (x^{\frac{1}{2}})^{3}

1^{3} = 1

3 \cdot 1^{2} x^{\frac{1}{2}} = 3 x^{\frac{1}{2}}

3 \cdot 1 \cdot (x^{\frac{1}{2}})^{2} = 3 x

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

= 1 - 3 x^{\frac{1}{2}} + 3 x - x^{\frac{3}{2}}

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