展开 (x^4-4x)^{1/2}*2(x^3-1)

解答

展开

(x^{4} - 4 x)^{\frac{1}{2}} \cdot 2 (x^{3} - 1)

2 (x^{4} - 4 x)^{\frac{1}{2}} x^{3} - 2 (x^{4} - 4 x)^{\frac{1}{2}}

求解步骤

(x^{4} - 4 x)^{\frac{1}{2}} \cdot 2 (x^{3} - 1)

= 2 (x^{4} - 4 x)^{\frac{1}{2}} (x^{3} - 1)

使用分配律:

a (b - c) = ab - a c

2 (x^{4} - 4 x)^{\frac{1}{2}} (x^{3} - 1) = 2 (x^{4} - 4 x)^{\frac{1}{2}} x^{3} - 2 (x^{4} - 4 x)^{\frac{1}{2}} \cdot 1

= 2 (x^{4} - 4 x)^{\frac{1}{2}} x^{3} - 2 (x^{4} - 4 x)^{\frac{1}{2}} \cdot 1

数字相乘:

2 \cdot 1 = 2

= 2 (x^{4} - 4 x)^{\frac{1}{2}} x^{3} - 2 (x^{4} - 4 x)^{\frac{1}{2}}

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