展开 (u-1)^2(u)^{1/2}

解答

展开

(u - 1)^{2} (u)^{\frac{1}{2}}

u^{\frac{5}{2}} - 2 u^{\frac{3}{2}} + u^{\frac{1}{2}}

求解步骤

(u - 1)^{2} u^{\frac{1}{2}}

= u^{\frac{1}{2}} (u - 1)^{2}

展开

(u - 1)^{2} : u^{2} - 2 u + 1

= u^{\frac{1}{2}} (u^{2} - 2 u + 1)

使用分配律:

m (a + b + c) = ma + mb + m c

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

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

u^{\frac{1}{2}} u^{2} = u^{\frac{5}{2}}

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

u^{\frac{1}{2}} \cdot 1 = u^{\frac{1}{2}}

= u^{\frac{5}{2}} - 2 u^{\frac{3}{2}} + u^{\frac{1}{2}}

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