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受欢迎的代数 >

展开 (1/x+y)^5

解答

展开

(\frac{1}{x} + y)^{5}

解答

\frac{1}{x ^{5}} + \frac{5 y}{x ^{4}} + \frac{10 y ^{2}}{x ^{3}} + \frac{10 y ^{3}}{x ^{2}} + \frac{5 y ^{4}}{x} + y^{5}

求解步骤

(\frac{1}{x} + y)^{5}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{1}{x}, b = y

= i = 0 \sum 5 (i 5) (\frac{1}{x})^{(5 - i)} y^{i}

展开求和

= \frac{5 !}{0 ! ( 5 - 0 ) !} (\frac{1}{x})^{5} y^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{1}{x})^{4} y^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{1}{x})^{3} y^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{1}{x})^{2} y^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{1}{x})^{1} y^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} (\frac{1}{x})^{0} y^{5}

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} (\frac{1}{x})^{5} y^{0} : \frac{1}{x ^{5}}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (\frac{1}{x})^{4} y^{1} : \frac{5 y}{x ^{4}}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (\frac{1}{x})^{3} y^{2} : \frac{10 y ^{2}}{x ^{3}}

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (\frac{1}{x})^{2} y^{3} : \frac{10 y ^{3}}{x ^{2}}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (\frac{1}{x})^{1} y^{4} : \frac{5 y ^{4}}{x}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} (\frac{1}{x})^{0} y^{5} : y^{5}

= \frac{1}{x ^{5}} + \frac{5 y}{x ^{4}} + \frac{10 y ^{2}}{x ^{3}} + \frac{10 y ^{3}}{x ^{2}} + \frac{5 y ^{4}}{x} + y^{5}

流行的例子

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e x p an d 2 π r (r + h)

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