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受欢迎的代数 >

展开 (1+3/x)^6

解答

展开

(1 + \frac{3}{x})^{6}

解答

1 + \frac{18}{x} + \frac{135}{x ^{2}} + \frac{540}{x ^{3}} + \frac{1215}{x ^{4}} + \frac{1458}{x ^{5}} + \frac{729}{x ^{6}}

求解步骤

(1 + \frac{3}{x})^{6}

使用二项式定理:

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

a = 1, b = \frac{3}{x}

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (\frac{3}{x})^{i}

展开求和

= \frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (\frac{3}{x})^{0} + \frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (\frac{3}{x})^{1} + \frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (\frac{3}{x})^{2} + \frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (\frac{3}{x})^{3} + \frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (\frac{3}{x})^{4} + \frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (\frac{3}{x})^{5} + \frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (\frac{3}{x})^{6}

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (\frac{3}{x})^{0} : 1

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} \cdot 1^{5} (\frac{3}{x})^{1} : \frac{18}{x}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (\frac{3}{x})^{2} : \frac{135}{x ^{2}}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (\frac{3}{x})^{3} : \frac{540}{x ^{3}}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (\frac{3}{x})^{4} : \frac{1215}{x ^{4}}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (\frac{3}{x})^{5} : \frac{1458}{x ^{5}}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (\frac{3}{x})^{6} : \frac{729}{x ^{6}}

= 1 + \frac{18}{x} + \frac{135}{x ^{2}} + \frac{540}{x ^{3}} + \frac{1215}{x ^{4}} + \frac{1458}{x ^{5}} + \frac{729}{x ^{6}}

流行的例子

化简 (60.3)/(s(s(s+4)(s+6)+60.3))

s im pl i f y \frac{60.3}{s ( s ( s + 4 ) ( s + 6 ) + 60.3 )}

展开 (-4-3n)-8

e x p an d (- 4 - 3 n) - 8

展开 A(e^{6t-3e^t}+e^{6t-3e^t}t(6-3e^t))

e x p an d A (e^{6 t - 3 e^{t}} + e^{6 t - 3 e^{t}} t (6 - 3 e^{t}))

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e x p an d \frac{- 4 x ^{2} + 3 x - 5}{x ^{2} ( 4 x - 9 )}

展开 (2b(300-4b))/3

e x p an d \frac{2 b ( 300 - 4 b )}{3}