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受欢迎的代数 >

展开 (x/2-2/x)^6

解答

展开

(\frac{x}{2} - \frac{2}{x})^{6}

解答

\frac{x ^{6}}{64} - \frac{3 x ^{4}}{8} + \frac{15 x ^{2}}{4} - 20 + \frac{60}{x ^{2}} - \frac{96}{x ^{4}} + \frac{64}{x ^{6}}

求解步骤

(\frac{x}{2} - \frac{2}{x})^{6}

使用二项式定理:

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

a = \frac{x}{2}, b = - \frac{2}{x}

= i = 0 \sum 6 (i 6) (\frac{x}{2})^{(6 - i)} (- \frac{2}{x})^{i}

展开求和

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

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} (\frac{x}{2})^{6} (- \frac{2}{x})^{0} : \frac{x ^{6}}{64}

化简

\frac{6 !}{1 ! ( 6 - 1 ) !} (\frac{x}{2})^{5} (- \frac{2}{x})^{1} : - \frac{3 x ^{4}}{8}

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} (\frac{x}{2})^{4} (- \frac{2}{x})^{2} : \frac{15 x ^{2}}{4}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} (\frac{x}{2})^{3} (- \frac{2}{x})^{3} : - 20

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} (\frac{x}{2})^{2} (- \frac{2}{x})^{4} : \frac{60}{x ^{2}}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} (\frac{x}{2})^{1} (- \frac{2}{x})^{5} : - \frac{96}{x ^{4}}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} (\frac{x}{2})^{0} (- \frac{2}{x})^{6} : \frac{64}{x ^{6}}

= \frac{x ^{6}}{64} - \frac{3 x ^{4}}{8} + \frac{15 x ^{2}}{4} - 20 + \frac{60}{x ^{2}} - \frac{96}{x ^{4}} + \frac{64}{x ^{6}}

流行的例子

化简 1/2+3/44 (5(0.6)-((0.6)^3)/3)

s im pl i f y \frac{1}{2} + \frac{3}{44} (5 (0.6) - \frac{( 0.6 ) ^{3}}{3})

展开 (x^2-3)dx

e x p an d (x^{2} - 3) d x

s im pl i f y (n + i)^{2}

展开 1/(\sqrt[3]{1+x^2)}

e x p an d \frac{1}{3 1 + x ^{2}}

化简 (4y+1/6)(4y-1/6)

s im pl i f y (4 y + \frac{1}{6}) (4 y - \frac{1}{6})