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受欢迎的代数 >

展开 (x+1/(2x^2))^8

解答

展开

(x + \frac{1}{2 x ^{2}})^{8}

解答

x^{8} + 4 x^{5} + 7 x^{2} + \frac{7}{x} + \frac{35}{8 x ^{4}} + \frac{7}{4 x ^{7}} + \frac{7}{16 x ^{10}} + \frac{1}{16 x ^{13}} + \frac{1}{256 x ^{16}}

求解步骤

(x + \frac{1}{2 x ^{2}})^{8}

使用二项式定理:

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

a = x, b = \frac{1}{2 x ^{2}}

= i = 0 \sum 8 (i 8) x^{(8 - i)} (\frac{1}{2 x ^{2}})^{i}

展开求和

= \frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (\frac{1}{2 x ^{2}})^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (\frac{1}{2 x ^{2}})^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (\frac{1}{2 x ^{2}})^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (\frac{1}{2 x ^{2}})^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (\frac{1}{2 x ^{2}})^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (\frac{1}{2 x ^{2}})^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (\frac{1}{2 x ^{2}})^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (\frac{1}{2 x ^{2}})^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (\frac{1}{2 x ^{2}})^{8}

化简

\frac{8 !}{0 ! ( 8 - 0 ) !} x^{8} (\frac{1}{2 x ^{2}})^{0} : x^{8}

化简

\frac{8 !}{1 ! ( 8 - 1 ) !} x^{7} (\frac{1}{2 x ^{2}})^{1} : 4 x^{5}

化简

\frac{8 !}{2 ! ( 8 - 2 ) !} x^{6} (\frac{1}{2 x ^{2}})^{2} : 7 x^{2}

化简

\frac{8 !}{3 ! ( 8 - 3 ) !} x^{5} (\frac{1}{2 x ^{2}})^{3} : \frac{7}{x}

化简

\frac{8 !}{4 ! ( 8 - 4 ) !} x^{4} (\frac{1}{2 x ^{2}})^{4} : \frac{35}{8 x ^{4}}

化简

\frac{8 !}{5 ! ( 8 - 5 ) !} x^{3} (\frac{1}{2 x ^{2}})^{5} : \frac{7}{4 x ^{7}}

化简

\frac{8 !}{6 ! ( 8 - 6 ) !} x^{2} (\frac{1}{2 x ^{2}})^{6} : \frac{7}{16 x ^{10}}

化简

\frac{8 !}{7 ! ( 8 - 7 ) !} x^{1} (\frac{1}{2 x ^{2}})^{7} : \frac{1}{16 x ^{13}}

化简

\frac{8 !}{8 ! ( 8 - 8 ) !} x^{0} (\frac{1}{2 x ^{2}})^{8} : \frac{1}{256 x ^{16}}

= x^{8} + 4 x^{5} + 7 x^{2} + \frac{7}{x} + \frac{35}{8 x ^{4}} + \frac{7}{4 x ^{7}} + \frac{7}{16 x ^{10}} + \frac{1}{16 x ^{13}} + \frac{1}{256 x ^{16}}

流行的例子

展开 (1-1/(x^2))^6

e x p an d (1 - \frac{1}{x ^{2}})^{6}

化简 (s+30sqrt(10)-100)(s-100-30sqrt(10))

s im pl i f y (s + 3010 - 100) (s - 100 - 3010)

展开 ((0.05+2x)^2)/((2-x)(8-x))

e x p an d \frac{( 0.05 + 2 x ) ^{2}}{( 2 - x ) ( 8 - x )}

展开 ((x+8)(x-10))/(x+6)

e x p an d \frac{( x + 8 ) ( x - 10 )}{x + 6}

展开 ((304x^5dx))/((3x^6+1)^3)

e x p an d \frac{( 304 x ^{5} d x )}{( 3 x ^{6} + 1 ) ^{3}}