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受欢迎的代数 >

展开 (x^2-2/x)^8

解答

展开

(x^{2} - \frac{2}{x})^{8}

解答

x^{16} - 16 x^{13} + 112 x^{10} - 448 x^{7} + 1120 x^{4} - 1792 x + \frac{1792}{x ^{2}} - \frac{1024}{x ^{5}} + \frac{256}{x ^{8}}

求解步骤

(x^{2} - \frac{2}{x})^{8}

使用二项式定理:

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

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

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

展开求和

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

化简

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

化简

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

化简

\frac{8 !}{2 ! ( 8 - 2 ) !} (x^{2})^{6} (- \frac{2}{x})^{2} : 112 x^{10}

化简

\frac{8 !}{3 ! ( 8 - 3 ) !} (x^{2})^{5} (- \frac{2}{x})^{3} : - 448 x^{7}

化简

\frac{8 !}{4 ! ( 8 - 4 ) !} (x^{2})^{4} (- \frac{2}{x})^{4} : 1120 x^{4}

化简

\frac{8 !}{5 ! ( 8 - 5 ) !} (x^{2})^{3} (- \frac{2}{x})^{5} : - 1792 x

化简

\frac{8 !}{6 ! ( 8 - 6 ) !} (x^{2})^{2} (- \frac{2}{x})^{6} : \frac{1792}{x ^{2}}

化简

\frac{8 !}{7 ! ( 8 - 7 ) !} (x^{2})^{1} (- \frac{2}{x})^{7} : - \frac{1024}{x ^{5}}

化简

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

= x^{16} - 16 x^{13} + 112 x^{10} - 448 x^{7} + 1120 x^{4} - 1792 x + \frac{1792}{x ^{2}} - \frac{1024}{x ^{5}} + \frac{256}{x ^{8}}

流行的例子

展开 ln(x)(1-y/x)

e x p an d ln (x) (1 - \frac{y}{x})

展开 (2x^5+1/x)^{24}

e x p an d (2 x^{5} + \frac{1}{x})^{24}

展开 ((a+b+c)(-a+b+c)(a-b+c)(a+b-c))/(16)

e x p an d \frac{( a + b + c ) ( - a + b + c ) ( a - b + c ) ( a + b - c )}{16}

展开 (-3+5)(-3+1)(-3-5)(-3-1)

e x p an d (- 3 + 5) (- 3 + 1) (- 3 - 5) (- 3 - 1)

化简 (x-3)(x-1/5)

s im pl i f y (x - 3) (x - \frac{1}{5})