zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

展开 (1-1/(x^2))^6

解答

展开

(1 - \frac{1}{x ^{2}})^{6}

解答

1 - \frac{6}{x ^{2}} + \frac{15}{x ^{4}} - \frac{20}{x ^{6}} + \frac{15}{x ^{8}} - \frac{6}{x ^{10}} + \frac{1}{x ^{12}}

求解步骤

(1 - \frac{1}{x ^{2}})^{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{1}{x ^{2}}

= i = 0 \sum 6 (i 6) \cdot 1^{(6 - i)} (- \frac{1}{x ^{2}})^{i}

展开求和

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

化简

\frac{6 !}{0 ! ( 6 - 0 ) !} \cdot 1^{6} (- \frac{1}{x ^{2}})^{0} : 1

化简

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

化简

\frac{6 !}{2 ! ( 6 - 2 ) !} \cdot 1^{4} (- \frac{1}{x ^{2}})^{2} : \frac{15}{x ^{4}}

化简

\frac{6 !}{3 ! ( 6 - 3 ) !} \cdot 1^{3} (- \frac{1}{x ^{2}})^{3} : - \frac{20}{x ^{6}}

化简

\frac{6 !}{4 ! ( 6 - 4 ) !} \cdot 1^{2} (- \frac{1}{x ^{2}})^{4} : \frac{15}{x ^{8}}

化简

\frac{6 !}{5 ! ( 6 - 5 ) !} \cdot 1^{1} (- \frac{1}{x ^{2}})^{5} : - \frac{6}{x ^{10}}

化简

\frac{6 !}{6 ! ( 6 - 6 ) !} \cdot 1^{0} (- \frac{1}{x ^{2}})^{6} : \frac{1}{x ^{12}}

= 1 - \frac{6}{x ^{2}} + \frac{15}{x ^{4}} - \frac{20}{x ^{6}} + \frac{15}{x ^{8}} - \frac{6}{x ^{10}} + \frac{1}{x ^{12}}

流行的例子

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}}

化简 (2i+5)(x+iy)^2

s im pl i f y (2 i + 5) (x + i y)^{2}