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 (2x+1/x)^5

解答

展开

(2 x + \frac{1}{x})^{5}

解答

32 x^{5} + 80 x^{3} + 80 x + \frac{40}{x} + \frac{10}{x ^{3}} + \frac{1}{x ^{5}}

求解步骤

(2 x + \frac{1}{x})^{5}

使用二项式定理:

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

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

= i = 0 \sum 5 (i 5) (2 x)^{(5 - i)} (\frac{1}{x})^{i}

展开求和

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

化简

\frac{5 !}{0 ! ( 5 - 0 ) !} (2 x)^{5} (\frac{1}{x})^{0} : 32 x^{5}

化简

\frac{5 !}{1 ! ( 5 - 1 ) !} (2 x)^{4} (\frac{1}{x})^{1} : 80 x^{3}

化简

\frac{5 !}{2 ! ( 5 - 2 ) !} (2 x)^{3} (\frac{1}{x})^{2} : 80 x

化简

\frac{5 !}{3 ! ( 5 - 3 ) !} (2 x)^{2} (\frac{1}{x})^{3} : \frac{40}{x}

化简

\frac{5 !}{4 ! ( 5 - 4 ) !} (2 x)^{1} (\frac{1}{x})^{4} : \frac{10}{x ^{3}}

化简

\frac{5 !}{5 ! ( 5 - 5 ) !} (2 x)^{0} (\frac{1}{x})^{5} : \frac{1}{x ^{5}}

= 32 x^{5} + 80 x^{3} + 80 x + \frac{40}{x} + \frac{10}{x ^{3}} + \frac{1}{x ^{5}}

流行的例子

化简 (5sqrt(x)-10)(3-sqrt(x))

s im pl i f y (5 x - 10) (3 - x)

展开 (20(s+1))/(s(5s^2+6s+2))

e x p an d \frac{20 ( s + 1 )}{s ( 5 s ^{2} + 6 s + 2 )}

展开 (-x^2+0.5x+5)dx

e x p an d (- x^{2} + 0.5 x + 5) d x

展开 (a+5)-b/(b-4)+(2(b+3))/a

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

化简 (a/6+(b^3)/5)(a/6-(b^3)/5)

s im pl i f y (\frac{a}{6} + \frac{b ^{3}}{5}) (\frac{a}{6} - \frac{b ^{3}}{5})