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 (sqrt(3x)-1/y)^4

解答

展开

(3 x - \frac{1}{y})^{4}

解答

9 x^{2} - \frac{12 3 x x}{y} + \frac{18 x}{y ^{2}} - \frac{4 3 x}{y ^{3}} + \frac{1}{y ^{4}}

求解步骤

(3 x - \frac{1}{y})^{4}

使用二项式定理:

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

a = 3 x, b = - \frac{1}{y}

= i = 0 \sum 4 (i 4) (3 x)^{(4 - i)} (- \frac{1}{y})^{i}

展开求和

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

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (- \frac{1}{y})^{0} : 9 x^{2}

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- \frac{1}{y})^{1} : - \frac{12 3 ( x ) ^{3}}{y}

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- \frac{1}{y})^{2} : \frac{18 x}{y ^{2}}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- \frac{1}{y})^{3} : - \frac{4 3 x}{y ^{3}}

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- \frac{1}{y})^{4} : \frac{1}{y ^{4}}

= 9 x^{2} - \frac{12 3 ( x ) ^{3}}{y} + \frac{18 x}{y ^{2}} - \frac{4 3 x}{y ^{3}} + \frac{1}{y ^{4}}

化简

\frac{12 3 ( x ) ^{3}}{y} : \frac{12 3 x x}{y}

= 9 x^{2} - \frac{12 3 x x}{y} + \frac{18 x}{y ^{2}} - \frac{4 3 x}{y ^{3}} + \frac{1}{y ^{4}}

流行的例子

展开 (x+ix^2)^2-2(x+ix^2)

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

化简 3(1+cos(x))

s im pl i f y 3 (1 + cos (x))

展开 (cos(2x)-1)(x+arcsin^2(x))

e x p an d (cos (2 x) - 1) (x + arcsin^{2} (x))

展开 ((y^2+1)(y^4-y^2+1))/(2y^3)

e x p an d \frac{( y ^{2} + 1 ) ( y ^{4} - y ^{2} + 1 )}{2 y ^{3}}

展开-(120)/((3-1)^6)-cos(3-1)

e x p an d - \frac{120}{( 3 - 1 ) ^{6}} - cos (3 - 1)