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受欢迎的代数 >

展开 (x^2+3/x)^4

解答

展开

(x^{2} + \frac{3}{x})^{4}

解答

x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}

求解步骤

(x^{2} + \frac{3}{x})^{4}

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{3}{x}

= i = 0 \sum 4 (i 4) (x^{2})^{(4 - i)} (\frac{3}{x})^{i}

展开求和

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

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{2})^{4} (\frac{3}{x})^{0} : x^{8}

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (\frac{3}{x})^{1} : 12 x^{5}

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{2})^{2} (\frac{3}{x})^{2} : 54 x^{2}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{2})^{1} (\frac{3}{x})^{3} : \frac{108}{x}

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{2})^{0} (\frac{3}{x})^{4} : \frac{81}{x ^{4}}

= x^{8} + 12 x^{5} + 54 x^{2} + \frac{108}{x} + \frac{81}{x ^{4}}

流行的例子

展开 b(5,-pi/3)

e x p an d b (5, - \frac{π}{3})

展开 (2t-3)e^{(((t+2))/3)}

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

展开 (2(x+2))/x

e x p an d \frac{2 ( x + 2 )}{x}

展开 (a+b)left(a-b)

e x p an d (a + b) l e f t (a - b)

展开 (2pi+16)× 12

e x p an d (2 π + 16) \times 12