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受欢迎的代数 >

展开 (2x^2-3/x)^4

解答

展开

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

解答

16 x^{8} - 96 x^{5} + 216 x^{2} - \frac{216}{x} + \frac{81}{x ^{4}}

求解步骤

(2 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 = 2 x^{2}, b = - \frac{3}{x}

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

展开求和

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

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 x^{2})^{4} (- \frac{3}{x})^{0} : 16 x^{8}

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} (2 x^{2})^{3} (- \frac{3}{x})^{1} : - 96 x^{5}

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 x^{2})^{2} (- \frac{3}{x})^{2} : 216 x^{2}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} (2 x^{2})^{1} (- \frac{3}{x})^{3} : - \frac{216}{x}

化简

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

= 16 x^{8} - 96 x^{5} + 216 x^{2} - \frac{216}{x} + \frac{81}{x ^{4}}

流行的例子

展开 10000(-0.2e^{-0.2t}t-e^{-0.2t})

e x p an d 10000 (- 0.2 e^{- 0.2 t} t - e^{- 0.2 t})

展开 100x-0.5x^2-60x-300

e x p an d 100 x - 0.5 x^{2} - 60 x - 300

化简 (x-1)(x-2i)(x-3i)

s im pl i f y (x - 1) (x - 2 i) (x - 3 i)

展开 (sin(x)-1)(2sin(x)-1)

e x p an d (sin (x) - 1) (2 sin (x) - 1)

展开 ((y^2-1)(3x^2+8x))/y

e x p an d \frac{( y ^{2} - 1 ) ( 3 x ^{2} + 8 x )}{y}