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受欢迎的代数 >

展开 (2x^2-2/x)^7

解答

展开

(2 x^{2} - \frac{2}{x})^{7}

解答

128 x^{14} - 896 x^{11} + 2688 x^{8} - 4480 x^{5} + 4480 x^{2} - \frac{2688}{x} + \frac{896}{x ^{4}} - \frac{128}{x ^{7}}

求解步骤

(2 x^{2} - \frac{2}{x})^{7}

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{2}{x}

= i = 0 \sum 7 (i 7) (2 x^{2})^{(7 - i)} (- \frac{2}{x})^{i}

展开求和

= \frac{7 !}{0 ! ( 7 - 0 ) !} (2 x^{2})^{7} (- \frac{2}{x})^{0} + \frac{7 !}{1 ! ( 7 - 1 ) !} (2 x^{2})^{6} (- \frac{2}{x})^{1} + \frac{7 !}{2 ! ( 7 - 2 ) !} (2 x^{2})^{5} (- \frac{2}{x})^{2} + \frac{7 !}{3 ! ( 7 - 3 ) !} (2 x^{2})^{4} (- \frac{2}{x})^{3} + \frac{7 !}{4 ! ( 7 - 4 ) !} (2 x^{2})^{3} (- \frac{2}{x})^{4} + \frac{7 !}{5 ! ( 7 - 5 ) !} (2 x^{2})^{2} (- \frac{2}{x})^{5} + \frac{7 !}{6 ! ( 7 - 6 ) !} (2 x^{2})^{1} (- \frac{2}{x})^{6} + \frac{7 !}{7 ! ( 7 - 7 ) !} (2 x^{2})^{0} (- \frac{2}{x})^{7}

化简

\frac{7 !}{0 ! ( 7 - 0 ) !} (2 x^{2})^{7} (- \frac{2}{x})^{0} : 128 x^{14}

化简

\frac{7 !}{1 ! ( 7 - 1 ) !} (2 x^{2})^{6} (- \frac{2}{x})^{1} : - 896 x^{11}

化简

\frac{7 !}{2 ! ( 7 - 2 ) !} (2 x^{2})^{5} (- \frac{2}{x})^{2} : 2688 x^{8}

化简

\frac{7 !}{3 ! ( 7 - 3 ) !} (2 x^{2})^{4} (- \frac{2}{x})^{3} : - 4480 x^{5}

化简

\frac{7 !}{4 ! ( 7 - 4 ) !} (2 x^{2})^{3} (- \frac{2}{x})^{4} : 4480 x^{2}

化简

\frac{7 !}{5 ! ( 7 - 5 ) !} (2 x^{2})^{2} (- \frac{2}{x})^{5} : - \frac{2688}{x}

化简

\frac{7 !}{6 ! ( 7 - 6 ) !} (2 x^{2})^{1} (- \frac{2}{x})^{6} : \frac{896}{x ^{4}}

化简

\frac{7 !}{7 ! ( 7 - 7 ) !} (2 x^{2})^{0} (- \frac{2}{x})^{7} : - \frac{128}{x ^{7}}

= 128 x^{14} - 896 x^{11} + 2688 x^{8} - 4480 x^{5} + 4480 x^{2} - \frac{2688}{x} + \frac{896}{x ^{4}} - \frac{128}{x ^{7}}

流行的例子

展开 (x-w)/((x-y)(w-y))

e x p an d \frac{x - w}{( x - y ) ( w - y )}

展开 (1/9 (e^{3x}*3x-e^{3x})+e^x+C)/(e^{3x)}

e x p an d \frac{\frac{1}{9} ( e ^{3 x} \cdot 3 x - e ^{3 x} ) + e ^{x} + C}{e ^{3 x}}

化简 (sqrt(x^2-16)-6)^2

s im pl i f y (x^{2} - 16 - 6)^{2}

展开 (x^2+1)/(x(x-1)^3)

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

展开 (e^{-s}-1)^2

e x p an d (e^{- s} - 1)^{2}