展开 (2x^2+1)*(x-2/x)^4

解答

展开

(2 x^{2} + 1) \cdot (x - \frac{2}{x})^{4}

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

求解步骤

(2 x^{2} + 1) (x - \frac{2}{x})^{4}

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

使用分配律:

a (b + c) = ab + a c

(x - \frac{2}{x})^{4} (2 x^{2} + 1) = (x - \frac{2}{x})^{4} \cdot 2 x^{2} + (x - \frac{2}{x})^{4} \cdot 1

= (x - \frac{2}{x})^{4} \cdot 2 x^{2} + (x - \frac{2}{x})^{4} \cdot 1

化简

(x - \frac{2}{x})^{4} \cdot 2 x^{2} + (x - \frac{2}{x})^{4} \cdot 1 : \frac{2 ( x ^{2} - 2 ) ^{4}}{x ^{2}} + \frac{( x ^{2} - 2 ) ^{4}}{x ^{4}}

= \frac{2 ( x ^{2} - 2 ) ^{4}}{x ^{2}} + \frac{( x ^{2} - 2 ) ^{4}}{x ^{4}}

e x p an d \frac{a}{12} \cdot \frac{9}{10}

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

e x p an d (1 - x) ((- 2 - x) (1 - x) - \frac{1}{4})

e x p an d \frac{12}{x ( x ^{2} + 6 )}

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