展开 (4-x/(16))^6(x-1/x)^2

解答

展开

(4 - \frac{x}{16})^{6} (x - \frac{1}{x})^{2}

\frac{4096 ( x ^{4} - 2 x ^{2} + 1 )}{x ^{2}} - \frac{384 ( x ^{4} - 2 x ^{2} + 1 )}{x} + 15 x^{4} - 30 x^{2} + 15 - \frac{5 ( x ^{4} - 2 x ^{2} + 1 ) x}{16} + \frac{15 ( x ^{4} - 2 x ^{2} + 1 ) x ^{2}}{4096} - \frac{3 ( x ^{4} - 2 x ^{2} + 1 ) x ^{3}}{131072} + \frac{( x ^{4} - 2 x ^{2} + 1 ) x ^{4}}{16777216}

求解步骤

(4 - \frac{x}{16})^{6} (x - \frac{1}{x})^{2}

展开

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

= (4 - \frac{x}{16})^{6} \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}}

= \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (4 - \frac{x}{16})^{6}

展开

(4 - \frac{x}{16})^{6} : 4096 - 384 x + 15 x^{2} - \frac{5 x ^{3}}{16} + \frac{15 x ^{4}}{4096} - \frac{3 x ^{5}}{131072} + \frac{x ^{6}}{16777216}

= \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (4096 - 384 x + 15 x^{2} - \frac{5 x ^{3}}{16} + \frac{15 x ^{4}}{4096} - \frac{3 x ^{5}}{131072} + \frac{x ^{6}}{16777216})

打开括号

= \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot 4096 + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- 384 x) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot 15 x^{2} + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- \frac{5 x ^{3}}{16}) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot \frac{15 x ^{4}}{4096} + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- \frac{3 x ^{5}}{131072}) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot \frac{x ^{6}}{16777216}

化简

\frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot 4096 + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- 384 x) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot 15 x^{2} + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- \frac{5 x ^{3}}{16}) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot \frac{15 x ^{4}}{4096} + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} (- \frac{3 x ^{5}}{131072}) + \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} \cdot \frac{x ^{6}}{16777216} : \frac{4096 ( x ^{4} - 2 x ^{2} + 1 )}{x ^{2}} - \frac{384 ( x ^{4} - 2 x ^{2} + 1 )}{x} + 15 x^{4} - 30 x^{2} + 15 - \frac{5 ( x ^{4} - 2 x ^{2} + 1 ) x}{16} + \frac{15 ( x ^{4} - 2 x ^{2} + 1 ) x ^{2}}{4096} - \frac{3 ( x ^{4} - 2 x ^{2} + 1 ) x ^{3}}{131072} + \frac{( x ^{4} - 2 x ^{2} + 1 ) x ^{4}}{16777216}

= \frac{4096 ( x ^{4} - 2 x ^{2} + 1 )}{x ^{2}} - \frac{384 ( x ^{4} - 2 x ^{2} + 1 )}{x} + 15 x^{4} - 30 x^{2} + 15 - \frac{5 ( x ^{4} - 2 x ^{2} + 1 ) x}{16} + \frac{15 ( x ^{4} - 2 x ^{2} + 1 ) x ^{2}}{4096} - \frac{3 ( x ^{4} - 2 x ^{2} + 1 ) x ^{3}}{131072} + \frac{( x ^{4} - 2 x ^{2} + 1 ) x ^{4}}{16777216}

e x p an d \frac{\frac{d}{d x} ( 5 )}{4 ( 3 x ^{2} + 6 x ^{4} + 2 ) ^{3}}

e x p an d (1 + sin (x)) (1 - csc (x))

e x p an d \frac{2 z ^{3} + 6 z ^{2} + 5 z + 1}{z ^{2} ( 2 z + 1 )}

e x p an d A (3, - 2)

e x p an d A (3, - 1)