展开 Re(x+1/x)^4

解答

展开

R e (x + \frac{1}{x})^{4}

e R x^{4} + 4 e R x^{2} + 6 e R + \frac{4 e R}{x ^{2}} + \frac{e R}{x ^{4}}

求解步骤

R e (x + \frac{1}{x})^{4}

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

= e R (x^{4} + 4 x^{2} + \frac{4}{x ^{2}} + \frac{1}{x ^{4}} + 6)

= e R (x^{4} + 4 x^{2} + 6 + \frac{4}{x ^{2}} + \frac{1}{x ^{4}})

打开括号

= R e x^{4} + R e 4 x^{2} + R e 6 + R e \frac{4}{x ^{2}} + R e \frac{1}{x ^{4}}

= e R x^{4} + 4 e R x^{2} + 6 e R + e \frac{4}{x ^{2}} R + e \frac{1}{x ^{4}} R

化简

e R x^{4} + 4 e R x^{2} + 6 e R + e \frac{4}{x ^{2}} R + e \frac{1}{x ^{4}} R : e R x^{4} + 4 e R x^{2} + 6 e R + \frac{4 e R}{x ^{2}} + \frac{e R}{x ^{4}}

= e R x^{4} + 4 e R x^{2} + 6 e R + \frac{4 e R}{x ^{2}} + \frac{e R}{x ^{4}}

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

e x p an d \frac{20}{( x - 4 ) ( x + 1 )}

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

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

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