erweitern (x^2+2)(2x-1/x)^4

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

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

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

Vereinfache

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

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

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

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

e x p an d \frac{2 x ^{2} - 3}{( x ^{2} - 9 ) ( x ^{2} - 4 )}

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

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