erweitern (2x+y)*(x+y/x)^5

Lösung

erweitern

(2 x + y) \cdot (x + \frac{y}{x})^{5}

\frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

Schritte zur Lösung

(2 x + y) (x + \frac{y}{x})^{5}

= (x + \frac{y}{x})^{5} (2 x + y)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

(x + \frac{y}{x})^{5} (2 x + y) = (x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y

= (x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y

Vereinfache

(x + \frac{y}{x})^{5} \cdot 2 x + (x + \frac{y}{x})^{5} y : \frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

= \frac{2 ( x ^{2} + y ) ^{5}}{x ^{4}} + \frac{( x ^{2} + y ) ^{5} y}{x ^{5}}

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

e x p an d \frac{( 3 x - 11 ) ^{2}}{64}

e x p an d \frac{2 x ^{3} - x + 4}{( x + 1 ) ( x ^{2} - 4 ) ^{2}}

e x p an d (5 x^{3} - 3)^{5} 4 - 4 x^{5} - 3

e x p an d A (3, 2, - 4) B (- 5, 4, 4)