erweitern (5x^3(4e^{x/y}y^3-e^{x/y}xy^2))*y

Lösung

erweitern

(5 x^{3} (4 e^{\frac{x}{y}} y^{3} - e^{\frac{x}{y}} x y^{2})) \cdot y

20 e^{\frac{x}{y}} x^{3} y^{4} - 5 e^{\frac{x}{y}} x^{4} y^{3}

Schritte zur Lösung

(5 x^{3} (4 e^{\frac{x}{y}} y^{3} - e^{\frac{x}{y}} x y^{2})) y

Entferne die Klammern:

(a) = a

= 5 x^{3} (4 e^{\frac{x}{y}} y^{3} - e^{\frac{x}{y}} x y^{2}) y

= 5 x^{3} y (4 e^{\frac{x}{y}} y^{3} - e^{\frac{x}{y}} x y^{2})

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = 5 x^{3} y, b = 4 e^{\frac{x}{y}} y^{3}, c = e^{\frac{x}{y}} x y^{2}

= 5 x^{3} y \cdot 4 e^{\frac{x}{y}} y^{3} - 5 x^{3} y e^{\frac{x}{y}} x y^{2}

= 5 \cdot 4 e^{\frac{x}{y}} x^{3} y^{3} y - 5 e^{\frac{x}{y}} x^{3} x y^{2} y

Vereinfache

5 \cdot 4 e^{\frac{x}{y}} x^{3} y^{3} y - 5 e^{\frac{x}{y}} x^{3} x y^{2} y : 20 e^{\frac{x}{y}} x^{3} y^{4} - 5 e^{\frac{x}{y}} x^{4} y^{3}

= 20 e^{\frac{x}{y}} x^{3} y^{4} - 5 e^{\frac{x}{y}} x^{4} y^{3}

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

e x p an d \frac{0.5 ( 3 s + 1 )}{3 s ^{2} + s + 2 k}

e x p an d \frac{( x ^{2} - 3 ) ^{4} sin ( 2 x )}{5 x - 1}

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

s im pl i f y (x - x^{2}) (1 + x)