erweitern (2x^2(x^3+y^4)+3x^2)e^{x^3+y^3}

Lösung

erweitern

(2 x^{2} (x^{3} + y^{4}) + 3 x^{2}) e^{x^{3} + y^{3}}

2 e^{x^{3} + y^{3}} x^{5} + 2 e^{x^{3} + y^{3}} x^{2} y^{4} + 3 e^{x^{3} + y^{3}} x^{2}

Schritte zur Lösung

(2 x^{2} (x^{3} + y^{4}) + 3 x^{2}) e^{x^{3} + y^{3}}

= e^{x^{3} + y^{3}} (2 x^{2} (x^{3} + y^{4}) + 3 x^{2})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = e^{x^{3} + y^{3}}, b = 2 x^{2} (x^{3} + y^{4}), c = 3 x^{2}

= e^{x^{3} + y^{3}} \cdot 2 x^{2} (x^{3} + y^{4}) + e^{x^{3} + y^{3}} \cdot 3 x^{2}

= 2 e^{x^{3} + y^{3}} x^{2} (x^{3} + y^{4}) + 3 e^{x^{3} + y^{3}} x^{2}

Multipliziere aus

2 e^{x^{3} + y^{3}} x^{2} (x^{3} + y^{4}) : 2 e^{x^{3} + y^{3}} x^{5} + 2 e^{x^{3} + y^{3}} x^{2} y^{4}

= 2 e^{x^{3} + y^{3}} x^{5} + 2 e^{x^{3} + y^{3}} x^{2} y^{4} + 3 e^{x^{3} + y^{3}} x^{2}

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

e x p an d (l^{3} o^{4} v^{5} - 6 e^{3}) (l^{3} o^{4} v^{5} + 6 e^{3})

e x p an d \frac{9 ( a - 2 )}{2 a + 4}

e x p an d (7 + 2) (3 - 8)

e x p an d 20 x (x + 9)^{4} d x