erweitern (x+deltax)^3

Lösung

erweitern

(x + d e lt a x)^{3}

x^{3} + 3 d e l a x^{3} t + 3 d e^{2} l^{2} a^{2} x^{3} t^{2} + d e^{3} l^{3} a^{3} x^{3} t^{3}

Schritte zur Lösung

(x + d e lt a x)^{3}

= (x + d e l a x t)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = x, b = d e lt a x

= x^{3} + 3 x^{2} d e lt a x + 3 x (d e lt a x)^{2} + (d e lt a x)^{3}

Vereinfache

x^{3} + 3 x^{2} d e lt a x + 3 x (d e lt a x)^{2} + (d e lt a x)^{3} : x^{3} + 3 d e l a x^{3} t + 3 d e^{2} l^{2} a^{2} x^{3} t^{2} + d e^{3} l^{3} a^{3} x^{3} t^{3}

= x^{3} + 3 d e l a x^{3} t + 3 d e^{2} l^{2} a^{2} x^{3} t^{2} + d e^{3} l^{3} a^{3} x^{3} t^{3}

e x p an d \frac{10 x ^{3} + 20 x + 2}{( x ^{2} + 2 ) ( x ^{2} + 1 )}

e x p an d (\frac{x}{7 - 2 x}) (2 x^{2} - 7) (- 7 - x)

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

e x p an d (x^{3} + y^{3}) d x - x y^{2} d y

e x p an d - y l e f t (x - y)