erweitern (x-Δx)^3

Lösung

erweitern

(x - Δ x)^{3}

x^{3} - 3Δ x^{3} + 3 Δ^{2} x^{3} - Δ^{3} x^{3}

Schritte zur Lösung

(x - Δ x)^{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 = Δ x

= x^{3} - 3 x^{2} Δ x + 3 x (Δ x)^{2} - (Δ x)^{3}

Vereinfache

x^{3} - 3 x^{2} Δ x + 3 x (Δ x)^{2} - (Δ x)^{3} : x^{3} - 3Δ x^{3} + 3 Δ^{2} x^{3} - Δ^{3} x^{3}

= x^{3} - 3Δ x^{3} + 3 Δ^{2} x^{3} - Δ^{3} x^{3}

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

e x p an d (2 A x + B) e^{x} + e^{x} (A x^{2} + B x)

e x p an d \frac{( 6 - x ) ^{2}}{9}

e x p an d a (arctan (wT) - arctan (w Y))

e x p an d a^{2} b^{2} - c^{2} d^{2} (sin (2 α) + 1)