faktorisieren (0.5(e^x-e^{-x}))^2

Lösung

faktorisieren

(0.5 (e^{x} - e^{- x}))^{2}

0.25 e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

Schritte zur Lösung

(0.5 (e^{x} - e^{- x}))^{2}

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= 0. 5^{2} (e^{x} - e^{- x})^{2}

(e^{x} - e^{- x})^{2} = (e^{- x} (e^{x} + 1) (e^{x} - 1))^{2}

= 0. 5^{2} (e^{- x} (e^{x} + 1) (e^{x} - 1))^{2}

(e^{- x} (e^{x} + 1) (e^{x} - 1))^{2} = e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

= 0. 5^{2} e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

0. 5^{2} = 0.25

= 0.25 e^{- 2 x} (e^{x} + 1)^{2} (e^{x} - 1)^{2}

f a c t or 8 \cdot e^{2} - e^{5}

f a c t or c e^{t} - c^{2} e^{2 t}

f a c t or 9^{2} - 30 X + 25

f a c t or (2 x y)^{3} + 2 x^{2} y^{- 1}

f a c t or x^{5} + 4 x^{3} - 3 x^{2} + 4 x - 3 x d x