erweitern (x-8)(x-3)^2ln(x/4)

Lösung

erweitern

(x - 8) (x - 3)^{2} ln (\frac{x}{4})

x^{3} ln (\frac{x}{4}) - 14 x^{2} ln (\frac{x}{4}) + 57 x ln (\frac{x}{4}) - 72 ln (\frac{x}{4})

Schritte zur Lösung

(x - 8) (x - 3)^{2} ln (\frac{x}{4})

= ln (\frac{x}{4}) (x - 8) (x - 3)^{2}

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (x - 3)^{2} ln (\frac{x}{4}), b = x, c = 8

= (x - 3)^{2} ln (\frac{x}{4}) x - (x - 3)^{2} ln (\frac{x}{4}) \cdot 8

= x ln (\frac{x}{4}) (x - 3)^{2} - 8 ln (\frac{x}{4}) (x - 3)^{2}

Vereinfache

x ln (\frac{x}{4}) (x - 3)^{2} - 8 ln (\frac{x}{4}) (x - 3)^{2} : x^{3} ln (\frac{x}{4}) - 14 x^{2} ln (\frac{x}{4}) + 57 x ln (\frac{x}{4}) - 72 ln (\frac{x}{4})

= x^{3} ln (\frac{x}{4}) - 14 x^{2} ln (\frac{x}{4}) + 57 x ln (\frac{x}{4}) - 72 ln (\frac{x}{4})

e x p an d \frac{e ^{- x}}{x ( x + 1 )}

s im pl i f y (1 - i 3)^{5}

e x p an d \frac{( s - 4 ) ( z ^{2} - 1.2 z + 0.2 )}{( s - 1 ) ( s + 2 )}

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

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