erweitern (x-9)(x-3)^2ln(x/6)

Lösung

erweitern

(x - 9) (x - 3)^{2} ln (\frac{x}{6})

x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})

Schritte zur Lösung

(x - 9) (x - 3)^{2} ln (\frac{x}{6})

= ln (\frac{x}{6}) (x - 9) (x - 3)^{2}

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (x - 3)^{2} ln (\frac{x}{6}), b = x, c = 9

= (x - 3)^{2} ln (\frac{x}{6}) x - (x - 3)^{2} ln (\frac{x}{6}) \cdot 9

= x ln (\frac{x}{6}) (x - 3)^{2} - 9 ln (\frac{x}{6}) (x - 3)^{2}

Vereinfache

x ln (\frac{x}{6}) (x - 3)^{2} - 9 ln (\frac{x}{6}) (x - 3)^{2} : x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})

= x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})

e x p an d ln (x) (4 x^{3} + 6 x + 1)

s im pl i f y 2 j w (2 j w + 1)

e x p an d \frac{p}{3} - (\frac{q}{2})^{2}

s im pl i f y (\frac{a}{2} - 1) (\frac{a}{2} + 1)

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