erweitern x^{4/5}(5x-20)^2

Lösung

erweitern

x^{\frac{4}{5}} (5 x - 20)^{2}

25 x^{\frac{14}{5}} - 200 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 400

Schritte zur Lösung

x^{\frac{4}{5}} (5 x - 20)^{2}

Schreibe

(5 x - 20)^{2}

um:

25 x^{2} - 200 x + 400

= x^{\frac{4}{5}} (25 x^{2} - 200 x + 400)

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

x^{\frac{4}{5}} (25 x^{2} - 200 x + 400) = x^{\frac{4}{5}} \cdot 25 x^{2} + x^{\frac{4}{5}} (- 200 x) + x^{\frac{4}{5}} \cdot 400

= x^{\frac{4}{5}} \cdot 25 x^{2} + x^{\frac{4}{5}} (- 200 x) + x^{\frac{4}{5}} \cdot 400

x^{\frac{4}{5}} \cdot 25 x^{2} = 25 x^{\frac{14}{5}}

x^{\frac{4}{5}} (- 200 x) = - 200 x^{\frac{9}{5}}

= 25 x^{\frac{14}{5}} - 200 x^{\frac{9}{5}} + x^{\frac{4}{5}} \cdot 400

s im pl i f y ((\frac{3590675}{13422})^{\frac{1}{16}} - 1) \cdot 100

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

\frac{d ^{2}}{d x ^{2}} ((y) (- x^{2} + 3 y^{2}))

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

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