erweitern 4(x^{1/3}+1)^7

Lösung

erweitern

4 (x^{\frac{1}{3}} + 1)^{7}

4 x^{\frac{7}{3}} + 28 x^{2} + 84 x^{\frac{5}{3}} + 140 x^{\frac{4}{3}} + 140 x + 84 x^{\frac{2}{3}} + 28 x^{\frac{1}{3}} + 4

Schritte zur Lösung

4 (x^{\frac{1}{3}} + 1)^{7}

Schreibe

(x^{\frac{1}{3}} + 1)^{7}

um:

x^{\frac{7}{3}} + 7 x^{2} + 21 x^{\frac{5}{3}} + 35 x^{\frac{4}{3}} + 35 x + 21 x^{\frac{2}{3}} + 7 x^{\frac{1}{3}} + 1

= 4 (x^{\frac{7}{3}} + 7 x^{2} + 21 x^{\frac{5}{3}} + 35 x^{\frac{4}{3}} + 35 x + 21 x^{\frac{2}{3}} + 7 x^{\frac{1}{3}} + 1)

Setze Klammern

= 4 x^{\frac{7}{3}} + 4 \cdot 7 x^{2} + 4 \cdot 21 x^{\frac{5}{3}} + 4 \cdot 35 x^{\frac{4}{3}} + 4 \cdot 35 x + 4 \cdot 21 x^{\frac{2}{3}} + 4 \cdot 7 x^{\frac{1}{3}} + 4 \cdot 1

4 \cdot 7 x^{2} = 28 x^{2}

4 \cdot 21 x^{\frac{5}{3}} = 84 x^{\frac{5}{3}}

4 \cdot 35 x^{\frac{4}{3}} = 140 x^{\frac{4}{3}}

4 \cdot 35 x = 140 x

4 \cdot 21 x^{\frac{2}{3}} = 84 x^{\frac{2}{3}}

4 \cdot 7 x^{\frac{1}{3}} = 28 x^{\frac{1}{3}}

4 \cdot 1 = 4

= 4 x^{\frac{7}{3}} + 28 x^{2} + 84 x^{\frac{5}{3}} + 140 x^{\frac{4}{3}} + 140 x + 84 x^{\frac{2}{3}} + 28 x^{\frac{1}{3}} + 4

\frac{d ^{2}}{d x ^{2}} ((y) (4 y + 1))

e x p an d \frac{13 x + 6}{( x + 1 ) ( x - 1 )}

s im pl i f y (\frac{1}{x} + x) \cdot (1 - \frac{1}{x + 1})

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

e x p an d sin (a) (1 - cos (b)) + sin (b) (1 - cos (a))