erweitern (x+2/3)^3

Lösung

erweitern

(x + \frac{2}{3})^{3}

\frac{27 x ^{3} + 54 x ^{2} + 36 x + 8}{27}

Schritte zur Lösung

(x + \frac{2}{3})^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(x + \frac{2}{3})^{3} = x^{3} + 3 x^{2} \frac{2}{3} + 3 x (\frac{2}{3})^{2} + (\frac{2}{3})^{3}

= x^{3} + 3 x^{2} \frac{2}{3} + 3 x (\frac{2}{3})^{2} + (\frac{2}{3})^{3}

Vereinfache

x^{3} + 3 x^{2} \frac{2}{3} + 3 x (\frac{2}{3})^{2} + (\frac{2}{3})^{3} : \frac{27 x ^{3} + 54 x ^{2} + 36 x + 8}{27}

= \frac{27 x ^{3} + 54 x ^{2} + 36 x + 8}{27}

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

s im pl i f y (3 n - 3) 2

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

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

e x p an d 3 (- 10 + 5)