erweitern (x+1/2)^3

Lösung

erweitern

(x + \frac{1}{2})^{3}

\frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

Schritte zur Lösung

(x + \frac{1}{2})^{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{1}{2})^{3} = x^{3} + 3 x^{2} \frac{1}{2} + 3 x (\frac{1}{2})^{2} + (\frac{1}{2})^{3}

= x^{3} + 3 x^{2} \frac{1}{2} + 3 x (\frac{1}{2})^{2} + (\frac{1}{2})^{3}

Vereinfache

x^{3} + 3 x^{2} \frac{1}{2} + 3 x (\frac{1}{2})^{2} + (\frac{1}{2})^{3} : \frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

= \frac{8 x ^{3} + 6 x + 12 x ^{2} + 1}{8}

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

s im pl i f y (x + 3 + 5) (x + 3 - 5)

e x p an d - 25 (0.08 x + 0.04 y = 330)

e x p an d (1 + x) d y - y d x

e x p an d (m - 3) (m + 3)^{'}