erweitern (2x-1/2)^3

Lösung

erweitern

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

\frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

Schritte zur Lösung

(2 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}

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

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

Vereinfache

(2 x)^{3} - 3 (2 x)^{2} \frac{1}{2} + 3 \cdot 2 x (\frac{1}{2})^{2} - (\frac{1}{2})^{3} : \frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

= \frac{64 x ^{3} - 48 x ^{2} + 12 x - 1}{8}

e x p an d \frac{p - 11}{( p - 1 ) ^{2}}

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

s im pl i f y (1 + x 7)^{2}

e x p an d x^{3} y d x + (3 x^{4} - y^{3}) d y

e x p an d 3 (e - 3 e) + ln (3)