erweitern (3x-1/3)^3

Lösung

erweitern

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

\frac{729 x ^{3} - 243 x ^{2} + 27 x - 1}{27}

Schritte zur Lösung

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

Wende Formel für perfekte dritte Potenzen an:

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

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

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

Vereinfache

(3 x)^{3} - 3 (3 x)^{2} \frac{1}{3} + 3 \cdot 3 x (\frac{1}{3})^{2} - (\frac{1}{3})^{3} : \frac{729 x ^{3} - 243 x ^{2} + 27 x - 1}{27}

= \frac{729 x ^{3} - 243 x ^{2} + 27 x - 1}{27}

\frac{d ^{3}}{d x ^{3}} ((y) (5 x^{4} - x^{3} + 2 x))

e x p an d \frac{2 x - 5}{( 2 x - 4 ) ( x - 4 ) ( x - 1 )}

e x p an d 12 (\frac{3 π ^{3}}{2 x ^{2}} - \frac{π ^{5}}{20 x ^{4}})

e x p an d 1 n (5 e^{2 x})

\frac{d ^{2}}{d x ^{2}} ((y) (2 + 0.1 (x - 2) e^{- x + 4}))