erweitern ((2x+c)^3)/(27)

Lösung

erweitern

\frac{( 2 x + c ) ^{3}}{27}

\frac{8 x ^{3}}{27} + \frac{4 c x ^{2}}{9} + \frac{2 c ^{2} x}{9} + \frac{c ^{3}}{27}

Schritte zur Lösung

\frac{( 2 x + c ) ^{3}}{27}

(2 x + c)^{3} = 8 x^{3} + 12 c x^{2} + 6 c^{2} x + c^{3}

= \frac{8 x ^{3} + 12 c x ^{2} + 6 c ^{2} x + c ^{3}}{27}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{8 x ^{3} + 12 c x ^{2} + 6 c ^{2} x + c ^{3}}{27} = \frac{8 x ^{3}}{27} + \frac{12 c x ^{2}}{27} + \frac{6 c ^{2} x}{27} + \frac{c ^{3}}{27}

= \frac{8 x ^{3}}{27} + \frac{12 c x ^{2}}{27} + \frac{6 c ^{2} x}{27} + \frac{c ^{3}}{27}

Streiche

\frac{12 c x ^{2}}{27} : \frac{4 c x ^{2}}{9}

= \frac{8 x ^{3}}{27} + \frac{4 c x ^{2}}{9} + \frac{6 c ^{2} x}{27} + \frac{c ^{3}}{27}

Streiche

\frac{6 c ^{2} x}{27} : \frac{2 c ^{2} x}{9}

= \frac{8 x ^{3}}{27} + \frac{4 c x ^{2}}{9} + \frac{2 c ^{2} x}{9} + \frac{c ^{3}}{27}

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

e x p an d (- 30, 30) y (20, - 20)

e x p an d (3 e^{x}) (24 x^{7} - 18 x)

e x p an d (8 x - 3) 3 e - x + 3

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