erweitern ((x+2)^3(9x-2))/(12)

Lösung

erweitern

\frac{( x + 2 ) ^{3} ( 9 x - 2 )}{12}

\frac{3 x ^{4}}{4} + \frac{13 x ^{3}}{3} + 8 x^{2} + 4 x - \frac{4}{3}

Schritte zur Lösung

\frac{( x + 2 ) ^{3} ( 9 x - 2 )}{12}

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

= \frac{( x ^{3} + 6 x ^{2} + 12 x + 8 ) ( 9 x - 2 )}{12}

Multipliziere aus

(x^{3} + 6 x^{2} + 12 x + 8) (9 x - 2) : 9 x^{4} + 52 x^{3} + 96 x^{2} + 48 x - 16

= \frac{9 x ^{4} + 52 x ^{3} + 96 x ^{2} + 48 x - 16}{12}

Wende Bruchregel an:

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

\frac{9 x ^{4} + 52 x ^{3} + 96 x ^{2} + 48 x - 16}{12} = \frac{9 x ^{4}}{12} + \frac{52 x ^{3}}{12} + \frac{96 x ^{2}}{12} + \frac{48 x}{12} - \frac{16}{12}

= \frac{9 x ^{4}}{12} + \frac{52 x ^{3}}{12} + \frac{96 x ^{2}}{12} + \frac{48 x}{12} - \frac{16}{12}

\frac{9 x ^{4}}{12} = \frac{3 x ^{4}}{4}

\frac{52 x ^{3}}{12} = \frac{13 x ^{3}}{3}

\frac{96 x ^{2}}{12} = 8 x^{2}

\frac{48 x}{12} = 4 x

\frac{16}{12} = \frac{4}{3}

= \frac{3 x ^{4}}{4} + \frac{13 x ^{3}}{3} + 8 x^{2} + 4 x - \frac{4}{3}

e x p an d \frac{( 4 x + 12 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{4}

e x p an d (t - a) (H (t - a) - H (t - b))

e x p an d \frac{( 8 - x )}{( x + 2 ) ^{2}}

e x p an d (x - 4) 3 x

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