erweitern ((2x^2-6x+9)^2)/2

Lösung

erweitern

\frac{( 2 x ^{2} - 6 x + 9 ) ^{2}}{2}

2 x^{4} - 12 x^{3} + 36 x^{2} - 54 x + \frac{81}{2}

Schritte zur Lösung

\frac{( 2 x ^{2} - 6 x + 9 ) ^{2}}{2}

(2 x^{2} - 6 x + 9)^{2} = 4 x^{4} - 24 x^{3} + 72 x^{2} - 108 x + 81

= \frac{4 x ^{4} - 24 x ^{3} + 72 x ^{2} - 108 x + 81}{2}

Wende Bruchregel an:

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

\frac{4 x ^{4} - 24 x ^{3} + 72 x ^{2} - 108 x + 81}{2} = \frac{4 x ^{4}}{2} - \frac{24 x ^{3}}{2} + \frac{72 x ^{2}}{2} - \frac{108 x}{2} + \frac{81}{2}

= \frac{4 x ^{4}}{2} - \frac{24 x ^{3}}{2} + \frac{72 x ^{2}}{2} - \frac{108 x}{2} + \frac{81}{2}

\frac{4 x ^{4}}{2} = 2 x^{4}

\frac{24 x ^{3}}{2} = 12 x^{3}

\frac{72 x ^{2}}{2} = 36 x^{2}

\frac{108 x}{2} = 54 x

= 2 x^{4} - 12 x^{3} + 36 x^{2} - 54 x + \frac{81}{2}

e x p an d (35) (67)

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

e x p an d (6 e + 7 z) (6 e - 7 z)

e x p an d \frac{3 ( x + h ) + 4}{2 ( x + h ) - 9}

e x p an d \frac{4 ( x + h ) + 7}{5 ( x + h ) - 6}