erweitern-((x+αt)^2)/2

Lösung

erweitern

- \frac{( x + α t ) ^{2}}{2}

- \frac{x ^{2}}{2} - αx t - \frac{α ^{2} t ^{2}}{2}

Schritte zur Lösung

- \frac{( x + α t ) ^{2}}{2}

(x + α t)^{2} = x^{2} + 2 αx t + α^{2} t^{2}

= - \frac{x ^{2} + 2 αx t + α ^{2} t ^{2}}{2}

Wende Bruchregel an:

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

\frac{x ^{2} + 2 αx t + α ^{2} t ^{2}}{2} = - (\frac{x ^{2}}{2}) - (\frac{2 αx t}{2}) - (\frac{α ^{2} t ^{2}}{2})

= - (\frac{x ^{2}}{2}) - (\frac{2 αx t}{2}) - (\frac{α ^{2} t ^{2}}{2})

Entferne die Klammern:

(a) = a

= - \frac{x ^{2}}{2} - \frac{2 αx t}{2} - \frac{α ^{2} t ^{2}}{2}

Teile die Zahlen:

\frac{2}{2} = 1

= - \frac{x ^{2}}{2} - αx t - \frac{α ^{2} t ^{2}}{2}

e x p an d sin (o) (180 - 2 x)

e x p an d \frac{3 ( x + 4 ) ( x + 1 )}{( x + 2 ) ( x - 2 )}

e x p an d (x 1 + x) (1 + 1 + x)

s im pl i f y (x - 3) (x + \frac{1}{4}) (x - 2) (x^{2} + 1) (x + 3)

e x p an d \frac{1}{( ( 2 n - 1 ) ( 2 n + 1 ) ( 2 n + 3 ) )}