erweitern ((t+2)^4)/2

Lösung

erweitern

\frac{( t + 2 ) ^{4}}{2}

\frac{t ^{4}}{2} + 4 t^{3} + 12 t^{2} + 16 t + 8

Schritte zur Lösung

\frac{( t + 2 ) ^{4}}{2}

(t + 2)^{4} = t^{4} + 8 t^{3} + 24 t^{2} + 32 t + 16

= \frac{t ^{4} + 8 t ^{3} + 24 t ^{2} + 32 t + 16}{2}

Wende Bruchregel an:

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

\frac{t ^{4} + 8 t ^{3} + 24 t ^{2} + 32 t + 16}{2} = \frac{t ^{4}}{2} + \frac{8 t ^{3}}{2} + \frac{24 t ^{2}}{2} + \frac{32 t}{2} + \frac{16}{2}

= \frac{t ^{4}}{2} + \frac{8 t ^{3}}{2} + \frac{24 t ^{2}}{2} + \frac{32 t}{2} + \frac{16}{2}

\frac{8 t ^{3}}{2} = 4 t^{3}

\frac{24 t ^{2}}{2} = 12 t^{2}

\frac{32 t}{2} = 16 t

\frac{16}{2} = 8

= \frac{t ^{4}}{2} + 4 t^{3} + 12 t^{2} + 16 t + 8

e x p an d 0.5 (2 x + 20) (5, 2) + 2 x (15 - 2 x)

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

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

e x p an d 2 (1 + x)^{8} d x

d e g 2 r a d [\frac{( 1 + ln ( x ) ) ^{2}}{x}]^{^{'}}