erweitern ((1+s)^4)/(p^2n^2)

Lösung

erweitern

\frac{( 1 + s ) ^{4}}{p ^{2} n ^{2}}

\frac{1}{n ^{2} p ^{2}} + \frac{4 s}{n ^{2} p ^{2}} + \frac{6 s ^{2}}{n ^{2} p ^{2}} + \frac{4 s ^{3}}{n ^{2} p ^{2}} + \frac{s ^{4}}{n ^{2} p ^{2}}

Schritte zur Lösung

\frac{( 1 + s ) ^{4}}{p ^{2} n ^{2}}

(1 + s)^{4} = 1 + 4 s + 6 s^{2} + 4 s^{3} + s^{4}

= \frac{1 + 4 s + 6 s ^{2} + 4 s ^{3} + s ^{4}}{n ^{2} p ^{2}}

Wende Bruchregel an:

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

\frac{1 + 4 s + 6 s ^{2} + 4 s ^{3} + s ^{4}}{p ^{2} n ^{2}} = \frac{1}{p ^{2} n ^{2}} + \frac{4 s}{p ^{2} n ^{2}} + \frac{6 s ^{2}}{p ^{2} n ^{2}} + \frac{4 s ^{3}}{p ^{2} n ^{2}} + \frac{s ^{4}}{p ^{2} n ^{2}}

= \frac{1}{n ^{2} p ^{2}} + \frac{4 s}{n ^{2} p ^{2}} + \frac{6 s ^{2}}{n ^{2} p ^{2}} + \frac{4 s ^{3}}{n ^{2} p ^{2}} + \frac{s ^{4}}{n ^{2} p ^{2}}

e x p an d 11 + - 36

e x p an d 2 \times 3 - 9

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

e x p an d \frac{b ^{2} c}{( a - b ) ( a - c ) ( b + c )}

e x p an d \frac{8 ^{5}}{8 ^{3}}