erweitern (((k+1)^2(k+2)^2))/4

Lösung

erweitern

\frac{( ( k + 1 ) ^{2} ( k + 2 ) ^{2} )}{4}

\frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{13 k ^{2}}{4} + 3 k + 1

Schritte zur Lösung

\frac{( k + 1 ) ^{2} ( k + 2 ) ^{2}}{4}

(k + 1)^{2} = k^{2} + 2 k + 1

= \frac{( k ^{2} + 2 k + 1 ) ( k + 2 ) ^{2}}{4}

(k + 2)^{2} = k^{2} + 4 k + 4

= \frac{( k ^{2} + 2 k + 1 ) ( k ^{2} + 4 k + 4 )}{4}

Multipliziere aus

(k^{2} + 2 k + 1) (k^{2} + 4 k + 4) : k^{4} + 6 k^{3} + 13 k^{2} + 12 k + 4

= \frac{k ^{4} + 6 k ^{3} + 13 k ^{2} + 12 k + 4}{4}

Wende Bruchregel an:

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

\frac{k ^{4} + 6 k ^{3} + 13 k ^{2} + 12 k + 4}{4} = \frac{k ^{4}}{4} + \frac{6 k ^{3}}{4} + \frac{13 k ^{2}}{4} + \frac{12 k}{4} + \frac{4}{4}

= \frac{k ^{4}}{4} + \frac{6 k ^{3}}{4} + \frac{13 k ^{2}}{4} + \frac{12 k}{4} + \frac{4}{4}

Wende Regel an

\frac{a}{a} = 1

\frac{4}{4} = 1

= \frac{k ^{4}}{4} + \frac{6 k ^{3}}{4} + \frac{13 k ^{2}}{4} + \frac{12 k}{4} + 1

Streiche

\frac{6 k ^{3}}{4} : \frac{3 k ^{3}}{2}

= \frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{13 k ^{2}}{4} + \frac{12 k}{4} + 1

Teile die Zahlen:

\frac{12}{4} = 3

= \frac{k ^{4}}{4} + \frac{3 k ^{3}}{2} + \frac{13 k ^{2}}{4} + 3 k + 1

e x p an d (e^{- 5 t} + 2)^{2}

e x p an d \frac{s + 3}{( s ^{2} + 4 s + 5 ) ( s + 5 )}

s im pl i f y (3 x + 2)^{2}

e x p an d (sin (2 t) - cos (2 t))^{2}

s im pl i f y (x - 2 + 5) (x - 2 - 5)