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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Wende Regel an

\frac{a}{a} = 1

\frac{4}{4} = 1

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

Streiche

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

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

Teile die Zahlen:

\frac{12}{4} = 3

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

e x p an d \frac{1}{( x - 1 ) ^{3}}

e x p an d lo g_{10} (3 x^{7} y^{2} z)

e x p an d (e^{t} + e^{3 t})^{2}

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

e x p an d (2 - \frac{x}{16})^{9}