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

Lösung

erweitern

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

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

Schritte zur Lösung

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

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

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

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

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

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

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

e x p an d sin (x) (sec (x) - 2)

s im pl i f y (3 u - u + 3) (2 u + u + 3)

s im pl i f y (cos (x) + sec (x))^{2} + sin^{2} (x) - tan^{2} (x) + 3