erweitern (1+(2x)/n)^3(2/n)

Lösung

erweitern

(1 + \frac{2 x}{n})^{3} (\frac{2}{n})

\frac{2 ( n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2} )}{n ^{4}}

Schritte zur Lösung

(1 + \frac{2 x}{n})^{3} (\frac{2}{n})

Apply rule:

(a) = a

(\frac{2}{n}) = \frac{2}{n}

= (1 + \frac{2 x}{n})^{3} \frac{2}{n}

= \frac{2}{n} (1 + \frac{2 x}{n})^{3}

Schreibe

(1 + \frac{2 x}{n})^{3}

um:

\frac{n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2}}{n ^{3}}

= \frac{2}{n} \cdot \frac{n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2}}{n ^{3}}

Vereinfache

\frac{2}{n} \cdot \frac{n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2}}{n ^{3}} : \frac{2 ( n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2} )}{n ^{4}}

= \frac{2 ( n ^{3} + 6 x n ^{2} + 8 x ^{3} + 12 n x ^{2} )}{n ^{4}}

e x p an d 8 (3)^{2} + 97 (3) + 12

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

e x p an d \frac{( 3 x ^{2} y ^{2} + 6 a x ^{3} )}{- 3 x ^{2}}

e x p an d \frac{A}{( x - D ) ^{2}}

s im pl i f y \frac{( 4 - 2 x ) ( 5 - 3 x )}{25 - 9 x}