erweitern (2+1/4)^8(2x-3/x)^2

Lösung

erweitern

(2 + \frac{1}{4})^{8} (2 x - \frac{3}{x})^{2}

\frac{43046721 ( 4 x ^{4} - 12 x ^{2} + 9 )}{65536 x ^{2}}

Schritte zur Lösung

(2 + \frac{1}{4})^{8} (2 x - \frac{3}{x})^{2}

Schreibe

(2 x - \frac{3}{x})^{2}

um:

\frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}}

= (2 + \frac{1}{4})^{8} \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}}

= \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} (2 + \frac{1}{4})^{8}

Schreibe

(2 + \frac{1}{4})^{8}

um:

256 + 256 + 112 + 28 + \frac{35}{8} + \frac{7}{16} + \frac{7}{256} + \frac{1}{1024} + \frac{1}{65536}

= \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} (256 + 256 + 112 + 28 + \frac{35}{8} + \frac{7}{16} + \frac{7}{256} + \frac{1}{1024} + \frac{1}{65536})

Setze Klammern

= \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 256 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 256 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 112 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 28 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{35}{8} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{7}{16} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{7}{256} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{1}{1024} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{1}{65536}

Vereinfache

\frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 256 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 256 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 112 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot 28 + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{35}{8} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{7}{16} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{7}{256} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{1}{1024} + \frac{4 x ^{4} - 12 x ^{2} + 9}{x ^{2}} \cdot \frac{1}{65536} : \frac{43046721 ( 4 x ^{4} - 12 x ^{2} + 9 )}{65536 x ^{2}}

= \frac{43046721 ( 4 x ^{4} - 12 x ^{2} + 9 )}{65536 x ^{2}}

e x p an d \frac{240}{( s + 1 ) ( s + 2 ) ( s + 3 ) ( s + 4 )}

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

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

s im pl i f y 15 (\frac{1}{56250000} - \frac{1}{225000000})

s im pl i f y ((\frac{9}{x - 4}) + 3 (100 - x)) (x - 4)