erweitern (((4-x^2)^4))/2

Lösung

erweitern

\frac{( ( 4 - x ^{2} ) ^{4} )}{2}

\frac{x ^{8}}{2} - 8 x^{6} + 48 x^{4} - 128 x^{2} + 128

Schritte zur Lösung

\frac{( 4 - x ^{2} ) ^{4}}{2}

(4 - x^{2})^{4} = 256 - 256 x^{2} + 96 x^{4} - 16 x^{6} + x^{8}

= \frac{256 - 256 x ^{2} + 96 x ^{4} - 16 x ^{6} + x ^{8}}{2}

Wende Bruchregel an:

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

\frac{256 - 256 x ^{2} + 96 x ^{4} - 16 x ^{6} + x ^{8}}{2} = \frac{256}{2} - \frac{256 x ^{2}}{2} + \frac{96 x ^{4}}{2} - \frac{16 x ^{6}}{2} + \frac{x ^{8}}{2}

= \frac{256}{2} - \frac{256 x ^{2}}{2} + \frac{96 x ^{4}}{2} - \frac{16 x ^{6}}{2} + \frac{x ^{8}}{2}

\frac{256}{2} = 128

\frac{256 x ^{2}}{2} = 128 x^{2}

\frac{96 x ^{4}}{2} = 48 x^{4}

\frac{16 x ^{6}}{2} = 8 x^{6}

= 128 - 128 x^{2} + 48 x^{4} - 8 x^{6} + \frac{x ^{8}}{2}

Rewrite in standard form

= \frac{x ^{8}}{2} - 8 x^{6} + 48 x^{4} - 128 x^{2} + 128

s im pl i f y (x + 1) (\frac{2 x}{x + 1} + 1)

e x p an d \frac{5 x + 13}{( 2 x + 1 ) ( x + 4 )}

e x p an d lo g_{10} (\frac{a - b}{a + b})

s im pl i f y 100 \cdot (10 \frac{44786}{46931} - 1)

s im pl i f y - \frac{0.0951}{( x - 1 ) ( x - 0.9048 )}