erweitern ((2+x)^6)/(64)

Lösung

erweitern

\frac{( 2 + x ) ^{6}}{64}

\frac{x ^{6}}{64} + \frac{3 x ^{5}}{16} + \frac{15 x ^{4}}{16} + \frac{5 x ^{3}}{2} + \frac{15 x ^{2}}{4} + 3 x + 1

Schritte zur Lösung

\frac{( 2 + x ) ^{6}}{64}

(2 + x)^{6} = 64 + 192 x + 240 x^{2} + 160 x^{3} + 60 x^{4} + 12 x^{5} + x^{6}

= \frac{64 + 192 x + 240 x ^{2} + 160 x ^{3} + 60 x ^{4} + 12 x ^{5} + x ^{6}}{64}

Wende Bruchregel an:

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

\frac{64 + 192 x + 240 x ^{2} + 160 x ^{3} + 60 x ^{4} + 12 x ^{5} + x ^{6}}{64} = \frac{64}{64} + \frac{192 x}{64} + \frac{240 x ^{2}}{64} + \frac{160 x ^{3}}{64} + \frac{60 x ^{4}}{64} + \frac{12 x ^{5}}{64} + \frac{x ^{6}}{64}

= \frac{64}{64} + \frac{192 x}{64} + \frac{240 x ^{2}}{64} + \frac{160 x ^{3}}{64} + \frac{60 x ^{4}}{64} + \frac{12 x ^{5}}{64} + \frac{x ^{6}}{64}

Wende Regel an

\frac{a}{a} = 1

\frac{64}{64} = 1

= 1 + \frac{192 x}{64} + \frac{240 x ^{2}}{64} + \frac{160 x ^{3}}{64} + \frac{60 x ^{4}}{64} + \frac{12 x ^{5}}{64} + \frac{x ^{6}}{64}

\frac{192 x}{64} = 3 x

\frac{240 x ^{2}}{64} = \frac{15 x ^{2}}{4}

\frac{160 x ^{3}}{64} = \frac{5 x ^{3}}{2}

\frac{60 x ^{4}}{64} = \frac{15 x ^{4}}{16}

\frac{12 x ^{5}}{64} = \frac{3 x ^{5}}{16}

= 1 + 3 x + \frac{15 x ^{2}}{4} + \frac{5 x ^{3}}{2} + \frac{15 x ^{4}}{16} + \frac{3 x ^{5}}{16} + \frac{x ^{6}}{64}

Rewrite in standard form

= \frac{x ^{6}}{64} + \frac{3 x ^{5}}{16} + \frac{15 x ^{4}}{16} + \frac{5 x ^{3}}{2} + \frac{15 x ^{2}}{4} + 3 x + 1

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