erweitern (5(x-3)^5)/(16)

Lösung

erweitern

\frac{5 ( x - 3 ) ^{5}}{16}

\frac{5 x ^{5}}{16} - \frac{75 x ^{4}}{16} + \frac{225 x ^{3}}{8} - \frac{675 x ^{2}}{8} + \frac{2025 x}{16} - \frac{1215}{16}

Schritte zur Lösung

\frac{5 ( x - 3 ) ^{5}}{16}

(x - 3)^{5} = x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243

= \frac{5 ( x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243 )}{16}

Multipliziere aus

5 (x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243) : 5 x^{5} - 75 x^{4} + 450 x^{3} - 1350 x^{2} + 2025 x - 1215

= \frac{5 x ^{5} - 75 x ^{4} + 450 x ^{3} - 1350 x ^{2} + 2025 x - 1215}{16}

Wende Bruchregel an:

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

\frac{5 x ^{5} - 75 x ^{4} + 450 x ^{3} - 1350 x ^{2} + 2025 x - 1215}{16} = \frac{5 x ^{5}}{16} - \frac{75 x ^{4}}{16} + \frac{450 x ^{3}}{16} - \frac{1350 x ^{2}}{16} + \frac{2025 x}{16} - \frac{1215}{16}

= \frac{5 x ^{5}}{16} - \frac{75 x ^{4}}{16} + \frac{450 x ^{3}}{16} - \frac{1350 x ^{2}}{16} + \frac{2025 x}{16} - \frac{1215}{16}

Streiche

\frac{450 x ^{3}}{16} : \frac{225 x ^{3}}{8}

= \frac{5 x ^{5}}{16} - \frac{75 x ^{4}}{16} + \frac{225 x ^{3}}{8} - \frac{1350 x ^{2}}{16} + \frac{2025 x}{16} - \frac{1215}{16}

Streiche

\frac{1350 x ^{2}}{16} : \frac{675 x ^{2}}{8}

= \frac{5 x ^{5}}{16} - \frac{75 x ^{4}}{16} + \frac{225 x ^{3}}{8} - \frac{675 x ^{2}}{8} + \frac{2025 x}{16} - \frac{1215}{16}

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