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

Lösung

erweitern

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

\frac{a ^{4}}{4} - a^{3} x + \frac{3 a ^{2} x ^{2}}{2} - a x^{3} + \frac{x ^{4}}{4}

Schritte zur Lösung

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

(a - x)^{4} = a^{4} - 4 a^{3} x + 6 a^{2} x^{2} - 4 a x^{3} + x^{4}

= \frac{a ^{4} - 4 a ^{3} x + 6 a ^{2} x ^{2} - 4 a x ^{3} + x ^{4}}{4}

Wende Bruchregel an:

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

\frac{a ^{4} - 4 a ^{3} x + 6 a ^{2} x ^{2} - 4 a x ^{3} + x ^{4}}{4} = \frac{a ^{4}}{4} - \frac{4 a ^{3} x}{4} + \frac{6 a ^{2} x ^{2}}{4} - \frac{4 a x ^{3}}{4} + \frac{x ^{4}}{4}

= \frac{a ^{4}}{4} - \frac{4 a ^{3} x}{4} + \frac{6 a ^{2} x ^{2}}{4} - \frac{4 a x ^{3}}{4} + \frac{x ^{4}}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= \frac{a ^{4}}{4} - a^{3} x + \frac{6 a ^{2} x ^{2}}{4} - \frac{4 a x ^{3}}{4} + \frac{x ^{4}}{4}

Streiche

\frac{6 a ^{2} x ^{2}}{4} : \frac{3 a ^{2} x ^{2}}{2}

= \frac{a ^{4}}{4} - a^{3} x + \frac{3 a ^{2} x ^{2}}{2} - \frac{4 a x ^{3}}{4} + \frac{x ^{4}}{4}

Teile die Zahlen:

\frac{4}{4} = 1

= \frac{a ^{4}}{4} - a^{3} x + \frac{3 a ^{2} x ^{2}}{2} - a x^{3} + \frac{x ^{4}}{4}

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