erweitern ((2a-1)/b)^4

Lösung

erweitern

(\frac{2 a - 1}{b})^{4}

\frac{16 a ^{4}}{b ^{4}} - \frac{32 a ^{3}}{b ^{4}} + \frac{24 a ^{2}}{b ^{4}} - \frac{8 a}{b ^{4}} + \frac{1}{b ^{4}}

Schritte zur Lösung

(\frac{2 a - 1}{b})^{4}

Wende Exponentenregel an:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 2 a - 1 ) ^{4}}{b ^{4}}

(2 a - 1)^{4} = 16 a^{4} - 32 a^{3} + 24 a^{2} - 8 a + 1

= \frac{16 a ^{4} - 32 a ^{3} + 24 a ^{2} - 8 a + 1}{b ^{4}}

Wende Bruchregel an:

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

\frac{16 a ^{4} - 32 a ^{3} + 24 a ^{2} - 8 a + 1}{b ^{4}} = \frac{16 a ^{4}}{b ^{4}} - \frac{32 a ^{3}}{b ^{4}} + \frac{24 a ^{2}}{b ^{4}} - \frac{8 a}{b ^{4}} + \frac{1}{b ^{4}}

= \frac{16 a ^{4}}{b ^{4}} - \frac{32 a ^{3}}{b ^{4}} + \frac{24 a ^{2}}{b ^{4}} - \frac{8 a}{b ^{4}} + \frac{1}{b ^{4}}

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