erweitern \sqrt[7]{x-1}*(x-1)^7

Lösung

erweitern

7 x - 1 \cdot (x - 1)^{7}

x^{7} 7 x - 1 - 7 x^{6} 7 x - 1 + 21 x^{5} 7 x - 1 - 35 x^{4} 7 x - 1 + 35 x^{3} 7 x - 1 - 21 x^{2} 7 x - 1 + 7 x 7 x - 1 - 7 x - 1

Schritte zur Lösung

7 x - 1 (x - 1)^{7}

= (x - 1)^{7} 7 x - 1

Schreibe

(x - 1)^{7}

um:

x^{7} - 7 x^{6} + 21 x^{5} - 35 x^{4} + 35 x^{3} - 21 x^{2} + 7 x - 1

= (x^{7} - 7 x^{6} + 21 x^{5} - 35 x^{4} + 35 x^{3} - 21 x^{2} + 7 x - 1) 7 x - 1

= 7 x - 1 (x^{7} - 7 x^{6} + 21 x^{5} - 35 x^{4} + 35 x^{3} - 21 x^{2} + 7 x - 1)

Setze Klammern

= 7 x - 1 x^{7} + 7 x - 1 (- 7 x^{6}) + 7 x - 1 \cdot 21 x^{5} + 7 x - 1 (- 35 x^{4}) + 7 x - 1 \cdot 35 x^{3} + 7 x - 1 (- 21 x^{2}) + 7 x - 1 \cdot 7 x + 7 x - 1 (- 1)

Vereinfache

7 x - 1 x^{7} + 7 x - 1 (- 7 x^{6}) + 7 x - 1 \cdot 21 x^{5} + 7 x - 1 (- 35 x^{4}) + 7 x - 1 \cdot 35 x^{3} + 7 x - 1 (- 21 x^{2}) + 7 x - 1 \cdot 7 x + 7 x - 1 (- 1) : x^{7} 7 x - 1 - 7 x^{6} 7 x - 1 + 21 x^{5} 7 x - 1 - 35 x^{4} 7 x - 1 + 35 x^{3} 7 x - 1 - 21 x^{2} 7 x - 1 + 7 x 7 x - 1 - 7 x - 1

= x^{7} 7 x - 1 - 7 x^{6} 7 x - 1 + 21 x^{5} 7 x - 1 - 35 x^{4} 7 x - 1 + 35 x^{3} 7 x - 1 - 21 x^{2} 7 x - 1 + 7 x 7 x - 1 - 7 x - 1

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