erweitern (x-1+6i)(x-1-6i)(x-1)(x-2)(2x-1)

Lösung

erweitern

(x - 1 + 6 i) (x - 1 - 6 i) (x - 1) (x - 2) (2 x - 1)

2 x^{5} - 11 x^{4} + 95 x^{3} - 275 x^{2} + 263 x - 74

Schritte zur Lösung

(x - 1 + 6 i) (x - 1 - 6 i) (x - 1) (x - 2) (2 x - 1)

Schreibe

(x - 1 + 6 i) (x - 1 - 6 i) (x - 1) (x - 2) (2 x - 1)

um:

(x - 1 + 6 i) (x - 1 - 6 i) (x^{2} - 3 x + 2) (2 x - 1)

= (x - 1 + 6 i) (x - 1 - 6 i) (x^{2} - 3 x + 2) (2 x - 1)

Schreibe

(x - 1 + 6 i) (x - 1 - 6 i)

um:

x^{2} - 2 x + 37

= (x^{2} - 2 x + 37) (x^{2} - 3 x + 2) (2 x - 1)

Schreibe

(x^{2} - 2 x + 37) (x^{2} - 3 x + 2)

um:

x^{4} - 5 x^{3} + 45 x^{2} - 115 x + 74

= (x^{4} - 5 x^{3} + 45 x^{2} - 115 x + 74) (2 x - 1)

Setze Klammern

= x^{4} \cdot 2 x + x^{4} (- 1) - 5 x^{3} \cdot 2 x - 5 x^{3} (- 1) + 45 x^{2} \cdot 2 x + 45 x^{2} (- 1) - 115 x \cdot 2 x - 115 x (- 1) + 74 \cdot 2 x + 74 (- 1)

Vereinfache

x^{4} \cdot 2 x + x^{4} (- 1) - 5 x^{3} \cdot 2 x - 5 x^{3} (- 1) + 45 x^{2} \cdot 2 x + 45 x^{2} (- 1) - 115 x \cdot 2 x - 115 x (- 1) + 74 \cdot 2 x + 74 (- 1) : 2 x^{5} - 11 x^{4} + 95 x^{3} - 275 x^{2} + 263 x - 74

= 2 x^{5} - 11 x^{4} + 95 x^{3} - 275 x^{2} + 263 x - 74

e x p an d \frac{s ^{2} + s + 2}{( s + 1 ) ^{3}}

e x p an d x (θ - sin (θ))

s im pl i f y (x - 14) (x - \frac{5}{2}) (x - \frac{9}{2})

e x p an d \frac{( - z + 6 ) ^{3}}{54}

s im pl i f y 2 (2 + lo g_{2} (375))