erweitern (x-4)(x-(1+i))(x-(1+i))

Lösung

erweitern

(x - 4) (x - (1 + i)) (x - (1 + i))

(x^{3} - 6 x^{2} + 8 x) + (- 8 - 2 x^{2} + 10 x) i

Schritte zur Lösung

(x - 4) (x - (1 + i)) (x - (1 + i))

Schreibe

(x - 4) (x - (1 + i)) (x - (1 + i))

um:

(4 i + x^{2} - 5 x - x i + 4) (x - (1 + i))

= (4 i + x^{2} - 5 x - x i + 4) (x - (1 + i))

Setze Klammern

= 4 i x + 4 i (- (1 + i)) + x^{2} x + x^{2} (- (1 + i)) - 5 xx - 5 x (- (1 + i)) - x i x - x i (- (1 + i)) + 4 x + 4 (- (1 + i))

Vereinfache

4 i x + 4 i (- (1 + i)) + x^{2} x + x^{2} (- (1 + i)) - 5 xx - 5 x (- (1 + i)) - x i x - x i (- (1 + i)) + 4 x + 4 (- (1 + i)) : - 8 i + x^{3} - 6 x^{2} - 2 x^{2} i + 10 x i + 8 x

= - 8 i + x^{3} - 6 x^{2} - 2 x^{2} i + 10 x i + 8 x

Rewrite in standard complex form:

(x^{3} - 6 x^{2} + 8 x) + (- 8 - 2 x^{2} + 10 x) i

= (x^{3} - 6 x^{2} + 8 x) + (- 8 - 2 x^{2} + 10 x) i

e x p an d K \cdot (1 + \frac{1}{t s} + d s)

e x p an d ln (x) (x + 2) (x + 8)

e x p an d (x^{3} + y^{3}) d x - 3 x y^{2} d y

e x p an d \frac{6}{x ^{4} ( x - 2 ) ^{2}}

s im pl i f y (lo g_{4} (x)) (x - 3)