erweitern (x-2i)(x+2i)(x-3-i)(x-3+i)

Lösung

erweitern

(x - 2 i) (x + 2 i) (x - 3 - i) (x - 3 + i)

x^{4} - 6 x^{3} + 14 x^{2} - 24 x + 40

Schritte zur Lösung

(x - 2 i) (x + 2 i) (x - 3 - i) (x - 3 + i)

Schreibe

(x - 2 i) (x + 2 i) (x - 3 - i) (x - 3 + i)

um:

(x^{2} + 4) (x - 3 - i) (x - 3 + i)

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

Schreibe

(x^{2} + 4) (x - 3 - i)

um:

x^{3} - 3 x^{2} - x^{2} i + 4 x - 12 - 4 i

= (x^{3} - 3 x^{2} - x^{2} i + 4 x - 12 - 4 i) (x - 3 + i)

Setze Klammern

= x^{3} x + x^{3} (- 3) + x^{3} i - 3 x^{2} x - 3 x^{2} (- 3) - 3 x^{2} i - x^{2} i x - x^{2} i (- 3) - x^{2} ii + 4 xx + 4 x (- 3) + 4 x i - 12 x - 12 (- 3) - 12 i - 4 i x - 4 i (- 3) - 4 ii

Vereinfache

x^{3} x + x^{3} (- 3) + x^{3} i - 3 x^{2} x - 3 x^{2} (- 3) - 3 x^{2} i - x^{2} i x - x^{2} i (- 3) - x^{2} ii + 4 xx + 4 x (- 3) + 4 x i - 12 x - 12 (- 3) - 12 i - 4 i x - 4 i (- 3) - 4 ii : x^{4} - 6 x^{3} + 14 x^{2} - 24 x + 40

= x^{4} - 6 x^{3} + 14 x^{2} - 24 x + 40

e x p an d 2 (cot (x) - tan (x)) sin (2 x)

e x p an d \frac{x ( x - 11 ) ^{2}}{( x + 6 ) ^{3}}

e x p an d ln (3) (14 - x)

e x p an d 3 (4 x + 3 y = 8)

s im pl i f y 3 (x - \frac{1}{2})