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Beliebt Algebra >

erweitern (x+2-2i)(x-3+sqrt(5))(x)(x)(x-1)

Lösung

erweitern

(x + 2 - 2 i) (x - 3 + 5) (x) (x) (x - 1)

Lösung

(x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{4} + 5 x^{3} - 25 x^{2}) + (- 2 x^{4} + 8 x^{3} - 6 x^{2} - 25 x^{3} + 25 x^{2}) i

Schritte zur Lösung

(x + 2 - 2 i) (x - 3 + 5) (x) (x) (x - 1)

Apply rule:

(a) = a

(x) = x

= (x + 2 - 2 i) (x - 3 + 5) xx (x - 1)

Vereinfache

(x + 2 - 2 i) (x - 3 + 5) xx (x - 1) : x^{2} (x + 2 - 2 i) (x - 3 + 5) (x - 1)

= x^{2} (x + 2 - 2 i) (x - 3 + 5) (x - 1)

Schreibe

x^{2} (x - 1)

um:

x^{3} - x^{2}

= (x^{3} - x^{2}) (x + 2 - 2 i) (x - 3 + 5)

Schreibe

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

um:

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

= (x^{4} + x^{3} - 2 x^{3} i - 2 x^{2} + 2 x^{2} i) (x - 3 + 5)

Setze Klammern

= x^{4} x + x^{4} (- 3) + x^{4} 5 + x^{3} x + x^{3} (- 3) + x^{3} 5 - 2 x^{3} i x - 2 x^{3} i (- 3) - 2 x^{3} i 5 - 2 x^{2} x - 2 x^{2} (- 3) - 2 x^{2} 5 + 2 x^{2} i x + 2 x^{2} i (- 3) + 2 x^{2} i 5

Vereinfache

x^{4} x + x^{4} (- 3) + x^{4} 5 + x^{3} x + x^{3} (- 3) + x^{3} 5 - 2 x^{3} i x - 2 x^{3} i (- 3) - 2 x^{3} i 5 - 2 x^{2} x - 2 x^{2} (- 3) - 2 x^{2} 5 + 2 x^{2} i x + 2 x^{2} i (- 3) + 2 x^{2} i 5 : x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{4} + 5 x^{3} - 2 x^{4} i + 8 x^{3} i - 25 x^{2} - 6 x^{2} i - 25 x^{3} i + 25 x^{2} i

= x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{4} + 5 x^{3} - 2 x^{4} i + 8 x^{3} i - 25 x^{2} - 6 x^{2} i - 25 x^{3} i + 25 x^{2} i

Rewrite in standard complex form:

(x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{4} + 5 x^{3} - 25 x^{2}) + (- 2 x^{4} + 8 x^{3} - 6 x^{2} - 25 x^{3} + 25 x^{2}) i

= (x^{5} - 2 x^{4} - 5 x^{3} + 6 x^{2} + 5 x^{4} + 5 x^{3} - 25 x^{2}) + (- 2 x^{4} + 8 x^{3} - 6 x^{2} - 25 x^{3} + 25 x^{2}) i

Beliebte Beispiele

erweitern V(5,-3)F(5,2)

e x p an d V (5, - 3) F (5, 2)

erweitern (2w^2-64)/(w(w-8))

e x p an d \frac{2 w ^{2} - 64}{w ( w - 8 )}

erweitern 1/(x(x_{2)-4)(x-2)}

e x p an d \frac{1}{x ( x _{2} - 4 ) ( x - 2 )}

erweitern (16)/((x^2× (x-4)))

e x p an d \frac{16}{( x ^{2} \times ( x - 4 ) )}

erweitern (17x-27)/((2x-3)(3x-5))

e x p an d \frac{17 x - 27}{( 2 x - 3 ) ( 3 x - 5 )}