vereinfachen (x-9)^2(x-2i)^2

Lösung

vereinfachen

(x - 9)^{2} (x - 2 i)^{2}

(x^{4} - 18 x^{3} + 77 x^{2} + 72 x - 324) + (- 4 x^{3} + 72 x^{2} - 324 x) i

Schritte zur Lösung

(x - 9)^{2} (x - 2 i)^{2}

Schreibe

(x - 9)^{2}

um:

x^{2} - 18 x + 81

= (x^{2} - 18 x + 81) (x - 2 i)^{2}

= (x - 2 i)^{2} (x^{2} - 18 x + 81)

Schreibe

(x - 2 i)^{2}

um:

x^{2} - 4 x i - 4

= (x^{2} - 4 x i - 4) (x^{2} - 18 x + 81)

Setze Klammern

= x^{2} x^{2} + x^{2} (- 18 x) + x^{2} \cdot 81 - 4 x i x^{2} - 4 x i (- 18 x) - 4 x i 81 - 4 x^{2} - 4 (- 18 x) - 4 \cdot 81

Vereinfache

x^{2} x^{2} + x^{2} (- 18 x) + x^{2} \cdot 81 - 4 x i x^{2} - 4 x i (- 18 x) - 4 x i 81 - 4 x^{2} - 4 (- 18 x) - 4 \cdot 81 : x^{4} - 18 x^{3} + 77 x^{2} - 4 x^{3} i + 72 x^{2} i - 324 x i + 72 x - 324

= x^{4} - 18 x^{3} + 77 x^{2} - 4 x^{3} i + 72 x^{2} i - 324 x i + 72 x - 324

Rewrite in standard complex form:

(x^{4} - 18 x^{3} + 77 x^{2} + 72 x - 324) + (- 4 x^{3} + 72 x^{2} - 324 x) i

= (x^{4} - 18 x^{3} + 77 x^{2} + 72 x - 324) + (- 4 x^{3} + 72 x^{2} - 324 x) i

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