erweitern (x^3-4x^2+x-4)(x^2=18x+82)

Lösung

erweitern

(x^{3} - 4 x^{2} + x - 4) (x^{2} = 18 x + 82)

x^{5} = 18 x - 328

Schritte zur Lösung

(x^{3} - 4 x^{2} + x - 4) (x^{2} = 18 x + 82)

= (x^{3} - 4 x^{2} + x - 4) (18 = x^{2} x + 82)

Setze Klammern

x^{3} x^{2} = 18 x + x^{3} \cdot 82 + (- 4 x^{2}) x^{2} = 18 x + (- 4 x^{2}) \cdot 82 + x x^{2} = 18 x + x \cdot 82 + (- 4) x^{2} = 18 x + (- 4) \cdot 82

Wende Minus-Plus Regeln an

+ (- a) = - a

x^{3} x^{2} = 18 x + 82 x^{3} - 4 x^{2} x^{2} = 18 x - 4 \cdot 82 x^{2} + x^{2} x = 18 x + 82 x - 4 x^{2} = 18 x - 4 \cdot 82

Vereinfache

x^{3} x^{2} = 18 x + 82 x^{3} - 4 x^{2} x^{2} = 18 x - 4 \cdot 82 x^{2} + x^{2} x = 18 x + 82 x - 4 x^{2} = 18 x - 4 \cdot 82 : x^{5} = 18 x - 328

x^{5} = 18 x - 328

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e x p an d \frac{7 x ^{2} - 9 x + 4}{( x - 1 ) ( x ^{2} + 2 )}