erweitern (x^2-3)(x^2+2x+1)(x-1)(x^2+3)

Lösung

erweitern

(x^{2} - 3) (x^{2} + 2 x + 1) (x - 1) (x^{2} + 3)

x^{7} + x^{6} - x^{5} - x^{4} - 9 x^{3} - 9 x^{2} + 9 x + 9

Schritte zur Lösung

(x^{2} - 3) (x^{2} + 2 x + 1) (x - 1) (x^{2} + 3)

Schreibe

(x^{2} - 3) (x^{2} + 2 x + 1) (x - 1) (x^{2} + 3)

um:

(x^{4} - 9) (x^{2} + 2 x + 1) (x - 1)

= (x^{4} - 9) (x^{2} + 2 x + 1) (x - 1)

Apply FOIL method

(x^{4} - 9) (x - 1) : x^{5} - x^{4} - 9 x + 9

= (x^{5} - x^{4} - 9 x + 9) (x^{2} + 2 x + 1)

Setze Klammern

= x^{5} x^{2} + x^{5} \cdot 2 x + x^{5} \cdot 1 - x^{4} x^{2} - x^{4} \cdot 2 x - x^{4} \cdot 1 - 9 x x^{2} - 9 x \cdot 2 x - 9 x \cdot 1 + 9 x^{2} + 9 \cdot 2 x + 9 \cdot 1

Vereinfache

x^{5} x^{2} + x^{5} \cdot 2 x + x^{5} \cdot 1 - x^{4} x^{2} - x^{4} \cdot 2 x - x^{4} \cdot 1 - 9 x x^{2} - 9 x \cdot 2 x - 9 x \cdot 1 + 9 x^{2} + 9 \cdot 2 x + 9 \cdot 1 : x^{7} + x^{6} - x^{5} - x^{4} - 9 x^{3} - 9 x^{2} + 9 x + 9

= x^{7} + x^{6} - x^{5} - x^{4} - 9 x^{3} - 9 x^{2} + 9 x + 9

e x p an d (3 x - 5) (x^{2} + x + 5)

s im pl i f y 1 + \frac{1}{2 + \frac{1}{1 + 2}}

s im pl i f y 2 π + 2 π

s im pl i f y - \frac{1}{4} \times 2

s im pl i f y x + 3 + 5 x