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

Lösung

erweitern

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

x^{8} - 16

Schritte zur Lösung

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

Schreibe

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

um:

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

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

Schreibe

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

um:

x^{6} - 4 x^{2} - 2 x^{5} + 8 x + 2 x^{4} - 8

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

Setze Klammern

= x^{6} x^{2} + x^{6} \cdot 2 x + x^{6} \cdot 2 - 4 x^{2} x^{2} - 4 x^{2} \cdot 2 x - 4 x^{2} \cdot 2 - 2 x^{5} x^{2} - 2 x^{5} \cdot 2 x - 2 x^{5} \cdot 2 + 8 x x^{2} + 8 x \cdot 2 x + 8 x \cdot 2 + 2 x^{4} x^{2} + 2 x^{4} \cdot 2 x + 2 x^{4} \cdot 2 - 8 x^{2} - 8 \cdot 2 x - 8 \cdot 2

Vereinfache

x^{6} x^{2} + x^{6} \cdot 2 x + x^{6} \cdot 2 - 4 x^{2} x^{2} - 4 x^{2} \cdot 2 x - 4 x^{2} \cdot 2 - 2 x^{5} x^{2} - 2 x^{5} \cdot 2 x - 2 x^{5} \cdot 2 + 8 x x^{2} + 8 x \cdot 2 x + 8 x \cdot 2 + 2 x^{4} x^{2} + 2 x^{4} \cdot 2 x + 2 x^{4} \cdot 2 - 8 x^{2} - 8 \cdot 2 x - 8 \cdot 2 : x^{8} - 16

= x^{8} - 16

f a c t or 55 x^{2} - 61 x y - 6 y^{2}

e x p an d (6 x + 5 y)^{3}

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

s im pl i f y (3 x^{- 7} \cdot y^{7} \cdot z^{- 5})^{- 1}

f a c t or 25 x^{4} y^{4} - 91 x^{2} y^{4} - 36 y^{4}