faktorisieren x^4-a^4+4x^3+4x^2

Lösung

faktorisieren

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

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

Schritte zur Lösung

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

Faktorisiere

x^{4} + 4 x^{3} + 4 x^{2} : x^{2} (x + 2)^{2}

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

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

a^{4} = (a^{2})^{2}

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

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Vereinfache

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

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

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

s im pl i f y \frac{( x - 1 ) ^{2}}{4 + x ^{2} - 1 + ( x + 1 ) ^{2}}

f a c t or x^{4} + x^{3} - 3 x^{2} - 5 x - 2

f a c t or a - 8 a \cdot b^{3}

s im pl i f y f (x) - 4 x^{2} + 100 x - 60

s im pl i f y x + \frac{y}{x ^{2}} - y + c - 2 \frac{y}{3} x^{2} - 3 y