faktorisieren x^4+7x^2y^2+16y^4

Lösung

faktorisieren

x^{4} + 7 x^{2} y^{2} + 16 y^{4}

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

Schritte zur Lösung

x^{4} + 7 x^{2} y^{2} + 16 y^{4}

Addiere und subtrahiere

x^{2} y^{2}

= x^{4} + 8 x^{2} y^{2} + 16 y^{4} - x^{2} y^{2}

Faktorisiere

x^{4} + 8 x^{2} y^{2} + 16 y^{4} : (x^{2} + 4 y^{2})^{2}

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

Wende Exponentenregel an:

a^{m} b^{m} = (ab)^{m}

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

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

Faktorisiere

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

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

s im pl i f y \frac{1}{x ^{- 1} \cdot x}

s im pl i f y 15 x^{2} x^{2} - 8 x^{4}

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

e x p an d (x^{5} + 4 x)^{3}

f a c t or - 4 x - 3 y