faktorisieren x^4+12x^2y^2+64y^4

Lösung

faktorisieren

x^{4} + 12 x^{2} y^{2} + 64 y^{4}

(x^{2} + 8 y^{2} + 2 x y) (x^{2} + 8 y^{2} - 2 x y)

Schritte zur Lösung

x^{4} + 12 x^{2} y^{2} + 64 y^{4}

Addiere und subtrahiere

4 x^{2} y^{2}

= x^{4} + 16 x^{2} y^{2} + 64 y^{4} - 4 x^{2} y^{2}

Faktorisiere

x^{4} + 16 x^{2} y^{2} + 64 y^{4} : (x^{2} + 8 y^{2})^{2}

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

Wende Exponentenregel an

= (x^{2} + 8 y^{2})^{2} - (2 x y)^{2}

Faktorisiere

(x^{2} + 8 y^{2})^{2} - (2 x y)^{2} : (x^{2} + 8 y^{2} + 2 x y) (x^{2} + 8 y^{2} - 2 x y)

= (x^{2} + 8 y^{2} + 2 x y) (x^{2} + 8 y^{2} - 2 x y)

s im pl i f y \frac{- 8}{25 x - 50}

e x p an d (1 + 2 x + y)^{2}

s im pl i f y (\frac{1}{5 \cdot a ^{3} + b ^{2}})^{2}

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

f a c t or z^{3} + 2 z^{2} - 68 z + 120