faktorisieren 49x^4+61x^2y^2+25y^4

Lösung

faktorisieren

49 x^{4} + 61 x^{2} y^{2} + 25 y^{4}

(7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)

Schritte zur Lösung

49 x^{4} + 61 x^{2} y^{2} + 25 y^{4}

Addiere und subtrahiere

9 x^{2} y^{2}

= 49 x^{4} + 70 x^{2} y^{2} + 25 y^{4} - 9 x^{2} y^{2}

Faktorisiere

49 x^{4} + 70 x^{2} y^{2} + 25 y^{4} : (7 x^{2} + 5 y^{2})^{2}

= (7 x^{2} + 5 y^{2})^{2} - 9 x^{2} y^{2}

Wende Exponentenregel an

= (7 x^{2} + 5 y^{2})^{2} - (3 x y)^{2}

Faktorisiere

(7 x^{2} + 5 y^{2})^{2} - (3 x y)^{2} : (7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)

= (7 x^{2} + 5 y^{2} + 3 x y) (7 x^{2} + 5 y^{2} - 3 x y)

s im pl i f y \frac{v ^{4} + 4 v ^{2} + 4}{4 - v ^{4}}

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

f a c t or 25 x^{2} - 15 x

s im pl i f y (a - bi) (c + d i)

s im pl i f y 5 (5 n - 2)