faktorisieren y^4-81x^4

Lösung

faktorisieren

y^{4} - 81 x^{4}

(y^{2} + 9 x^{2}) (y + 3 x) (y - 3 x)

Schritte zur Lösung

y^{4} - 81 x^{4}

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

81 x^{4} = (9 x^{2})^{2}

= (y^{2})^{2} - (9 x^{2})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

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

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

Faktorisiere

y^{2} - 9 x^{2} : (y + 3 x) (y - 3 x)

= (y^{2} + 9 x^{2}) (y + 3 x) (y - 3 x)

f (x) = 3 + 4 x^{5}

s im pl i f y (a^{2} + 1)^{2} + (a^{2} + 5)^{2} - 4 \cdot (a^{2} + 3)^{2}

s im pl i f y (14.5 - 5.3) \cdot x^{2.5} + (3.5) 2

s im pl i f y \frac{( x ^{3} - 49 x )}{( x ^{4} - 7 x ^{3} )}

s im pl i f y cos^{2} (x) sec^{2} (x)