faktorisieren 49x^2-100y^4

Lösung

faktorisieren

49 x^{2} - 100 y^{4}

(7 x + 10 y^{2}) (7 x - 10 y^{2})

Schritte zur Lösung

49 x^{2} - 100 y^{4}

49 x^{2} = (7 x)^{2}

100 y^{4} = (10 y^{2})^{2}

= (7 x)^{2} - (10 y^{2})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(7 x)^{2} - (10 y^{2})^{2} = (7 x + 10 y^{2}) (7 x - 10 y^{2})

= (7 x + 10 y^{2}) (7 x - 10 y^{2})

x^{2} + x^{2} = 2

- 3 x^{2} = - 363

- 6 \leq x \leq 2

- 12 \leq - 3 x + 3 < - 6

3 x \geq 6