faktorisieren x^4y^4-256z^4

Lösung

faktorisieren

x^{4} y^{4} - 256 z^{4}

(x^{2} y^{2} + 16 z^{2}) (x y + 4 z) (x y - 4 z)

Schritte zur Lösung

x^{4} y^{4} - 256 z^{4}

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

256 z^{4} = (16 z^{2})^{2}

= (x^{2} y^{2})^{2} - (16 z^{2})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(x^{2} y^{2})^{2} - (16 z^{2})^{2} = (x^{2} y^{2} + 16 z^{2}) (x^{2} y^{2} - 16 z^{2})

= (x^{2} y^{2} + 16 z^{2}) (x^{2} y^{2} - 16 z^{2})

Faktorisiere

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

= (x^{2} y^{2} + 16 z^{2}) (x y + 4 z) (x y - 4 z)

s im pl i f y (4 n^{4})^{5}

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

s im pl i f y \frac{\frac{s i n ^{2} ( x )}{2}}{\frac{x ^{2}}{4}}

s im pl i f y (3 x^{3} \cdot y^{- 2})^{- 4}