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Beliebt Algebra >

faktorisieren 256x^4-81y^4

Lösung

faktorisieren

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

Lösung

(16 x^{2} + 9 y^{2}) (4 x + 3 y) (4 x - 3 y)

Schritte zur Lösung

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

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

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

= (16 x^{2})^{2} - (9 y^{2})^{2}

Wende Formel zur Differenz von zwei Quadraten an:

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

(16 x^{2})^{2} - (9 y^{2})^{2} = (16 x^{2} + 9 y^{2}) (16 x^{2} - 9 y^{2})

= (16 x^{2} + 9 y^{2}) (16 x^{2} - 9 y^{2})

Faktorisiere

16 x^{2} - 9 y^{2} : (4 x + 3 y) (4 x - 3 y)

= (16 x^{2} + 9 y^{2}) (4 x + 3 y) (4 x - 3 y)

Beliebte Beispiele

- x^{2} + 17 x + 30 = 30

vereinfachen (3i^2+3i)/(4i)

s im pl i f y \frac{3 i ^{2} + 3 i}{4 i}

erweitern (x+1)(x-2)(x+3)(x+4)

e x p an d (x + 1) (x - 2) (x + 3) (x + 4)

vereinfachen ((a^{5/3}))/(y^4x^2)

s im pl i f y \frac{( a ^{\frac{5}{3}} )}{y ^{4} x ^{2}}

\frac{a}{6} = 5