faktorisieren (x^2-5)^3-64y^3

Lösung

faktorisieren

(x^{2} - 5)^{3} - 64 y^{3}

(x^{2} - 5 - 4 y) ((x^{2} - 5)^{2} + 4 y (x^{2} - 5) + 16 y^{2})

Schritte zur Lösung

(x^{2} - 5)^{3} - 64 y^{3}

Schreibe

(x^{2} - 5)^{3} - 64 y^{3}

um:

(x^{2} - 5)^{3} - (4 y)^{3}

= (x^{2} - 5)^{3} - (4 y)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

(x^{2} - 5)^{3} - (4 y)^{3} = ((x^{2} - 5) - 4 y) ((x^{2} - 5)^{2} + 4 (x^{2} - 5) y + 4^{2} y^{2})

= ((x^{2} - 5) - 4 y) ((x^{2} - 5)^{2} + 4 y (x^{2} - 5) + 4^{2} y^{2})

Fasse zusammen

= (x^{2} - 4 y - 5) (16 y^{2} + 4 y (x^{2} - 5) + (x^{2} - 5)^{2})

f a c t or tan (2 a + 2 b)

f (x) = (ln (cos (x)))^{2}

f a c t or 20 \cdot 20 \cdot 8

roo t s (ln (x))^{3} + C

f a c t or (x + 2)^{2} + (y + 5)^{2}