faktorisieren x^3y^3-125w^3

Lösung

faktorisieren

x^{3} y^{3} - 125 w^{3}

(x y - 5 w) (x^{2} y^{2} + 5 x y w + 25 w^{2})

Schritte zur Lösung

x^{3} y^{3} - 125 w^{3}

Schreibe

x^{3} y^{3}

um:

(x y)^{3}

Schreibe

125 w^{3}

um:

(5 w)^{3}

= (x y)^{3} - (5 w)^{3}

Wende Formel zur Differenz von dritten Potenzen an:

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

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

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

Vereinfache

(x y - 5 w) ((x y)^{2} + x y \cdot 5 w + (5 w)^{2}) : (x y - 5 w) (x^{2} y^{2} + 5 x y w + 25 w^{2})

= (x y - 5 w) (x^{2} y^{2} + 5 x y w + 25 w^{2})

f a c t or (5 x + 1) 2 + 11 (5 x + 1) + 30

f a c t or 27 a^{3 m} + 64 b^{6 n}

\frac{d ^{2}}{d x ^{2}} ((x) (2 C x))

s im pl i f y 144 x^{(2)} - y^{(2)} - 160 x - 5 y

s im pl i f y A (- 7.3)